1 \section{Operations on Arrays}
3 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
7 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
12 Calculates absolute difference between two arrays.
14 \cvdefC{void cvAbsDiff(const CvArr* src1, const CvArr* src2, CvArr* dst);}
15 \cvdefPy{AbsDiff(src1,src2,dst)-> None}
18 \cvarg{src1}{The first source array}
19 \cvarg{src2}{The second source array}
20 \cvarg{dst}{The destination array}
23 The function calculates absolute difference between two arrays.
25 \[ \texttt{dst}(i)_c = |\texttt{src1}(I)_c - \texttt{src2}(I)_c| \]
27 All the arrays must have the same data type and the same size (or ROI size).
30 Calculates absolute difference between an array and a scalar.
32 \cvdefC{void cvAbsDiffS(const CvArr* src, CvArr* dst, CvScalar value);}
33 \cvdefPy{AbsDiffS(src,value,dst)-> None}
36 #define cvAbs(src, dst) cvAbsDiffS(src, dst, cvScalarAll(0))
40 \cvarg{src}{The source array}
41 \cvarg{dst}{The destination array}
42 \cvarg{value}{The scalar}
45 The function calculates absolute difference between an array and a scalar.
47 \[ \texttt{dst}(i)_c = |\texttt{src}(I)_c - \texttt{value}_c| \]
49 All the arrays must have the same data type and the same size (or ROI size).
53 Computes the per-element sum of two arrays.
55 \cvdefC{void cvAdd(const CvArr* src1, const CvArr* src2, CvArr* dst, const CvArr* mask=NULL);}
56 \cvdefPy{Add(src1,src2,dst,mask=NULL)-> None}
59 \cvarg{src1}{The first source array}
60 \cvarg{src2}{The second source array}
61 \cvarg{dst}{The destination array}
62 \cvarg{mask}{Operation mask, 8-bit single channel array; specifies elements of the destination array to be changed}
65 The function adds one array to another:
68 dst(I)=src1(I)+src2(I) if mask(I)!=0
71 All the arrays must have the same type, except the mask, and the same size (or ROI size).
72 For types that have limited range this operation is saturating.
75 Computes the sum of an array and a scalar.
77 \cvdefC{void cvAddS(const CvArr* src, CvScalar value, CvArr* dst, const CvArr* mask=NULL);}
78 \cvdefPy{AddS(src,value,dst,mask=NULL)-> None}
81 \cvarg{src}{The source array}
82 \cvarg{value}{Added scalar}
83 \cvarg{dst}{The destination array}
84 \cvarg{mask}{Operation mask, 8-bit single channel array; specifies elements of the destination array to be changed}
87 The function adds a scalar \texttt{value} to every element in the source array \texttt{src1} and stores the result in \texttt{dst}.
88 For types that have limited range this operation is saturating.
91 dst(I)=src(I)+value if mask(I)!=0
94 All the arrays must have the same type, except the mask, and the same size (or ROI size).
97 \cvCPyFunc{AddWeighted}
98 Computes the weighted sum of two arrays.
100 \cvdefC{void cvAddWeighted(const CvArr* src1, double alpha,
101 const CvArr* src2, double beta,
102 double gamma, CvArr* dst);}
103 \cvdefPy{AddWeighted(src1,alpha,src2,beta,gamma,dst)-> None}
106 \cvarg{src1}{The first source array}
107 \cvarg{alpha}{Weight for the first array elements}
108 \cvarg{src2}{The second source array}
109 \cvarg{beta}{Weight for the second array elements}
110 \cvarg{dst}{The destination array}
111 \cvarg{gamma}{Scalar, added to each sum}
114 The function calculates the weighted sum of two arrays as follows:
117 dst(I)=src1(I)*alpha+src2(I)*beta+gamma
120 All the arrays must have the same type and the same size (or ROI size).
121 For types that have limited range this operation is saturating.
125 Calculates per-element bit-wise conjunction of two arrays.
127 \cvdefC{void cvAnd(const CvArr* src1, const CvArr* src2, CvArr* dst, const CvArr* mask=NULL);}
128 \cvdefPy{And(src1,src2,dst,mask=NULL)-> None}
131 \cvarg{src1}{The first source array}
132 \cvarg{src2}{The second source array}
133 \cvarg{dst}{The destination array}
134 \cvarg{mask}{Operation mask, 8-bit single channel array; specifies elements of the destination array to be changed}
137 The function calculates per-element bit-wise logical conjunction of two arrays:
140 dst(I)=src1(I)&src2(I) if mask(I)!=0
143 In the case of floating-point arrays their bit representations are used for the operation. All the arrays must have the same type, except the mask, and the same size.
146 Calculates per-element bit-wise conjunction of an array and a scalar.
148 \cvdefC{void cvAndS(const CvArr* src, CvScalar value, CvArr* dst, const CvArr* mask=NULL);}
149 \cvdefPy{AndS(src,value,dst,mask=NULL)-> None}
152 \cvarg{src}{The source array}
153 \cvarg{value}{Scalar to use in the operation}
154 \cvarg{dst}{The destination array}
155 \cvarg{mask}{Operation mask, 8-bit single channel array; specifies elements of the destination array to be changed}
158 The function calculates per-element bit-wise conjunction of an array and a scalar:
161 dst(I)=src(I)&value if mask(I)!=0
164 Prior to the actual operation, the scalar is converted to the same type as that of the array(s). In the case of floating-point arrays their bit representations are used for the operation. All the arrays must have the same type, except the mask, and the same size.
167 The following sample demonstrates how to calculate the absolute value of floating-point array elements by clearing the most-significant bit:
170 float a[] = { -1, 2, -3, 4, -5, 6, -7, 8, -9 };
171 CvMat A = cvMat(3, 3, CV\_32F, &a);
172 int i, absMask = 0x7fffffff;
173 cvAndS(&A, cvRealScalar(*(float*)&absMask), &A, 0);
174 for(i = 0; i < 9; i++ )
175 printf("%.1f ", a[i]);
178 The code should print:
181 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0
186 Calculates average (mean) of array elements.
188 \cvdefC{CvScalar cvAvg(const CvArr* arr, const CvArr* mask=NULL);}
189 \cvdefPy{Avg(arr,mask=NULL)-> CvScalar}
192 \cvarg{arr}{The array}
193 \cvarg{mask}{The optional operation mask}
196 The function calculates the average value \texttt{M} of array elements, independently for each channel:
200 N = \sum_I (\texttt{mask}(I) \ne 0)\\
201 M_c = \frac{\sum_{I, \, \texttt{mask}(I) \ne 0} \texttt{arr}(I)_c}{N}
205 If the array is \texttt{IplImage} and COI is set, the function processes the selected channel only and stores the average to the first scalar component $ S_0 $ .
208 Calculates average (mean) of array elements.
210 \cvdefC{void cvAvgSdv(const CvArr* arr, CvScalar* mean, CvScalar* stdDev, const CvArr* mask=NULL);}
211 \cvdefPy{AvgSdv(arr,mask=NULL)-> (mean, stdDev)}
214 \cvarg{arr}{The array}
216 \cvarg{mean}{Pointer to the output mean value, may be NULL if it is not needed}
217 \cvarg{stdDev}{Pointer to the output standard deviation}
219 \cvarg{mask}{The optional operation mask}
221 \cvarg{mean}{Mean value, a CvScalar}
222 \cvarg{stdDev}{Standard deviation, a CvScalar}
227 The function calculates the average value and standard deviation of array elements, independently for each channel:
231 N = \sum_I (\texttt{mask}(I) \ne 0)\\
232 mean_c = \frac{1}{N} \, \sum_{ I, \, \texttt{mask}(I) \ne 0} \texttt{arr}(I)_c\\
233 stdDev_c = \sqrt{\frac{1}{N} \, \sum_{ I, \, \texttt{mask}(I) \ne 0} (\texttt{arr}(I)_c - mean_c)^2}
237 If the array is \texttt{IplImage} and COI is set, the function processes the selected channel only and stores the average and standard deviation to the first components of the output scalars ($mean_0$ and $stdDev_0$).
239 \cvCPyFunc{CalcCovarMatrix}
240 Calculates covariance matrix of a set of vectors.
243 void cvCalcCovarMatrix(\par const CvArr** vects,\par int count,\par CvArr* covMat,\par CvArr* avg,\par int flags);}
244 \cvdefPy{CalcCovarMatrix(vects,covMat,avg,flags)-> None}
247 \cvarg{vects}{The input vectors, all of which must have the same type and the same size. The vectors do not have to be 1D, they can be 2D (e.g., images) and so forth}
249 \cvarg{count}{The number of input vectors}
251 \cvarg{covMat}{The output covariance matrix that should be floating-point and square}
252 \cvarg{avg}{The input or output (depending on the flags) array - the mean (average) vector of the input vectors}
253 \cvarg{flags}{The operation flags, a combination of the following values
255 \cvarg{CV\_COVAR\_SCRAMBLED}{The output covariance matrix is calculated as:
257 \texttt{scale} * [ \texttt{vects} [0]- \texttt{avg} ,\texttt{vects} [1]- \texttt{avg} ,...]^T \cdot [\texttt{vects} [0]-\texttt{avg} ,\texttt{vects} [1]-\texttt{avg} ,...]
259 that is, the covariance matrix is
260 $\texttt{count} \times \texttt{count}$.
261 Such an unusual covariance matrix is used for fast PCA
262 of a set of very large vectors (see, for example, the EigenFaces technique
263 for face recognition). Eigenvalues of this "scrambled" matrix will
264 match the eigenvalues of the true covariance matrix and the "true"
265 eigenvectors can be easily calculated from the eigenvectors of the
266 "scrambled" covariance matrix.}
267 \cvarg{CV\_COVAR\_NORMAL}{The output covariance matrix is calculated as:
269 \texttt{scale} * [ \texttt{vects} [0]- \texttt{avg} ,\texttt{vects} [1]- \texttt{avg} ,...] \cdot [\texttt{vects} [0]-\texttt{avg} ,\texttt{vects} [1]-\texttt{avg} ,...]^T
271 that is, \texttt{covMat} will be a covariance matrix
272 with the same linear size as the total number of elements in each
273 input vector. One and only one of \texttt{CV\_COVAR\_SCRAMBLED} and
274 \texttt{CV\_COVAR\_NORMAL} must be specified}
275 \cvarg{CV\_COVAR\_USE\_AVG}{If the flag is specified, the function does not calculate \texttt{avg} from the input vectors, but, instead, uses the passed \texttt{avg} vector. This is useful if \texttt{avg} has been already calculated somehow, or if the covariance matrix is calculated by parts - in this case, \texttt{avg} is not a mean vector of the input sub-set of vectors, but rather the mean vector of the whole set.}
276 \cvarg{CV\_COVAR\_SCALE}{If the flag is specified, the covariance matrix is scaled. In the "normal" mode \texttt{scale} is '1./count'; in the "scrambled" mode \texttt{scale} is the reciprocal of the total number of elements in each input vector. By default (if the flag is not specified) the covariance matrix is not scaled ('scale=1').}
278 \cvarg{CV\_COVAR\_ROWS}{Means that all the input vectors are stored as rows of a single matrix, \texttt{vects[0]}. \texttt{count} is ignored in this case, and \texttt{avg} should be a single-row vector of an appropriate size.}
279 \cvarg{CV\_COVAR\_COLS}{Means that all the input vectors are stored as columns of a single matrix, \texttt{vects[0]}. \texttt{count} is ignored in this case, and \texttt{avg} should be a single-column vector of an appropriate size.}
284 The function calculates the covariance matrix
285 and, optionally, the mean vector of the set of input vectors. The function
286 can be used for PCA, for comparing vectors using Mahalanobis distance and so forth.
288 \cvCPyFunc{CartToPolar}
289 Calculates the magnitude and/or angle of 2d vectors.
291 \cvdefC{void cvCartToPolar(\par const CvArr* x,\par const CvArr* y,\par CvArr* magnitude,\par CvArr* angle=NULL,\par int angleInDegrees=0);}
292 \cvdefPy{CartToPolar(x,y,magnitude,angle=NULL,angleInDegrees=0)-> None}
295 \cvarg{x}{The array of x-coordinates}
296 \cvarg{y}{The array of y-coordinates}
297 \cvarg{magnitude}{The destination array of magnitudes, may be set to NULL if it is not needed}
298 \cvarg{angle}{The destination array of angles, may be set to NULL if it is not needed. The angles are measured in radians $(0$ to $2 \pi )$ or in degrees (0 to 360 degrees).}
299 \cvarg{angleInDegrees}{The flag indicating whether the angles are measured in radians, which is default mode, or in degrees}
302 The function calculates either the magnitude, angle, or both of every 2d vector (x(I),y(I)):
306 magnitude(I)=sqrt(x(I)^2^+y(I)^2^ ),
307 angle(I)=atan(y(I)/x(I) )
311 The angles are calculated with 0.1 degree accuracy. For the (0,0) point, the angle is set to 0.
314 Calculates the cubic root
316 \cvdefC{float cvCbrt(float value);}
317 \cvdefPy{Cbrt(value)-> float}
320 \cvarg{value}{The input floating-point value}
324 The function calculates the cubic root of the argument, and normally it is faster than \texttt{pow(value,1./3)}. In addition, negative arguments are handled properly. Special values ($\pm \infty $, NaN) are not handled.
327 Clears a specific array element.
328 \cvdefC{void cvClearND(CvArr* arr, int* idx);}
329 \cvdefPy{ClearND(arr,idx)-> None}
332 \cvarg{arr}{Input array}
333 \cvarg{idx}{Array of the element indices}
336 The function \cvCPyCross{ClearND} clears (sets to zero) a specific element of a dense array or deletes the element of a sparse array. If the sparse array element does not exists, the function does nothing.
338 \cvCPyFunc{CloneImage}
339 Makes a full copy of an image, including the header, data, and ROI.
341 \cvdefC{IplImage* cvCloneImage(const IplImage* image);}
342 \cvdefPy{CloneImage(image)-> copy}
345 \cvarg{image}{The original image}
348 The returned \texttt{IplImage*} points to the image copy.
351 Creates a full matrix copy.
353 \cvdefC{CvMat* cvCloneMat(const CvMat* mat);}
354 \cvdefPy{CloneMat(mat)-> copy}
357 \cvarg{mat}{Matrix to be copied}
360 Creates a full copy of a matrix and returns a pointer to the copy.
362 \cvCPyFunc{CloneMatND}
363 Creates full copy of a multi-dimensional array and returns a pointer to the copy.
365 \cvdefC{CvMatND* cvCloneMatND(const CvMatND* mat);}
366 \cvdefPy{CloneMatND(mat)-> copy}
369 \cvarg{mat}{Input array}
374 \cvCPyFunc{CloneSparseMat}
375 Creates full copy of sparse array.
377 \cvdefC{CvSparseMat* cvCloneSparseMat(const CvSparseMat* mat);}
378 \cvdefPy{CloneSparseMat(mat) -> mat}
381 \cvarg{mat}{Input array}
384 The function creates a copy of the input array and returns pointer to the copy.
388 Performs per-element comparison of two arrays.
390 \cvdefC{void cvCmp(const CvArr* src1, const CvArr* src2, CvArr* dst, int cmpOp);}
391 \cvdefPy{Cmp(src1,src2,dst,cmpOp)-> None}
394 \cvarg{src1}{The first source array}
395 \cvarg{src2}{The second source array. Both source arrays must have a single channel.}
396 \cvarg{dst}{The destination array, must have 8u or 8s type}
397 \cvarg{cmpOp}{The flag specifying the relation between the elements to be checked
399 \cvarg{CV\_CMP\_EQ}{src1(I) "equal to" value}
400 \cvarg{CV\_CMP\_GT}{src1(I) "greater than" value}
401 \cvarg{CV\_CMP\_GE}{src1(I) "greater or equal" value}
402 \cvarg{CV\_CMP\_LT}{src1(I) "less than" value}
403 \cvarg{CV\_CMP\_LE}{src1(I) "less or equal" value}
404 \cvarg{CV\_CMP\_NE}{src1(I) "not equal" value}
408 The function compares the corresponding elements of two arrays and fills the destination mask array:
411 dst(I)=src1(I) op src2(I),
414 \texttt{dst(I)} is set to 0xff (all \texttt{1}-bits) if the specific relation between the elements is true and 0 otherwise. All the arrays must have the same type, except the destination, and the same size (or ROI size)
417 Performs per-element comparison of an array and a scalar.
419 \cvdefC{void cvCmpS(const CvArr* src, double value, CvArr* dst, int cmpOp);}
420 \cvdefPy{CmpS(src,value,dst,cmpOp)-> None}
423 \cvarg{src}{The source array, must have a single channel}
424 \cvarg{value}{The scalar value to compare each array element with}
425 \cvarg{dst}{The destination array, must have 8u or 8s type}
426 \cvarg{cmpOp}{The flag specifying the relation between the elements to be checked
428 \cvarg{CV\_CMP\_EQ}{src1(I) "equal to" value}
429 \cvarg{CV\_CMP\_GT}{src1(I) "greater than" value}
430 \cvarg{CV\_CMP\_GE}{src1(I) "greater or equal" value}
431 \cvarg{CV\_CMP\_LT}{src1(I) "less than" value}
432 \cvarg{CV\_CMP\_LE}{src1(I) "less or equal" value}
433 \cvarg{CV\_CMP\_NE}{src1(I) "not equal" value}
437 The function compares the corresponding elements of an array and a scalar and fills the destination mask array:
440 dst(I)=src(I) op scalar
443 where \texttt{op} is $=,\; >,\; \ge,\; <,\; \le\; or\; \ne$.
445 \texttt{dst(I)} is set to 0xff (all \texttt{1}-bits) if the specific relation between the elements is true and 0 otherwise. All the arrays must have the same size (or ROI size).
449 Converts one array to another.
451 \cvdefPy{Convert(src,dst)-> None}
454 \cvarg{src}{Source array}
455 \cvarg{dst}{Destination array}
459 The type of conversion is done with rounding and saturation, that is if the
460 result of scaling + conversion can not be represented exactly by a value
461 of the destination array element type, it is set to the nearest representable
462 value on the real axis.
464 All the channels of multi-channel arrays are processed independently.
468 \cvCPyFunc{ConvertScale}
469 Converts one array to another with optional linear transformation.
471 \cvdefC{void cvConvertScale(const CvArr* src, CvArr* dst, double scale=1, double shift=0);}
472 \cvdefPy{ConvertScale(src,dst,scale=1.0,shift=0.0)-> None}
476 #define cvCvtScale cvConvertScale
477 #define cvScale cvConvertScale
478 #define cvConvert(src, dst ) cvConvertScale((src), (dst), 1, 0 )
483 \cvarg{src}{Source array}
484 \cvarg{dst}{Destination array}
485 \cvarg{scale}{Scale factor}
486 \cvarg{shift}{Value added to the scaled source array elements}
490 The function has several different purposes, and thus has several different names. It copies one array to another with optional scaling, which is performed first, and/or optional type conversion, performed after:
493 \texttt{dst}(I) = \texttt{scale} \texttt{src}(I) + (\texttt{shift}_0,\texttt{shift}_1,...)
496 All the channels of multi-channel arrays are processed independently.
498 The type of conversion is done with rounding and saturation, that is if the
499 result of scaling + conversion can not be represented exactly by a value
500 of the destination array element type, it is set to the nearest representable
501 value on the real axis.
503 In the case of \texttt{scale=1, shift=0} no prescaling is done. This is a specially
504 optimized case and it has the appropriate \cvCPyCross{Convert} name. If
505 source and destination array types have equal types, this is also a
506 special case that can be used to scale and shift a matrix or an image
507 and that is caled \cvCPyCross{Scale}.
510 \cvCPyFunc{ConvertScaleAbs}
511 Converts input array elements to another 8-bit unsigned integer with optional linear transformation.
513 \cvdefC{void cvConvertScaleAbs(const CvArr* src, CvArr* dst, double scale=1, double shift=0);}
514 \cvdefPy{ConvertScaleAbs(src,dst,scale=1.0,shift=0.0)-> None}
517 \cvarg{src}{Source array}
518 \cvarg{dst}{Destination array (should have 8u depth)}
519 \cvarg{scale}{ScaleAbs factor}
520 \cvarg{shift}{Value added to the scaled source array elements}
523 The function is similar to \cvCPyCross{ConvertScale}, but it stores absolute values of the conversion results:
526 \texttt{dst}(I) = |\texttt{scale} \texttt{src}(I) + (\texttt{shift}_0,\texttt{shift}_1,...)|
529 The function supports only destination arrays of 8u (8-bit unsigned integers) type; for other types the function can be emulated by a combination of \cvCPyCross{ConvertScale} and \cvCPyCross{Abs} functions.
531 \cvCPyFunc{CvtScaleAbs}
532 Converts input array elements to another 8-bit unsigned integer with optional linear transformation.
534 \cvdefC{void cvCvtScaleAbs(const CvArr* src, CvArr* dst, double scale=1, double shift=0);}
535 \cvdefPy{CvtScaleAbs(src,dst,scale=1.0,shift=0.0)-> None}
538 \cvarg{src}{Source array}
539 \cvarg{dst}{Destination array (should have 8u depth)}
540 \cvarg{scale}{ScaleAbs factor}
541 \cvarg{shift}{Value added to the scaled source array elements}
546 The function is similar to \cvCPyCross{ConvertScale}, but it stores absolute values of the conversion results:
549 \texttt{dst}(I) = |\texttt{scale} \texttt{src}(I) + (\texttt{shift}_0,\texttt{shift}_1,...)|
552 The function supports only destination arrays of 8u (8-bit unsigned integers) type; for other types the function can be emulated by a combination of \cvCPyCross{ConvertScale} and \cvCPyCross{Abs} functions.
555 Copies one array to another.
557 \cvdefC{void cvCopy(const CvArr* src, CvArr* dst, const CvArr* mask=NULL);}
558 \cvdefPy{Copy(src,dst,mask=NULL)-> None}
561 \cvarg{src}{The source array}
562 \cvarg{dst}{The destination array}
563 \cvarg{mask}{Operation mask, 8-bit single channel array; specifies elements of the destination array to be changed}
567 The function copies selected elements from an input array to an output array:
570 \texttt{dst}(I)=\texttt{src}(I) \quad \text{if} \quad \texttt{mask}(I) \ne 0.
573 If any of the passed arrays is of \texttt{IplImage} type, then its ROI
574 and COI fields are used. Both arrays must have the same type, the same
575 number of dimensions, and the same size. The function can also copy sparse
576 arrays (mask is not supported in this case).
578 \cvCPyFunc{CountNonZero}
579 Counts non-zero array elements.
581 \cvdefC{int cvCountNonZero(const CvArr* arr);}
582 \cvdefPy{CountNonZero(arr)-> int}
585 \cvarg{arr}{The array must be a single-channel array or a multi-channel image with COI set}
589 The function returns the number of non-zero elements in arr:
591 \[ \sum_I (\texttt{arr}(I) \ne 0) \]
593 In the case of \texttt{IplImage} both ROI and COI are supported.
596 \cvCPyFunc{CreateData}
599 \cvdefC{void cvCreateData(CvArr* arr);}
600 \cvdefPy{CreateData(arr) -> None}
603 \cvarg{arr}{Array header}
607 The function allocates image, matrix or
608 multi-dimensional array data. Note that in the case of matrix types OpenCV
609 allocation functions are used and in the case of IplImage they are used
610 unless \texttt{CV\_TURN\_ON\_IPL\_COMPATIBILITY} was called. In the
611 latter case IPL functions are used to allocate the data.
613 \cvCPyFunc{CreateImage}
614 Creates an image header and allocates the image data.
616 \cvdefC{IplImage* cvCreateImage(CvSize size, int depth, int channels);}
617 \cvdefPy{CreateImage(size, depth, channels)->image}
620 \cvarg{size}{Image width and height}
621 \cvarg{depth}{Bit depth of image elements. See \cross{IplImage} for valid depths.}
622 \cvarg{channels}{Number of channels per pixel. See \cross{IplImage} for details. This function only creates images with interleaved channels.}
626 This call is a shortened form of
628 header = cvCreateImageHeader(size, depth, channels);
629 cvCreateData(header);
633 \cvCPyFunc{CreateImageHeader}
634 Creates an image header but does not allocate the image data.
636 \cvdefC{IplImage* cvCreateImageHeader(CvSize size, int depth, int channels);}
637 \cvdefPy{CreateImageHeader(size, depth, channels) -> image}
640 \cvarg{size}{Image width and height}
641 \cvarg{depth}{Image depth (see \cvCPyCross{CreateImage})}
642 \cvarg{channels}{Number of channels (see \cvCPyCross{CreateImage})}
646 This call is an analogue of
648 hdr=iplCreateImageHeader(channels, 0, depth,
649 channels == 1 ? "GRAY" : "RGB",
650 channels == 1 ? "GRAY" : channels == 3 ? "BGR" :
651 channels == 4 ? "BGRA" : "",
652 IPL_DATA_ORDER_PIXEL, IPL_ORIGIN_TL, 4,
653 size.width, size.height,
656 but it does not use IPL functions by default (see the \texttt{CV\_TURN\_ON\_IPL\_COMPATIBILITY} macro).
659 \cvCPyFunc{CreateMat}\label{cvCreateMat}
660 Creates a matrix header and allocates the matrix data.
662 \cvdefC{CvMat* cvCreateMat(\par int rows,\par int cols,\par int type);}
663 \cvdefPy{CreateMat(rows, cols, type) -> mat}
666 \cvarg{rows}{Number of rows in the matrix}
667 \cvarg{cols}{Number of columns in the matrix}
668 \cvarg{type}{The type of the matrix elements in the form \texttt{CV\_<bit depth><S|U|F>C<number of channels>}, where S=signed, U=unsigned, F=float. For example, CV\_8UC1 means the elements are 8-bit unsigned and the there is 1 channel, and CV\_32SC2 means the elements are 32-bit signed and there are 2 channels.}
672 This is the concise form for:
675 CvMat* mat = cvCreateMatHeader(rows, cols, type);
680 \cvCPyFunc{CreateMatHeader}
681 Creates a matrix header but does not allocate the matrix data.
683 \cvdefC{CvMat* cvCreateMatHeader(\par int rows,\par int cols,\par int type);}
684 \cvdefPy{CreateMatHeader(rows, cols, type) -> mat}
687 \cvarg{rows}{Number of rows in the matrix}
688 \cvarg{cols}{Number of columns in the matrix}
689 \cvarg{type}{Type of the matrix elements, see \cvCPyCross{CreateMat}}
692 The function allocates a new matrix header and returns a pointer to it. The matrix data can then be allocated using \cvCPyCross{CreateData} or set explicitly to user-allocated data via \cvCPyCross{SetData}.
694 \cvCPyFunc{CreateMatND}
695 Creates the header and allocates the data for a multi-dimensional dense array.
697 \cvdefC{CvMatND* cvCreateMatND(\par int dims,\par const int* sizes,\par int type);}
698 \cvdefPy{CreateMatND(dims, type) -> None}
702 \cvarg{dims}{List or tuple of array dimensions, up to 32 in length.}
704 \cvarg{dims}{Number of array dimensions. This must not exceed CV\_MAX\_DIM (32 by default, but can be changed at build time).}
705 \cvarg{sizes}{Array of dimension sizes.}
707 \cvarg{type}{Type of array elements, see \cvCPyCross{CreateMat}.}
710 This is a short form for:
714 CvMatND* mat = cvCreateMatNDHeader(dims, sizes, type);
719 \cvCPyFunc{CreateMatNDHeader}
720 Creates a new matrix header but does not allocate the matrix data.
722 \cvdefC{CvMatND* cvCreateMatNDHeader(\par int dims,\par const int* sizes,\par int type);}
723 \cvdefPy{CreateMatNDHeader(dims, type) -> None}
727 \cvarg{dims}{List or tuple of array dimensions, up to 32 in length.}
729 \cvarg{dims}{Number of array dimensions}
730 \cvarg{sizes}{Array of dimension sizes}
732 \cvarg{type}{Type of array elements, see \cvCPyCross{CreateMat}}
735 The function allocates a header for a multi-dimensional dense array. The array data can further be allocated using \cvCPyCross{CreateData} or set explicitly to user-allocated data via \cvCPyCross{SetData}.
738 \cvCPyFunc{CreateSparseMat}
739 Creates sparse array.
741 \cvdefC{CvSparseMat* cvCreateSparseMat(int dims, const int* sizes, int type);}
742 \cvdefPy{CreateSparseMat(dims, type) -> cvmat}
746 \cvarg{dims}{Number of array dimensions. In contrast to the dense matrix, the number of dimensions is practically unlimited (up to $2^{16}$).}
747 \cvarg{sizes}{Array of dimension sizes}
749 \cvarg{dims}{List or tuple of array dimensions.}
751 \cvarg{type}{Type of array elements. The same as for CvMat}
754 The function allocates a multi-dimensional sparse array. Initially the array contain no elements, that is \cvCPyCross{Get} or \cvCPyCross{GetReal} returns zero for every index.
757 \cvCPyFunc{CrossProduct}
758 Calculates the cross product of two 3D vectors.
760 \cvdefC{void cvCrossProduct(const CvArr* src1, const CvArr* src2, CvArr* dst);}
761 \cvdefPy{CrossProduct(src1,src2,dst)-> None}
764 \cvarg{src1}{The first source vector}
765 \cvarg{src2}{The second source vector}
766 \cvarg{dst}{The destination vector}
770 The function calculates the cross product of two 3D vectors:
772 \[ \texttt{dst} = \texttt{src1} \times \texttt{src2} \]
776 \texttt{dst}_1 = \texttt{src1}_2 \texttt{src2}_3 - \texttt{src1}_3 \texttt{src2}_2\\
777 \texttt{dst}_2 = \texttt{src1}_3 \texttt{src2}_1 - \texttt{src1}_1 \texttt{src2}_3\\
778 \texttt{dst}_3 = \texttt{src1}_1 \texttt{src2}_2 - \texttt{src1}_2 \texttt{src2}_1
782 \subsection{CvtPixToPlane}
784 Synonym for \cross{Split}.
787 Performs a forward or inverse Discrete Cosine transform of a 1D or 2D floating-point array.
789 \cvdefC{void cvDCT(const CvArr* src, CvArr* dst, int flags);}
790 \cvdefPy{DCT(src,dst,flags)-> None}
793 \cvarg{src}{Source array, real 1D or 2D array}
794 \cvarg{dst}{Destination array of the same size and same type as the source}
795 \cvarg{flags}{Transformation flags, a combination of the following values
797 \cvarg{CV\_DXT\_FORWARD}{do a forward 1D or 2D transform.}
798 \cvarg{CV\_DXT\_INVERSE}{do an inverse 1D or 2D transform.}
799 \cvarg{CV\_DXT\_ROWS}{do a forward or inverse transform of every individual row of the input matrix. This flag allows user to transform multiple vectors simultaneously and can be used to decrease the overhead (which is sometimes several times larger than the processing itself), to do 3D and higher-dimensional transforms and so forth.}
803 The function performs a forward or inverse transform of a 1D or 2D floating-point array:
805 Forward Cosine transform of 1D vector of $N$ elements:
806 \[Y = C^{(N)} \cdot X\]
808 \[C^{(N)}_{jk}=\sqrt{\alpha_j/N}\cos\left(\frac{\pi(2k+1)j}{2N}\right)\]
809 and $\alpha_0=1$, $\alpha_j=2$ for $j > 0$.
811 Inverse Cosine transform of 1D vector of N elements:
812 \[X = \left(C^{(N)}\right)^{-1} \cdot Y = \left(C^{(N)}\right)^T \cdot Y\]
813 (since $C^{(N)}$ is orthogonal matrix, $C^{(N)} \cdot \left(C^{(N)}\right)^T = I$)
815 Forward Cosine transform of 2D $M \times N$ matrix:
816 \[Y = C^{(N)} \cdot X \cdot \left(C^{(N)}\right)^T\]
818 Inverse Cosine transform of 2D vector of $M \times N$ elements:
819 \[X = \left(C^{(N)}\right)^T \cdot X \cdot C^{(N)}\]
823 Performs a forward or inverse Discrete Fourier transform of a 1D or 2D floating-point array.
825 \cvdefC{void cvDFT(const CvArr* src, CvArr* dst, int flags, int nonzeroRows=0);}
826 \cvdefPy{DFT(src,dst,flags,nonzeroRows=0)-> None}
829 \cvarg{src}{Source array, real or complex}
830 \cvarg{dst}{Destination array of the same size and same type as the source}
831 \cvarg{flags}{Transformation flags, a combination of the following values
833 \cvarg{CV\_DXT\_FORWARD}{do a forward 1D or 2D transform. The result is not scaled.}
834 \cvarg{CV\_DXT\_INVERSE}{do an inverse 1D or 2D transform. The result is not scaled. \texttt{CV\_DXT\_FORWARD} and \texttt{CV\_DXT\_INVERSE} are mutually exclusive, of course.}
835 \cvarg{CV\_DXT\_SCALE}{scale the result: divide it by the number of array elements. Usually, it is combined with \texttt{CV\_DXT\_INVERSE}, and one may use a shortcut \texttt{CV\_DXT\_INV\_SCALE}.}
836 \cvarg{CV\_DXT\_ROWS}{do a forward or inverse transform of every individual row of the input matrix. This flag allows the user to transform multiple vectors simultaneously and can be used to decrease the overhead (which is sometimes several times larger than the processing itself), to do 3D and higher-dimensional transforms and so forth.}
837 \cvarg{CV\_DXT\_INVERSE\_SCALE}{same as \texttt{CV\_DXT\_INVERSE + CV\_DXT\_SCALE}}
839 \cvarg{nonzeroRows}{Number of nonzero rows in the source array
840 (in the case of a forward 2d transform), or a number of rows of interest in
841 the destination array (in the case of an inverse 2d transform). If the value
842 is negative, zero, or greater than the total number of rows, it is
843 ignored. The parameter can be used to speed up 2d convolution/correlation
844 when computing via DFT. See the example below.}
847 The function performs a forward or inverse transform of a 1D or 2D floating-point array:
850 Forward Fourier transform of 1D vector of N elements:
851 \[y = F^{(N)} \cdot x, where F^{(N)}_{jk}=exp(-i \cdot 2\pi \cdot j \cdot k/N)\],
854 Inverse Fourier transform of 1D vector of N elements:
855 \[x'= (F^{(N)})^{-1} \cdot y = conj(F^(N)) \cdot y
858 Forward Fourier transform of 2D vector of M $\times$ N elements:
859 \[Y = F^{(M)} \cdot X \cdot F^{(N)}\]
861 Inverse Fourier transform of 2D vector of M $\times$ N elements:
862 \[X'= conj(F^{(M)}) \cdot Y \cdot conj(F^{(N)})
863 X = (1/(M \cdot N)) \cdot X'\]
866 In the case of real (single-channel) data, the packed format, borrowed from IPL, is used to represent the result of a forward Fourier transform or input for an inverse Fourier transform:
869 Re Y_{0,0} & Re Y_{0,1} & Im Y_{0,1} & Re Y_{0,2} & Im Y_{0,2} & \cdots & Re Y_{0,N/2-1} & Im Y_{0,N/2-1} & Re Y_{0,N/2} \\
870 Re Y_{1,0} & Re Y_{1,1} & Im Y_{1,1} & Re Y_{1,2} & Im Y_{1,2} & \cdots & Re Y_{1,N/2-1} & Im Y_{1,N/2-1} & Re Y_{1,N/2} \\
871 Im Y_{1,0} & Re Y_{2,1} & Im Y_{2,1} & Re Y_{2,2} & Im Y_{2,2} & \cdots & Re Y_{2,N/2-1} & Im Y_{2,N/2-1} & Im Y_{1,N/2} \\
873 Re Y_{M/2-1,0} & Re Y_{M-3,1} & Im Y_{M-3,1} & \hdotsfor{3} & Re Y_{M-3,N/2-1} & Im Y_{M-3,N/2-1}& Re Y_{M/2-1,N/2} \\
874 Im Y_{M/2-1,0} & Re Y_{M-2,1} & Im Y_{M-2,1} & \hdotsfor{3} & Re Y_{M-2,N/2-1} & Im Y_{M-2,N/2-1}& Im Y_{M/2-1,N/2} \\
875 Re Y_{M/2,0} & Re Y_{M-1,1} & Im Y_{M-1,1} & \hdotsfor{3} & Re Y_{M-1,N/2-1} & Im Y_{M-1,N/2-1}& Re Y_{M/2,N/2}
880 Note: the last column is present if \texttt{N} is even, the last row is present if \texttt{M} is even.
881 In the case of 1D real transform the result looks like the first row of the above matrix.
883 Here is the example of how to compute 2D convolution using DFT.
887 CvMat* A = cvCreateMat(M1, N1, CVg32F);
888 CvMat* B = cvCreateMat(M2, N2, A->type);
890 // it is also possible to have only abs(M2-M1)+1 times abs(N2-N1)+1
891 // part of the full convolution result
892 CvMat* conv = cvCreateMat(A->rows + B->rows - 1, A->cols + B->cols - 1,
895 // initialize A and B
898 int dftgM = cvGetOptimalDFTSize(A->rows + B->rows - 1);
899 int dftgN = cvGetOptimalDFTSize(A->cols + B->cols - 1);
901 CvMat* dftgA = cvCreateMat(dft\_M, dft\_N, A->type);
902 CvMat* dftgB = cvCreateMat(dft\_M, dft\_N, B->type);
905 // copy A to dftgA and pad dft\_A with zeros
906 cvGetSubRect(dftgA, &tmp, cvRect(0,0,A->cols,A->rows));
908 cvGetSubRect(dftgA, &tmp, cvRect(A->cols,0,dft\_A->cols - A->cols,A->rows));
910 // no need to pad bottom part of dftgA with zeros because of
911 // use nonzerogrows parameter in cvDFT() call below
913 cvDFT(dftgA, dft\_A, CV\_DXT\_FORWARD, A->rows);
915 // repeat the same with the second array
916 cvGetSubRect(dftgB, &tmp, cvRect(0,0,B->cols,B->rows));
918 cvGetSubRect(dftgB, &tmp, cvRect(B->cols,0,dft\_B->cols - B->cols,B->rows));
920 // no need to pad bottom part of dftgB with zeros because of
921 // use nonzerogrows parameter in cvDFT() call below
923 cvDFT(dftgB, dft\_B, CV\_DXT\_FORWARD, B->rows);
925 cvMulSpectrums(dftgA, dft\_B, dft\_A, 0 /* or CV\_DXT\_MUL\_CONJ to get
926 correlation rather than convolution */);
928 cvDFT(dftgA, dft\_A, CV\_DXT\_INV\_SCALE, conv->rows); // calculate only
930 cvGetSubRect(dftgA, &tmp, cvRect(0,0,conv->cols,conv->rows));
938 \cvCPyFunc{DecRefData}
939 Decrements an array data reference counter.
941 \cvdefC{void cvDecRefData(CvArr* arr);}
944 \cvarg{arr}{Pointer to an array header}
947 The function decrements the data reference counter in a \cross{CvMat} or
948 \cross{CvMatND} if the reference counter pointer
949 is not NULL. If the counter reaches zero, the data is deallocated. In the
950 current implementation the reference counter is not NULL only if the data
951 was allocated using the \cvCPyCross{CreateData} function. The counter will be NULL in other cases such as:
952 external data was assigned to the header using \cvCPyCross{SetData}, the matrix
953 header is part of a larger matrix or image, or the header was converted from an image or n-dimensional matrix header.
959 Returns the determinant of a matrix.
961 \cvdefC{double cvDet(const CvArr* mat);}
962 \cvdefPy{Det(mat)-> double}
965 \cvarg{mat}{The source matrix}
968 The function returns the determinant of the square matrix \texttt{mat}. The direct method is used for small matrices and Gaussian elimination is used for larger matrices. For symmetric positive-determined matrices, it is also possible to run
970 with $U = V = 0$ and then calculate the determinant as a product of the diagonal elements of $W$.
973 Performs per-element division of two arrays.
975 \cvdefC{void cvDiv(const CvArr* src1, const CvArr* src2, CvArr* dst, double scale=1);}
976 \cvdefPy{Div(src1,src2,dst,scale)-> None}
979 \cvarg{src1}{The first source array. If the pointer is NULL, the array is assumed to be all 1's.}
980 \cvarg{src2}{The second source array}
981 \cvarg{dst}{The destination array}
982 \cvarg{scale}{Optional scale factor}
985 The function divides one array by another:
988 \texttt{dst}(I)=\fork
989 {\texttt{scale} \cdot \texttt{src1}(I)/\texttt{src2}(I)}{if \texttt{src1} is not \texttt{NULL}}
990 {\texttt{scale}/\texttt{src2}(I)}{otherwise}
993 All the arrays must have the same type and the same size (or ROI size).
996 \cvCPyFunc{DotProduct}
997 Calculates the dot product of two arrays in Euclidian metrics.
999 \cvdefC{double cvDotProduct(const CvArr* src1, const CvArr* src2);}
1000 \cvdefPy{DotProduct(src1,src2)-> double}
1003 \cvarg{src1}{The first source array}
1004 \cvarg{src2}{The second source array}
1007 The function calculates and returns the Euclidean dot product of two arrays.
1010 src1 \bullet src2 = \sum_I (\texttt{src1}(I) \texttt{src2}(I))
1013 In the case of multiple channel arrays, the results for all channels are accumulated. In particular, \texttt{cvDotProduct(a,a)} where \texttt{a} is a complex vector, will return $||\texttt{a}||^2$.
1014 The function can process multi-dimensional arrays, row by row, layer by layer, and so on.
1017 Computes eigenvalues and eigenvectors of a symmetric matrix.
1020 void cvEigenVV(\par CvArr* mat,\par CvArr* evects,\par CvArr* evals,\par double eps=0,
1021 \par int lowindex = 0, \par int highindex = 0);}
1022 \cvdefPy{EigenVV(mat,evects,evals,eps,lowindex,highindex)-> None}
1025 \cvarg{mat}{The input symmetric square matrix, modified during the processing}
1026 \cvarg{evects}{The output matrix of eigenvectors, stored as subsequent rows}
1027 \cvarg{evals}{The output vector of eigenvalues, stored in the descending order (order of eigenvalues and eigenvectors is syncronized, of course)}
1028 \cvarg{eps}{Accuracy of diagonalization. Typically, \texttt{DBL\_EPSILON} (about $ 10^{-15} $) works well.
1029 THIS PARAMETER IS CURRENTLY IGNORED.}
1030 \cvarg{lowindex}{Optional index of largest eigenvalue/-vector to calculate.
1032 \cvarg{highindex}{Optional index of smallest eigenvalue/-vector to calculate.
1037 The function computes the eigenvalues and eigenvectors of matrix \texttt{A}:
1040 mat*evects(i,:)' = evals(i)*evects(i,:)' (in MATLAB notation)
1043 If either low- or highindex is supplied the other is required, too.
1044 Indexing is 1-based. Example: To calculate the largest eigenvector/-value set
1045 lowindex = highindex = 1.
1046 For legacy reasons this function always returns a square matrix the same size
1047 as the source matrix with eigenvectors and a vector the length of the source
1048 matrix with eigenvalues. The selected eigenvectors/-values are always in the
1049 first highindex - lowindex + 1 rows.
1051 The contents of matrix \texttt{A} is destroyed by the function.
1053 Currently the function is slower than \cvCPyCross{SVD} yet less accurate,
1054 so if \texttt{A} is known to be positively-defined (for example, it
1055 is a covariance matrix)it is recommended to use \cvCPyCross{SVD} to find
1056 eigenvalues and eigenvectors of \texttt{A}, especially if eigenvectors
1060 Calculates the exponent of every array element.
1062 \cvdefC{void cvExp(const CvArr* src, CvArr* dst);}
1063 \cvdefPy{Exp(src,dst)-> None}
1066 \cvarg{src}{The source array}
1067 \cvarg{dst}{The destination array, it should have \texttt{double} type or the same type as the source}
1071 The function calculates the exponent of every element of the input array:
1074 \texttt{dst} [I] = e^{\texttt{src}(I)}
1077 The maximum relative error is about $7 \times 10^{-6}$. Currently, the function converts denormalized values to zeros on output.
1079 \cvCPyFunc{FastArctan}
1080 Calculates the angle of a 2D vector.
1082 \cvdefC{float cvFastArctan(float y, float x);}
1083 \cvdefPy{FastArctan(y,x)-> float}
1086 \cvarg{x}{x-coordinate of 2D vector}
1087 \cvarg{y}{y-coordinate of 2D vector}
1091 The function calculates the full-range angle of an input 2D vector. The angle is
1092 measured in degrees and varies from 0 degrees to 360 degrees. The accuracy is about 0.1 degrees.
1095 Flip a 2D array around vertical, horizontal or both axes.
1097 \cvdefC{void cvFlip(const CvArr* src, CvArr* dst=NULL, int flipMode=0);}
1098 \cvdefPy{Flip(src,dst=NULL,flipMode=0)-> None}
1101 \cvarg{src}{Source array}
1102 \cvarg{dst}{Destination array.
1103 If $\texttt{dst} = \texttt{NULL}$ the flipping is done in place.}
1104 \cvarg{flipMode}{Specifies how to flip the array:
1105 0 means flipping around the x-axis, positive (e.g., 1) means flipping around y-axis, and negative (e.g., -1) means flipping around both axes. See also the discussion below for the formulas:}
1108 The function flips the array in one of three different ways (row and column indices are 0-based):
1111 dst(i,j) = \forkthree
1112 {\texttt{src}(rows(\texttt{src})-i-1,j)}{if $\texttt{flipMode} = 0$}
1113 {\texttt{src}(i,cols(\texttt{src})-j-1)}{if $\texttt{flipMode} > 0$}
1114 {\texttt{src}(rows(\texttt{src})-i-1,cols(\texttt{src})-j-1)}{if $\texttt{flipMode} < 0$}
1117 The example scenarios of function use are:
1119 \item vertical flipping of the image (flipMode = 0) to switch between top-left and bottom-left image origin, which is a typical operation in video processing under Win32 systems.
1120 \item horizontal flipping of the image with subsequent horizontal shift and absolute difference calculation to check for a vertical-axis symmetry (flipMode $>$ 0)
1121 \item simultaneous horizontal and vertical flipping of the image with subsequent shift and absolute difference calculation to check for a central symmetry (flipMode $<$ 0)
1122 \item reversing the order of 1d point arrays (flipMode > 0)
1129 Create a CvMat from an object that supports the array interface.
1131 \cvdefPy{fromarray(object, allowND = False) -> CvMat}
1134 \cvarg{object}{Any object that supports the array interface}
1135 \cvarg{allowND}{If true, will return a CvMatND}
1138 If the object supports the
1139 \href{http://docs.scipy.org/doc/numpy/reference/arrays.interface.html}{array interface},
1140 return a \cross{CvMat} (\texttt{allowND = False}) or \cross{CvMatND} (\texttt{allowND = True}).
1142 If \texttt{allowND = False}, then the object's array must be either 2D or 3D. If it is 2D, then the returned CvMat has a single channel. If it is 3D, then the returned CvMat will have N channels, where N is the last dimension of the array. In this case, N cannot be greater than OpenCV's channel limit, \texttt{CV\_CN\_MAX}.
1144 If \texttt{allowND = True}, then \texttt{fromarray} returns a single-channel \cross{CvMatND} with the same shape as the original array.
1146 For example, \href{http://numpy.scipy.org/}{NumPy} arrays support the array interface, so can be converted to OpenCV objects:
1149 >>> import cv, numpy
1150 >>> a = numpy.ones((480, 640))
1151 >>> mat = cv.fromarray(a)
1152 >>> print cv.GetDims(mat), cv.CV_MAT_CN(cv.GetElemType(mat))
1154 >>> a = numpy.ones((480, 640, 3))
1155 >>> mat = cv.fromarray(a)
1156 >>> print cv.GetDims(mat), cv.CV_MAT_CN(cv.GetElemType(mat))
1158 >>> a = numpy.ones((480, 640, 3))
1159 >>> mat = cv.fromarray(a, allowND = True)
1160 >>> print cv.GetDims(mat), cv.CV_MAT_CN(cv.GetElemType(mat))
1167 Performs generalized matrix multiplication.
1169 \cvdefC{void cvGEMM(\par const CvArr* src1, \par const CvArr* src2, double alpha,
1170 \par const CvArr* src3, \par double beta, \par CvArr* dst, \par int tABC=0);\newline
1171 \#define cvMatMulAdd(src1, src2, src3, dst ) cvGEMM(src1, src2, 1, src3, 1, dst, 0 )\par
1172 \#define cvMatMul(src1, src2, dst ) cvMatMulAdd(src1, src2, 0, dst )}
1174 \cvdefPy{GEMM(src1,src2,alphs,src3,beta,dst,tABC=0)-> None}
1177 \cvarg{src1}{The first source array}
1178 \cvarg{src2}{The second source array}
1179 \cvarg{src3}{The third source array (shift). Can be NULL, if there is no shift.}
1180 \cvarg{dst}{The destination array}
1181 \cvarg{tABC}{The operation flags that can be 0 or a combination of the following values
1183 \cvarg{CV\_GEMM\_A\_T}{transpose src1}
1184 \cvarg{CV\_GEMM\_B\_T}{transpose src2}
1185 \cvarg{CV\_GEMM\_C\_T}{transpose src3}
1188 For example, \texttt{CV\_GEMM\_A\_T+CV\_GEMM\_C\_T} corresponds to
1190 \texttt{alpha} \, \texttt{src1} ^T \, \texttt{src2} + \texttt{beta} \, \texttt{src3} ^T
1194 The function performs generalized matrix multiplication:
1197 \texttt{dst} = \texttt{alpha} \, op(\texttt{src1}) \, op(\texttt{src2}) + \texttt{beta} \, op(\texttt{src3}) \quad \text{where $op(X)$ is $X$ or $X^T$}
1200 All the matrices should have the same data type and coordinated sizes. Real or complex floating-point matrices are supported.
1205 Return a specific array element.
1208 CvScalar cvGet1D(const CvArr* arr, int idx0);
1209 CvScalar cvGet2D(const CvArr* arr, int idx0, int idx1);
1210 CvScalar cvGet3D(const CvArr* arr, int idx0, int idx1, int idx2);
1211 CvScalar cvGetND(const CvArr* arr, int* idx);
1215 \cvarg{arr}{Input array}
1216 \cvarg{idx0}{The first zero-based component of the element index}
1217 \cvarg{idx1}{The second zero-based component of the element index}
1218 \cvarg{idx2}{The third zero-based component of the element index}
1219 \cvarg{idx}{Array of the element indices}
1222 The functions return a specific array element. In the case of a sparse array the functions return 0 if the requested node does not exist (no new node is created by the functions).
1226 Return a specific array element.
1228 \cvdefPy{Get1D(arr, idx) -> scalar}
1231 \cvarg{arr}{Input array}
1232 \cvarg{idx}{Zero-based element index}
1235 Return a specific array element. Array must have dimension 3.
1238 Return a specific array element.
1240 \cvdefPy{ Get2D(arr, idx0, idx1) -> scalar }
1243 \cvarg{arr}{Input array}
1244 \cvarg{idx0}{Zero-based element row index}
1245 \cvarg{idx1}{Zero-based element column index}
1248 Return a specific array element. Array must have dimension 2.
1251 Return a specific array element.
1253 \cvdefPy{ Get3D(arr, idx0, idx1, idx2) -> scalar }
1256 \cvarg{arr}{Input array}
1257 \cvarg{idx0}{Zero-based element index}
1258 \cvarg{idx1}{Zero-based element index}
1259 \cvarg{idx2}{Zero-based element index}
1262 Return a specific array element. Array must have dimension 3.
1265 Return a specific array element.
1267 \cvdefPy{ GetND(arr, indices) -> scalar }
1270 \cvarg{arr}{Input array}
1271 \cvarg{indices}{List of zero-based element indices}
1274 Return a specific array element. The length of array indices must be the same as the dimension of the array.
1279 \cvCPyFunc{GetCol(s)}
1280 Returns array column or column span.
1282 \cvdefC{CvMat* cvGetCol(const CvArr* arr, CvMat* submat, int col);}
1283 \cvdefPy{GetCol(arr,row)-> submat}
1284 \cvdefC{CvMat* cvGetCols(const CvArr* arr, CvMat* submat, int startCol, int endCol);}
1285 \cvdefPy{GetCols(arr,startCol,endCol)-> submat}
1288 \cvarg{arr}{Input array}
1289 \cvarg{submat}{Pointer to the resulting sub-array header}
1290 \cvarg{col}{Zero-based index of the selected column}
1291 \cvarg{startCol}{Zero-based index of the starting column (inclusive) of the span}
1292 \cvarg{endCol}{Zero-based index of the ending column (exclusive) of the span}
1295 The functions \texttt{GetCol} and \texttt{GetCols} return the header, corresponding to a specified column span of the input array. \texttt{GetCol} is a shortcut for \cvCPyCross{GetCols}:
1298 cvGetCol(arr, submat, col); // ~ cvGetCols(arr, submat, col, col + 1);
1304 Returns array column.
1306 \cvdefPy{GetCol(arr,col)-> submat}
1309 \cvarg{arr}{Input array}
1310 \cvarg{col}{Zero-based index of the selected column}
1311 \cvarg{submat}{resulting single-column array}
1314 The function \texttt{GetCol} returns a single column from the input array.
1317 Returns array column span.
1319 \cvdefPy{GetCols(arr,startCol,endCol)-> submat}
1322 \cvarg{arr}{Input array}
1323 \cvarg{startCol}{Zero-based index of the starting column (inclusive) of the span}
1324 \cvarg{endCol}{Zero-based index of the ending column (exclusive) of the span}
1325 \cvarg{submat}{resulting multi-column array}
1328 The function \texttt{GetCols} returns a column span from the input array.
1333 Returns one of array diagonals.
1335 \cvdefC{CvMat* cvGetDiag(const CvArr* arr, CvMat* submat, int diag=0);}
1336 \cvdefPy{GetDiag(arr,diag=0)-> submat}
1339 \cvarg{arr}{Input array}
1340 \cvarg{submat}{Pointer to the resulting sub-array header}
1341 \cvarg{diag}{Array diagonal. Zero corresponds to the main diagonal, -1 corresponds to the diagonal above the main , 1 corresponds to the diagonal below the main, and so forth.}
1344 The function returns the header, corresponding to a specified diagonal of the input array.
1347 \subsection{cvGetDims, cvGetDimSize}\label{cvGetDims}
1349 Return number of array dimensions and their sizes or the size of a particular dimension.
1351 \cvdefC{int cvGetDims(const CvArr* arr, int* sizes=NULL);}
1352 \cvdefC{int cvGetDimSize(const CvArr* arr, int index);}
1355 \cvarg{arr}{Input array}
1356 \cvarg{sizes}{Optional output vector of the array dimension sizes. For
1357 2d arrays the number of rows (height) goes first, number of columns
1359 \cvarg{index}{Zero-based dimension index (for matrices 0 means number
1360 of rows, 1 means number of columns; for images 0 means height, 1 means
1364 The function \texttt{cvGetDims} returns the array dimensionality and the
1365 array of dimension sizes. In the case of \texttt{IplImage} or \cross{CvMat} it always
1366 returns 2 regardless of number of image/matrix rows. The function
1367 \texttt{cvGetDimSize} returns the particular dimension size (number of
1368 elements per that dimension). For example, the following code calculates
1369 total number of array elements in two ways:
1373 int sizes[CV_MAX_DIM];
1375 int dims = cvGetDims(arr, size);
1376 for(i = 0; i < dims; i++ )
1379 // via cvGetDims() and cvGetDimSize()
1381 int dims = cvGetDims(arr);
1382 for(i = 0; i < dims; i++ )
1383 total *= cvGetDimsSize(arr, i);
1389 Returns list of array dimensions
1391 \cvdefPy{GetDims(arr)-> list}
1394 \cvarg{arr}{Input array}
1397 The function returns a list of array dimensions.
1398 In the case of \texttt{IplImage} or \cross{CvMat} it always
1399 returns a list of length 2.
1403 \cvCPyFunc{GetElemType}
1404 Returns type of array elements.
1406 \cvdefC{int cvGetElemType(const CvArr* arr);}
1407 \cvdefPy{GetElemType(arr)-> int}
1410 \cvarg{arr}{Input array}
1413 The function returns type of the array elements
1414 as described in \cvCPyCross{CreateMat} discussion: \texttt{CV\_8UC1} ... \texttt{CV\_64FC4}.
1417 \cvCPyFunc{GetImage}
1418 Returns image header for arbitrary array.
1420 \cvdefC{IplImage* cvGetImage(const CvArr* arr, IplImage* imageHeader);}
1421 \cvdefPy{GetImage(arr) -> iplimage}
1424 \cvarg{arr}{Input array}
1426 \cvarg{imageHeader}{Pointer to \texttt{IplImage} structure used as a temporary buffer}
1430 The function returns the image header for the input array
1431 that can be a matrix - \cross{CvMat}, or an image - \texttt{IplImage*}. In
1432 the case of an image the function simply returns the input pointer. In the
1433 case of \cross{CvMat} it initializes an \texttt{imageHeader} structure
1434 with the parameters of the input matrix. Note that if we transform
1435 \texttt{IplImage} to \cross{CvMat} and then transform CvMat back to
1436 IplImage, we can get different headers if the ROI is set, and thus some
1437 IPL functions that calculate image stride from its width and align may
1438 fail on the resultant image.
1440 \cvCPyFunc{GetImageCOI}
1441 Returns the index of the channel of interest.
1443 \cvdefC{int cvGetImageCOI(const IplImage* image);}
1444 \cvdefPy{GetImageCOI(image)-> channel}
1447 \cvarg{image}{A pointer to the image header}
1450 Returns the channel of interest of in an IplImage. Returned values correspond to the \texttt{coi} in \cvCPyCross{SetImageCOI}.
1452 \cvCPyFunc{GetImageROI}
1453 Returns the image ROI.
1455 \cvdefC{CvRect cvGetImageROI(const IplImage* image);}
1456 \cvdefPy{GetImageROI(image)-> CvRect}
1459 \cvarg{image}{A pointer to the image header}
1462 If there is no ROI set, \texttt{cvRect(0,0,image->width,image->height)} is returned.
1465 Returns matrix header for arbitrary array.
1467 \cvdefC{CvMat* cvGetMat(const CvArr* arr, CvMat* header, int* coi=NULL, int allowND=0);}
1468 \cvdefPy{GetMat(arr) -> cvmat }
1471 \cvarg{arr}{Input array}
1473 \cvarg{header}{Pointer to \cross{CvMat} structure used as a temporary buffer}
1474 \cvarg{coi}{Optional output parameter for storing COI}
1475 \cvarg{allowND}{If non-zero, the function accepts multi-dimensional dense arrays (CvMatND*) and returns 2D (if CvMatND has two dimensions) or 1D matrix (when CvMatND has 1 dimension or more than 2 dimensions). The array must be continuous.}
1479 The function returns a matrix header for the input array that can be a matrix -
1481 \cross{CvMat}, an image - \texttt{IplImage} or a multi-dimensional dense array - \cross{CvMatND} (latter case is allowed only if \texttt{allowND != 0}) . In the case of matrix the function simply returns the input pointer. In the case of \texttt{IplImage*} or \cross{CvMatND} it initializes the \texttt{header} structure with parameters of the current image ROI and returns the pointer to this temporary structure. Because COI is not supported by \cross{CvMat}, it is returned separately.
1483 The function provides an easy way to handle both types of arrays - \texttt{IplImage} and \cross{CvMat} - using the same code. Reverse transform from \cross{CvMat} to \texttt{IplImage} can be done using the \cvCPyCross{GetImage} function.
1485 Input array must have underlying data allocated or attached, otherwise the function fails.
1487 If the input array is \texttt{IplImage} with planar data layout and COI set, the function returns the pointer to the selected plane and COI = 0. It enables per-plane processing of multi-channel images with planar data layout using OpenCV functions.
1490 \cvCPyFunc{GetNextSparseNode}
1491 Returns the next sparse matrix element
1493 \cvdefC{CvSparseNode* cvGetNextSparseNode(CvSparseMatIterator* matIterator);}
1496 \cvarg{matIterator}{Sparse array iterator}
1500 The function moves iterator to the next sparse matrix element and returns pointer to it. In the current version there is no any particular order of the elements, because they are stored in the hash table. The sample below demonstrates how to iterate through the sparse matrix:
1502 Using \cvCPyCross{InitSparseMatIterator} and \cvCPyCross{GetNextSparseNode} to calculate sum of floating-point sparse array.
1506 int i, dims = cvGetDims(array);
1507 CvSparseMatIterator mat_iterator;
1508 CvSparseNode* node = cvInitSparseMatIterator(array, &mat_iterator);
1510 for(; node != 0; node = cvGetNextSparseNode(&mat_iterator ))
1512 /* get pointer to the element indices */
1513 int* idx = CV_NODE_IDX(array, node);
1514 /* get value of the element (assume that the type is CV_32FC1) */
1515 float val = *(float*)CV_NODE_VAL(array, node);
1517 for(i = 0; i < dims; i++ )
1518 printf("%4d%s", idx[i], i < dims - 1 "," : "): ");
1519 printf("%g\n", val);
1524 printf("\nTotal sum = %g\n", sum);
1529 \cvCPyFunc{GetOptimalDFTSize}
1530 Returns optimal DFT size for a given vector size.
1532 \cvdefC{int cvGetOptimalDFTSize(int size0);}
1533 \cvdefPy{GetOptimalDFTSize(size0)-> int}
1536 \cvarg{size0}{Vector size}
1539 The function returns the minimum number
1540 \texttt{N} that is greater than or equal to \texttt{size0}, such that the DFT
1541 of a vector of size \texttt{N} can be computed fast. In the current
1542 implementation $N=2^p \times 3^q \times 5^r$, for some $p$, $q$, $r$.
1544 The function returns a negative number if \texttt{size0} is too large
1545 (very close to \texttt{INT\_MAX})
1549 \cvCPyFunc{GetRawData}
1550 Retrieves low-level information about the array.
1552 \cvdefC{void cvGetRawData(const CvArr* arr, uchar** data,
1553 int* step=NULL, CvSize* roiSize=NULL);}
1556 \cvarg{arr}{Array header}
1557 \cvarg{data}{Output pointer to the whole image origin or ROI origin if ROI is set}
1558 \cvarg{step}{Output full row length in bytes}
1559 \cvarg{roiSize}{Output ROI size}
1562 The function fills output variables with low-level information about the array data. All output parameters are optional, so some of the pointers may be set to \texttt{NULL}. If the array is \texttt{IplImage} with ROI set, the parameters of ROI are returned.
1564 The following example shows how to get access to array elements. GetRawData calculates the absolute value of the elements in a single-channel, floating-point array.
1573 cvGetRawData(array, (uchar**)&data, &step, &size);
1574 step /= sizeof(data[0]);
1576 for(y = 0; y < size.height; y++, data += step )
1577 for(x = 0; x < size.width; x++ )
1578 data[x] = (float)fabs(data[x]);
1582 \cvCPyFunc{GetReal?D}
1583 Return a specific element of single-channel array.
1586 double cvGetReal1D(const CvArr* arr, int idx0); \newline
1587 double cvGetReal2D(const CvArr* arr, int idx0, int idx1); \newline
1588 double cvGetReal3D(const CvArr* arr, int idx0, int idx1, int idx2); \newline
1589 double cvGetRealND(const CvArr* arr, int* idx);
1593 \cvarg{arr}{Input array. Must have a single channel.}
1594 \cvarg{idx0}{The first zero-based component of the element index}
1595 \cvarg{idx1}{The second zero-based component of the element index}
1596 \cvarg{idx2}{The third zero-based component of the element index}
1597 \cvarg{idx}{Array of the element indices}
1601 The functions \texttt{cvGetReal*D} return a specific element of a single-channel array. If the array has multiple channels, a runtime error is raised. Note that \cvCPyCross{Get} function can be used safely for both single-channel and multiple-channel arrays though they are a bit slower.
1603 In the case of a sparse array the functions return 0 if the requested node does not exist (no new node is created by the functions).
1608 \cvCPyFunc{GetRow(s)}
1609 Returns array row or row span.
1611 \cvdefC{CvMat* cvGetRow(const CvArr* arr, CvMat* submat, int row);}
1612 \cvdefPy{GetRow(arr,row)-> submat}
1613 \cvdefC{CvMat* cvGetRows(const CvArr* arr, CvMat* submat, int startRow, int endRow, int deltaRow=1);}
1614 \cvdefPy{GetRows(arr,startRow,endRow,deltaRow=1)-> submat}
1617 \cvarg{arr}{Input array}
1618 \cvarg{submat}{Pointer to the resulting sub-array header}
1619 \cvarg{row}{Zero-based index of the selected row}
1620 \cvarg{startRow}{Zero-based index of the starting row (inclusive) of the span}
1621 \cvarg{endRow}{Zero-based index of the ending row (exclusive) of the span}
1622 \cvarg{deltaRow}{Index step in the row span. That is, the function extracts every \texttt{deltaRow}-th row from \texttt{startRow} and up to (but not including) \texttt{endRow}.}
1625 The functions return the header, corresponding to a specified row/row span of the input array. Note that \texttt{GetRow} is a shortcut for \cvCPyCross{GetRows}:
1628 cvGetRow(arr, submat, row ) ~ cvGetRows(arr, submat, row, row + 1, 1);
1636 \cvdefPy{GetRow(arr,row)-> submat}
1639 \cvarg{arr}{Input array}
1640 \cvarg{row}{Zero-based index of the selected row}
1641 \cvarg{submat}{resulting single-row array}
1644 The function \texttt{GetRow} returns a single row from the input array.
1647 Returns array row span.
1649 \cvdefPy{GetRows(arr,startRow,endRow,deltaRow=1)-> submat}
1652 \cvarg{arr}{Input array}
1653 \cvarg{startRow}{Zero-based index of the starting row (inclusive) of the span}
1654 \cvarg{endRow}{Zero-based index of the ending row (exclusive) of the span}
1655 \cvarg{deltaRow}{Index step in the row span.}
1656 \cvarg{submat}{resulting multi-row array}
1659 The function \texttt{GetRows} returns a row span from the input array.
1664 Returns size of matrix or image ROI.
1666 \cvdefC{CvSize cvGetSize(const CvArr* arr);}
1667 \cvdefPy{GetSize(arr)-> CvSize}
1670 \cvarg{arr}{array header}
1673 The function returns number of rows (CvSize::height) and number of columns (CvSize::width) of the input matrix or image. In the case of image the size of ROI is returned.
1676 \cvCPyFunc{GetSubRect}
1677 Returns matrix header corresponding to the rectangular sub-array of input image or matrix.
1679 \cvdefC{CvMat* cvGetSubRect(const CvArr* arr, CvMat* submat, CvRect rect);}
1680 \cvdefPy{GetSubRect(arr, rect) -> cvmat}
1683 \cvarg{arr}{Input array}
1685 \cvarg{submat}{Pointer to the resultant sub-array header}
1687 \cvarg{rect}{Zero-based coordinates of the rectangle of interest}
1690 The function returns header, corresponding to
1691 a specified rectangle of the input array. In other words, it allows
1692 the user to treat a rectangular part of input array as a stand-alone
1693 array. ROI is taken into account by the function so the sub-array of
1694 ROI is actually extracted.
1697 Checks that array elements lie between the elements of two other arrays.
1699 \cvdefC{void cvInRange(const CvArr* src, const CvArr* lower, const CvArr* upper, CvArr* dst);}
1700 \cvdefPy{InRange(src,lower,upper,dst)-> None}
1703 \cvarg{src}{The first source array}
1704 \cvarg{lower}{The inclusive lower boundary array}
1705 \cvarg{upper}{The exclusive upper boundary array}
1706 \cvarg{dst}{The destination array, must have 8u or 8s type}
1710 The function does the range check for every element of the input array:
1713 \texttt{dst}(I)=\texttt{lower}(I)_0 <= \texttt{src}(I)_0 < \texttt{upper}(I)_0
1716 For single-channel arrays,
1720 \texttt{lower}(I)_0 <= \texttt{src}(I)_0 < \texttt{upper}(I)_0 \land
1721 \texttt{lower}(I)_1 <= \texttt{src}(I)_1 < \texttt{upper}(I)_1
1724 For two-channel arrays and so forth,
1726 dst(I) is set to 0xff (all \texttt{1}-bits) if src(I) is within the range and 0 otherwise. All the arrays must have the same type, except the destination, and the same size (or ROI size).
1729 \cvCPyFunc{InRangeS}
1730 Checks that array elements lie between two scalars.
1732 \cvdefC{void cvInRangeS(const CvArr* src, CvScalar lower, CvScalar upper, CvArr* dst);}
1733 \cvdefPy{InRangeS(src,lower,upper,dst)-> None}
1736 \cvarg{src}{The first source array}
1737 \cvarg{lower}{The inclusive lower boundary}
1738 \cvarg{upper}{The exclusive upper boundary}
1739 \cvarg{dst}{The destination array, must have 8u or 8s type}
1743 The function does the range check for every element of the input array:
1746 \texttt{dst}(I)=\texttt{lower}_0 <= \texttt{src}(I)_0 < \texttt{upper}_0
1749 For single-channel arrays,
1753 \texttt{lower}_0 <= \texttt{src}(I)_0 < \texttt{upper}_0 \land
1754 \texttt{lower}_1 <= \texttt{src}(I)_1 < \texttt{upper}_1
1757 For two-channel arrays nd so forth,
1759 'dst(I)' is set to 0xff (all \texttt{1}-bits) if 'src(I)' is within the range and 0 otherwise. All the arrays must have the same size (or ROI size).
1762 \cvCPyFunc{IncRefData}
1763 Increments array data reference counter.
1765 \cvdefC{int cvIncRefData(CvArr* arr);}
1768 \cvarg{arr}{Array header}
1771 The function increments \cross{CvMat} or
1772 \cross{CvMatND} data reference counter and returns the new counter value
1773 if the reference counter pointer is not NULL, otherwise it returns zero.
1775 \cvCPyFunc{InitImageHeader}
1776 Initializes an image header that was previously allocated.
1778 \cvdefC{IplImage* cvInitImageHeader(\par IplImage* image,\par CvSize size,\par int depth,\par int channels,\par int origin=0,\par int align=4);}
1781 \cvarg{image}{Image header to initialize}
1782 \cvarg{size}{Image width and height}
1783 \cvarg{depth}{Image depth (see \cvCPyCross{CreateImage})}
1784 \cvarg{channels}{Number of channels (see \cvCPyCross{CreateImage})}
1785 \cvarg{origin}{Top-left \texttt{IPL\_ORIGIN\_TL} or bottom-left \texttt{IPL\_ORIGIN\_BL}}
1786 \cvarg{align}{Alignment for image rows, typically 4 or 8 bytes}
1789 The returned \texttt{IplImage*} points to the initialized header.
1791 \cvCPyFunc{InitMatHeader}
1792 Initializes a pre-allocated matrix header.
1795 CvMat* cvInitMatHeader(\par CvMat* mat,\par int rows,\par int cols,\par int type, \par void* data=NULL,\par int step=CV\_AUTOSTEP);
1799 \cvarg{mat}{A pointer to the matrix header to be initialized}
1800 \cvarg{rows}{Number of rows in the matrix}
1801 \cvarg{cols}{Number of columns in the matrix}
1802 \cvarg{type}{Type of the matrix elements, see \cvCPyCross{CreateMat}.}
1803 \cvarg{data}{Optional: data pointer assigned to the matrix header}
1804 \cvarg{step}{Optional: full row width in bytes of the assigned data. By default, the minimal possible step is used which assumes there are no gaps between subsequent rows of the matrix.}
1807 This function is often used to process raw data with OpenCV matrix functions. For example, the following code computes the matrix product of two matrices, stored as ordinary arrays:
1810 double a[] = { 1, 2, 3, 4,
1814 double b[] = { 1, 5, 9,
1822 cvInitMatHeader(&Ma, 3, 4, CV_64FC1, a);
1823 cvInitMatHeader(&Mb, 4, 3, CV_64FC1, b);
1824 cvInitMatHeader(&Mc, 3, 3, CV_64FC1, c);
1826 cvMatMulAdd(&Ma, &Mb, 0, &Mc);
1827 // the c array now contains the product of a (3x4) and b (4x3)
1831 \cvCPyFunc{InitMatNDHeader}
1832 Initializes a pre-allocated multi-dimensional array header.
1834 \cvdefC{CvMatND* cvInitMatNDHeader(\par CvMatND* mat,\par int dims,\par const int* sizes,\par int type,\par void* data=NULL);}
1837 \cvarg{mat}{A pointer to the array header to be initialized}
1838 \cvarg{dims}{The number of array dimensions}
1839 \cvarg{sizes}{An array of dimension sizes}
1840 \cvarg{type}{Type of array elements, see \cvCPyCross{CreateMat}}
1841 \cvarg{data}{Optional data pointer assigned to the matrix header}
1844 \cvCPyFunc{InitSparseMatIterator}
1845 Initializes sparse array elements iterator.
1847 \cvdefC{CvSparseNode* cvInitSparseMatIterator(const CvSparseMat* mat,
1848 CvSparseMatIterator* matIterator);}
1851 \cvarg{mat}{Input array}
1852 \cvarg{matIterator}{Initialized iterator}
1855 The function initializes iterator of
1856 sparse array elements and returns pointer to the first element, or NULL
1857 if the array is empty.
1862 Calculates the inverse square root.
1864 \cvdefC{float cvInvSqrt(float value);}
1865 \cvdefPy{InvSqrt(value)-> float}
1868 \cvarg{value}{The input floating-point value}
1872 The function calculates the inverse square root of the argument, and normally it is faster than \texttt{1./sqrt(value)}. If the argument is zero or negative, the result is not determined. Special values ($\pm \infty $ , NaN) are not handled.
1876 Synonym for \cross{Invert}
1879 Finds the inverse or pseudo-inverse of a matrix.
1881 \cvdefC{double cvInvert(const CvArr* src, CvArr* dst, int method=CV\_LU);}
1882 \cvdefPy{Invert(src,dst,method=CV\_LU)-> double}
1885 \cvarg{src}{The source matrix}
1886 \cvarg{dst}{The destination matrix}
1887 \cvarg{method}{Inversion method
1889 \cvarg{CV\_LU}{Gaussian elimination with optimal pivot element chosen}
1890 \cvarg{CV\_SVD}{Singular value decomposition (SVD) method}
1891 \cvarg{CV\_SVD\_SYM}{SVD method for a symmetric positively-defined matrix}
1895 The function inverts matrix \texttt{src1} and stores the result in \texttt{src2}.
1897 In the case of \texttt{LU} method, the function returns the \texttt{src1} determinant (src1 must be square). If it is 0, the matrix is not inverted and \texttt{src2} is filled with zeros.
1899 In the case of \texttt{SVD} methods, the function returns the inversed condition of \texttt{src1} (ratio of the smallest singular value to the largest singular value) and 0 if \texttt{src1} is all zeros. The SVD methods calculate a pseudo-inverse matrix if \texttt{src1} is singular.
1903 Determines if the argument is Infinity.
1905 \cvdefC{int cvIsInf(double value);}
1906 \cvdefPy{IsInf(value)-> int}
1909 \cvarg{value}{The input floating-point value}
1912 The function returns 1 if the argument is $\pm \infty $ (as defined by IEEE754 standard), 0 otherwise.
1915 Determines if the argument is Not A Number.
1917 \cvdefC{int cvIsNaN(double value);}
1918 \cvdefPy{IsNaN(value)-> int}
1921 \cvarg{value}{The input floating-point value}
1924 The function returns 1 if the argument is Not A Number (as defined by IEEE754 standard), 0 otherwise.
1928 Performs a look-up table transform of an array.
1930 \cvdefC{void cvLUT(const CvArr* src, CvArr* dst, const CvArr* lut);}
1931 \cvdefPy{LUT(src,dst,lut)-> None}
1934 \cvarg{src}{Source array of 8-bit elements}
1935 \cvarg{dst}{Destination array of a given depth and of the same number of channels as the source array}
1936 \cvarg{lut}{Look-up table of 256 elements; should have the same depth as the destination array. In the case of multi-channel source and destination arrays, the table should either have a single-channel (in this case the same table is used for all channels) or the same number of channels as the source/destination array.}
1939 The function fills the destination array with values from the look-up table. Indices of the entries are taken from the source array. That is, the function processes each element of \texttt{src} as follows:
1942 \texttt{dst}_i \leftarrow \texttt{lut}_{\texttt{src}_i + d}
1949 {0}{if \texttt{src} has depth \texttt{CV\_8U}}
1950 {128}{if \texttt{src} has depth \texttt{CV\_8S}}
1954 Calculates the natural logarithm of every array element's absolute value.
1956 \cvdefC{void cvLog(const CvArr* src, CvArr* dst);}
1957 \cvdefPy{Log(src,dst)-> None}
1960 \cvarg{src}{The source array}
1961 \cvarg{dst}{The destination array, it should have \texttt{double} type or the same type as the source}
1964 The function calculates the natural logarithm of the absolute value of every element of the input array:
1967 \texttt{dst} [I] = \fork
1968 {\log{|\texttt{src}(I)}}{if $\texttt{src}[I] \ne 0$ }
1969 {\texttt{C}}{otherwise}
1972 Where \texttt{C} is a large negative number (about -700 in the current implementation).
1974 \cvCPyFunc{Mahalonobis}
1975 Calculates the Mahalonobis distance between two vectors.
1977 \cvdefC{double cvMahalanobis(\par const CvArr* vec1,\par const CvArr* vec2,\par CvArr* mat);}
1978 \cvdefPy{Mahalonobis(vec1,vec2,mat)-> None}
1981 \cvarg{vec1}{The first 1D source vector}
1982 \cvarg{vec2}{The second 1D source vector}
1983 \cvarg{mat}{The inverse covariance matrix}
1987 The function calculates and returns the weighted distance between two vectors:
1990 d(\texttt{vec1},\texttt{vec2})=\sqrt{\sum_{i,j}{\texttt{icovar(i,j)}\cdot(\texttt{vec1}(I)-\texttt{vec2}(I))\cdot(\texttt{vec1(j)}-\texttt{vec2(j)})}}
1993 The covariance matrix may be calculated using the \cvCPyCross{CalcCovarMatrix} function and further inverted using the \cvCPyCross{Invert} function (CV\_SVD method is the prefered one because the matrix might be singular).
1998 Initializes matrix header (lightweight variant).
2000 \cvdefC{CvMat cvMat(\par int rows,\par int cols,\par int type,\par void* data=NULL);}
2003 \cvarg{rows}{Number of rows in the matrix}
2004 \cvarg{cols}{Number of columns in the matrix}
2005 \cvarg{type}{Type of the matrix elements - see \cvCPyCross{CreateMat}}
2006 \cvarg{data}{Optional data pointer assigned to the matrix header}
2009 Initializes a matrix header and assigns data to it. The matrix is filled \textit{row}-wise (the first \texttt{cols} elements of data form the first row of the matrix, etc.)
2011 This function is a fast inline substitution for \cvCPyCross{InitMatHeader}. Namely, it is equivalent to:
2015 cvInitMatHeader(&mat, rows, cols, type, data, CV\_AUTOSTEP);
2020 Finds per-element maximum of two arrays.
2022 \cvdefC{void cvMax(const CvArr* src1, const CvArr* src2, CvArr* dst);}
2023 \cvdefPy{Max(src1,src2,dst)-> None}
2026 \cvarg{src1}{The first source array}
2027 \cvarg{src2}{The second source array}
2028 \cvarg{dst}{The destination array}
2031 The function calculates per-element maximum of two arrays:
2034 \texttt{dst}(I)=\max(\texttt{src1}(I), \texttt{src2}(I))
2037 All the arrays must have a single channel, the same data type and the same size (or ROI size).
2041 Finds per-element maximum of array and scalar.
2043 \cvdefC{void cvMaxS(const CvArr* src, double value, CvArr* dst);}
2044 \cvdefPy{MaxS(src,value,dst)-> None}
2047 \cvarg{src}{The first source array}
2048 \cvarg{value}{The scalar value}
2049 \cvarg{dst}{The destination array}
2052 The function calculates per-element maximum of array and scalar:
2055 \texttt{dst}(I)=\max(\texttt{src}(I), \texttt{value})
2058 All the arrays must have a single channel, the same data type and the same size (or ROI size).
2062 Composes a multi-channel array from several single-channel arrays or inserts a single channel into the array.
2064 \cvdefC{void cvMerge(const CvArr* src0, const CvArr* src1,
2065 const CvArr* src2, const CvArr* src3, CvArr* dst);}
2068 #define cvCvtPlaneToPix cvMerge
2071 \cvdefPy{Merge(src0,src1,src2,src3,dst)-> None}
2074 \cvarg{src0}{Input channel 0}
2075 \cvarg{src1}{Input channel 1}
2076 \cvarg{src2}{Input channel 2}
2077 \cvarg{src3}{Input channel 3}
2078 \cvarg{dst}{Destination array}
2081 The function is the opposite to \cvCPyCross{Split}. If the destination array has N channels then if the first N input channels are not NULL, they all are copied to the destination array; if only a single source channel of the first N is not NULL, this particular channel is copied into the destination array; otherwise an error is raised. The rest of the source channels (beyond the first N) must always be NULL. For IplImage \cvCPyCross{Copy} with COI set can be also used to insert a single channel into the image.
2084 Finds per-element minimum of two arrays.
2086 \cvdefC{void cvMin(const CvArr* src1, const CvArr* src2, CvArr* dst);}
2087 \cvdefPy{Min(src1,src2,dst)-> None}
2090 \cvarg{src1}{The first source array}
2091 \cvarg{src2}{The second source array}
2092 \cvarg{dst}{The destination array}
2096 The function calculates per-element minimum of two arrays:
2099 \texttt{dst}(I)=\min(\texttt{src1}(I),\texttt{src2}(I))
2102 All the arrays must have a single channel, the same data type and the same size (or ROI size).
2105 \cvCPyFunc{MinMaxLoc}
2106 Finds global minimum and maximum in array or subarray.
2108 \cvdefC{void cvMinMaxLoc(const CvArr* arr, double* minVal, double* maxVal,
2109 CvPoint* minLoc=NULL, CvPoint* maxLoc=NULL, const CvArr* mask=NULL);}
2110 \cvdefPy{MinMaxLoc(arr,mask=NULL)-> (minVal,maxVal,minLoc,maxLoc)}
2113 \cvarg{arr}{The source array, single-channel or multi-channel with COI set}
2114 \cvarg{minVal}{Pointer to returned minimum value}
2115 \cvarg{maxVal}{Pointer to returned maximum value}
2116 \cvarg{minLoc}{Pointer to returned minimum location}
2117 \cvarg{maxLoc}{Pointer to returned maximum location}
2118 \cvarg{mask}{The optional mask used to select a subarray}
2121 The function finds minimum and maximum element values
2122 and their positions. The extremums are searched across the whole array,
2123 selected \texttt{ROI} (in the case of \texttt{IplImage}) or, if \texttt{mask}
2124 is not \texttt{NULL}, in the specified array region. If the array has
2125 more than one channel, it must be \texttt{IplImage} with \texttt{COI}
2126 set. In the case of multi-dimensional arrays, \texttt{minLoc->x} and \texttt{maxLoc->x}
2127 will contain raw (linear) positions of the extremums.
2130 Finds per-element minimum of an array and a scalar.
2132 \cvdefC{void cvMinS(const CvArr* src, double value, CvArr* dst);}
2133 \cvdefPy{MinS(src,value,dst)-> None}
2136 \cvarg{src}{The first source array}
2137 \cvarg{value}{The scalar value}
2138 \cvarg{dst}{The destination array}
2141 The function calculates minimum of an array and a scalar:
2144 \texttt{dst}(I)=\min(\texttt{src}(I), \texttt{value})
2147 All the arrays must have a single channel, the same data type and the same size (or ROI size).
2151 Synonym for \cross{Flip}.
2153 \cvCPyFunc{MixChannels}
2154 Copies several channels from input arrays to certain channels of output arrays
2156 \cvdefC{void cvMixChannels(const CvArr** src, int srcCount, \par
2157 CvArr** dst, int dstCount, \par
2158 const int* fromTo, int pairCount);}
2159 \cvdefPy{MixChannels(src, dst, fromTo) -> None}
2162 \cvarg{src}{Input arrays}
2163 \cvC{\cvarg{srcCount}{The number of input arrays.}}
2164 \cvarg{dst}{Destination arrays}
2165 \cvC{\cvarg{dstCount}{The number of output arrays.}}
2166 \cvarg{fromTo}{The array of pairs of indices of the planes
2167 copied. \cvC{\texttt{fromTo[k*2]} is the 0-based index of the input channel in \texttt{src} and
2168 \texttt{fromTo[k*2+1]} is the index of the output channel in \texttt{dst}.
2169 Here the continuous channel numbering is used, that is, the first input image channels are indexed
2170 from \texttt{0} to \texttt{channels(src[0])-1}, the second input image channels are indexed from
2171 \texttt{channels(src[0])} to \texttt{channels(src[0]) + channels(src[1])-1} etc., and the same
2172 scheme is used for the output image channels.
2173 As a special case, when \texttt{fromTo[k*2]} is negative,
2174 the corresponding output channel is filled with zero.}\cvPy{Each pair \texttt{fromTo[k]=(i,j)}
2175 means that i-th plane from \texttt{src} is copied to the j-th plane in \texttt{dst}, where continuous
2176 plane numbering is used both in the input array list and the output array list.
2177 As a special case, when the \texttt{fromTo[k][0]} is negative, the corresponding output plane \texttt{j}
2178 is filled with zero.}}
2181 The function is a generalized form of \cvCPyCross{cvSplit} and \cvCPyCross{Merge}
2182 and some forms of \cross{CvtColor}. It can be used to change the order of the
2183 planes, add/remove alpha channel, extract or insert a single plane or
2184 multiple planes etc.
2186 As an example, this code splits a 4-channel RGBA image into a 3-channel
2187 BGR (i.e. with R and B swapped) and separate alpha channel image:
2191 rgba = cv.CreateMat(100, 100, cv.CV_8UC4)
2192 bgr = cv.CreateMat(100, 100, cv.CV_8UC3)
2193 alpha = cv.CreateMat(100, 100, cv.CV_8UC1)
2194 cv.Set(rgba, (1,2,3,4))
2195 cv.MixChannels([rgba], [bgr, alpha], [
2196 (0, 2), # rgba[0] -> bgr[2]
2197 (1, 1), # rgba[1] -> bgr[1]
2198 (2, 0), # rgba[2] -> bgr[0]
2199 (3, 3) # rgba[3] -> alpha[0]
2206 CvMat* rgba = cvCreateMat(100, 100, CV_8UC4);
2207 CvMat* bgr = cvCreateMat(rgba->rows, rgba->cols, CV_8UC3);
2208 CvMat* alpha = cvCreateMat(rgba->rows, rgba->cols, CV_8UC1);
2209 cvSet(rgba, cvScalar(1,2,3,4));
2211 CvArr* out[] = { bgr, alpha };
2212 int from_to[] = { 0,2, 1,1, 2,0, 3,3 };
2213 cvMixChannels(&bgra, 1, out, 2, from_to, 4);
2217 \subsection{MulAddS}
2219 Synonym for \cross{ScaleAdd}.
2222 Calculates the per-element product of two arrays.
2224 \cvdefC{void cvMul(const CvArr* src1, const CvArr* src2, CvArr* dst, double scale=1);}
2225 \cvdefPy{Mul(src1,src2,dst,scale)-> None}
2228 \cvarg{src1}{The first source array}
2229 \cvarg{src2}{The second source array}
2230 \cvarg{dst}{The destination array}
2231 \cvarg{scale}{Optional scale factor}
2235 The function calculates the per-element product of two arrays:
2238 \texttt{dst}(I)=\texttt{scale} \cdot \texttt{src1}(I) \cdot \texttt{src2}(I)
2241 All the arrays must have the same type and the same size (or ROI size).
2242 For types that have limited range this operation is saturating.
2244 \cvCPyFunc{MulSpectrums}
2245 Performs per-element multiplication of two Fourier spectrums.
2247 \cvdefC{void cvMulSpectrums(\par const CvArr* src1,\par const CvArr* src2,\par CvArr* dst,\par int flags);}
2248 \cvdefPy{MulSpectrums(src1,src2,dst,flags)-> None}
2251 \cvarg{src1}{The first source array}
2252 \cvarg{src2}{The second source array}
2253 \cvarg{dst}{The destination array of the same type and the same size as the source arrays}
2254 \cvarg{flags}{A combination of the following values;
2256 \cvarg{CV\_DXT\_ROWS}{treats each row of the arrays as a separate spectrum (see \cvCPyCross{DFT} parameters description).}
2257 \cvarg{CV\_DXT\_MUL\_CONJ}{conjugate the second source array before the multiplication.}
2262 The function performs per-element multiplication of the two CCS-packed or complex matrices that are results of a real or complex Fourier transform.
2264 The function, together with \cvCPyCross{DFT}, may be used to calculate convolution of two arrays rapidly.
2267 \cvCPyFunc{MulTransposed}
2268 Calculates the product of an array and a transposed array.
2270 \cvdefC{void cvMulTransposed(const CvArr* src, CvArr* dst, int order, const CvArr* delta=NULL, double scale=1.0);}
2271 \cvdefPy{MulTransposed(src,dst,order,delta=NULL,scale)-> None}
2274 \cvarg{src}{The source matrix}
2275 \cvarg{dst}{The destination matrix. Must be \texttt{CV\_32F} or \texttt{CV\_64F}.}
2276 \cvarg{order}{Order of multipliers}
2277 \cvarg{delta}{An optional array, subtracted from \texttt{src} before multiplication}
2278 \cvarg{scale}{An optional scaling}
2281 The function calculates the product of src and its transposition:
2284 \texttt{dst}=\texttt{scale} (\texttt{src}-\texttt{delta}) (\texttt{src}-\texttt{delta})^T
2287 if $\texttt{order}=0$, and
2290 \texttt{dst}=\texttt{scale} (\texttt{src}-\texttt{delta})^T (\texttt{src}-\texttt{delta})
2296 Calculates absolute array norm, absolute difference norm, or relative difference norm.
2298 \cvdefC{double cvNorm(const CvArr* arr1, const CvArr* arr2=NULL, int normType=CV\_L2, const CvArr* mask=NULL);}
2299 \cvdefPy{Norm(arr1,arr2,normType=CV\_L2,mask=NULL)-> double}
2302 \cvarg{arr1}{The first source image}
2303 \cvarg{arr2}{The second source image. If it is NULL, the absolute norm of \texttt{arr1} is calculated, otherwise the absolute or relative norm of \texttt{arr1}-\texttt{arr2} is calculated.}
2304 \cvarg{normType}{Type of norm, see the discussion}
2305 \cvarg{mask}{The optional operation mask}
2308 The function calculates the absolute norm of \texttt{arr1} if \texttt{arr2} is NULL:
2311 {||\texttt{arr1}||_C = \max_I |\texttt{arr1}(I)|}{if $\texttt{normType} = \texttt{CV\_C}$}
2312 {||\texttt{arr1}||_{L1} = \sum_I |\texttt{arr1}(I)|}{if $\texttt{normType} = \texttt{CV\_L1}$}
2313 {||\texttt{arr1}||_{L2} = \sqrt{\sum_I \texttt{arr1}(I)^2}}{if $\texttt{normType} = \texttt{CV\_L2}$}
2316 or the absolute difference norm if \texttt{arr2} is not NULL:
2319 {||\texttt{arr1}-\texttt{arr2}||_C = \max_I |\texttt{arr1}(I) - \texttt{arr2}(I)|}{if $\texttt{normType} = \texttt{CV\_C}$}
2320 {||\texttt{arr1}-\texttt{arr2}||_{L1} = \sum_I |\texttt{arr1}(I) - \texttt{arr2}(I)|}{if $\texttt{normType} = \texttt{CV\_L1}$}
2321 {||\texttt{arr1}-\texttt{arr2}||_{L2} = \sqrt{\sum_I (\texttt{arr1}(I) - \texttt{arr2}(I))^2}}{if $\texttt{normType} = \texttt{CV\_L2}$}
2324 or the relative difference norm if \texttt{arr2} is not NULL and \texttt{(normType \& CV\_RELATIVE) != 0}:
2328 {\frac{||\texttt{arr1}-\texttt{arr2}||_C }{||\texttt{arr2}||_C }}{if $\texttt{normType} = \texttt{CV\_RELATIVE\_C}$}
2329 {\frac{||\texttt{arr1}-\texttt{arr2}||_{L1} }{||\texttt{arr2}||_{L1}}}{if $\texttt{normType} = \texttt{CV\_RELATIVE\_L1}$}
2330 {\frac{||\texttt{arr1}-\texttt{arr2}||_{L2} }{||\texttt{arr2}||_{L2}}}{if $\texttt{normType} = \texttt{CV\_RELATIVE\_L2}$}
2333 The function returns the calculated norm. A multiple-channel array is treated as a single-channel, that is, the results for all channels are combined.
2336 Performs per-element bit-wise inversion of array elements.
2338 \cvdefC{void cvNot(const CvArr* src, CvArr* dst);}
2339 \cvdefPy{Not(src,dst)-> None}
2342 \cvarg{src}{The source array}
2343 \cvarg{dst}{The destination array}
2347 The function Not inverses every bit of every array element:
2355 Calculates per-element bit-wise disjunction of two arrays.
2357 \cvdefC{void cvOr(const CvArr* src1, const CvArr* src2, CvArr* dst, const CvArr* mask=NULL);}
2358 \cvdefPy{Or(src1,src2,dst,mask=NULL)-> None}
2361 \cvarg{src1}{The first source array}
2362 \cvarg{src2}{The second source array}
2363 \cvarg{dst}{The destination array}
2364 \cvarg{mask}{Operation mask, 8-bit single channel array; specifies elements of the destination array to be changed}
2368 The function calculates per-element bit-wise disjunction of two arrays:
2371 dst(I)=src1(I)|src2(I)
2374 In the case of floating-point arrays their bit representations are used for the operation. All the arrays must have the same type, except the mask, and the same size.
2377 Calculates a per-element bit-wise disjunction of an array and a scalar.
2379 \cvdefC{void cvOrS(const CvArr* src, CvScalar value, CvArr* dst, const CvArr* mask=NULL);}
2380 \cvdefPy{OrS(src,value,dst,mask=NULL)-> None}
2383 \cvarg{src}{The source array}
2384 \cvarg{value}{Scalar to use in the operation}
2385 \cvarg{dst}{The destination array}
2386 \cvarg{mask}{Operation mask, 8-bit single channel array; specifies elements of the destination array to be changed}
2390 The function OrS calculates per-element bit-wise disjunction of an array and a scalar:
2393 dst(I)=src(I)|value if mask(I)!=0
2396 Prior to the actual operation, the scalar is converted to the same type as that of the array(s). In the case of floating-point arrays their bit representations are used for the operation. All the arrays must have the same type, except the mask, and the same size.
2399 \cvCPyFunc{PerspectiveTransform}
2400 Performs perspective matrix transformation of a vector array.
2402 \cvdefC{void cvPerspectiveTransform(const CvArr* src, CvArr* dst, const CvMat* mat);}
2403 \cvdefPy{PerspectiveTransform(src,dst,mat)-> None}
2406 \cvarg{src}{The source three-channel floating-point array}
2407 \cvarg{dst}{The destination three-channel floating-point array}
2408 \cvarg{mat}{$3\times 3$ or $4 \times 4$ transformation matrix}
2412 The function transforms every element of \texttt{src} (by treating it as 2D or 3D vector) in the following way:
2414 \[ (x, y, z) \rightarrow (x'/w, y'/w, z'/w) \]
2419 (x', y', z', w') = \texttt{mat} \cdot
2420 \begin{bmatrix} x & y & z & 1 \end{bmatrix}
2424 \[ w = \fork{w'}{if $w' \ne 0$}{\infty}{otherwise} \]
2426 \cvCPyFunc{PolarToCart}
2427 Calculates Cartesian coordinates of 2d vectors represented in polar form.
2429 \cvdefC{void cvPolarToCart(\par const CvArr* magnitude,\par const CvArr* angle,\par CvArr* x,\par CvArr* y,\par int angleInDegrees=0);}
2430 \cvdefPy{PolarToCart(magnitude,angle,x,y,angleInDegrees=0)-> None}
2433 \cvarg{magnitude}{The array of magnitudes. If it is NULL, the magnitudes are assumed to be all 1's.}
2434 \cvarg{angle}{The array of angles, whether in radians or degrees}
2435 \cvarg{x}{The destination array of x-coordinates, may be set to NULL if it is not needed}
2436 \cvarg{y}{The destination array of y-coordinates, mau be set to NULL if it is not needed}
2437 \cvarg{angleInDegrees}{The flag indicating whether the angles are measured in radians, which is default mode, or in degrees}
2440 The function calculates either the x-coodinate, y-coordinate or both of every vector \texttt{magnitude(I)*exp(angle(I)*j), j=sqrt(-1)}:
2443 x(I)=magnitude(I)*cos(angle(I)),
2444 y(I)=magnitude(I)*sin(angle(I))
2449 Raises every array element to a power.
2451 \cvdefC{void cvPow(\par const CvArr* src,\par CvArr* dst,\par double power);}
2452 \cvdefPy{Pow(src,dst,power)-> None}
2455 \cvarg{src}{The source array}
2456 \cvarg{dst}{The destination array, should be the same type as the source}
2457 \cvarg{power}{The exponent of power}
2461 The function raises every element of the input array to \texttt{p}:
2464 \texttt{dst} [I] = \fork
2465 {\texttt{src}(I)^p}{if \texttt{p} is integer}
2466 {|\texttt{src}(I)^p|}{otherwise}
2469 That is, for a non-integer power exponent the absolute values of input array elements are used. However, it is possible to get true values for negative values using some extra operations, as the following example, computing the cube root of array elements, shows:
2473 CvSize size = cvGetSize(src);
2474 CvMat* mask = cvCreateMat(size.height, size.width, CV_8UC1);
2475 cvCmpS(src, 0, mask, CV_CMP_LT); /* find negative elements */
2476 cvPow(src, dst, 1./3);
2477 cvSubRS(dst, cvScalarAll(0), dst, mask); /* negate the results of negative inputs */
2478 cvReleaseMat(&mask);
2483 >>> src = cv.CreateMat(1, 10, cv.CV_32FC1)
2484 >>> mask = cv.CreateMat(src.rows, src.cols, cv.CV_8UC1)
2485 >>> dst = cv.CreateMat(src.rows, src.cols, cv.CV_32FC1)
2486 >>> cv.CmpS(src, 0, mask, cv.CV_CMP_LT) # find negative elements
2487 >>> cv.Pow(src, dst, 1. / 3)
2488 >>> cv.SubRS(dst, cv.ScalarAll(0), dst, mask) # negate the results of negative inputs
2492 For some values of \texttt{power}, such as integer values, 0.5, and -0.5, specialized faster algorithms are used.
2496 Return pointer to a particular array element.
2499 uchar* cvPtr1D(const CvArr* arr, int idx0, int* type=NULL); \newline
2500 uchar* cvPtr2D(const CvArr* arr, int idx0, int idx1, int* type=NULL); \newline
2501 uchar* cvPtr3D(const CvArr* arr, int idx0, int idx1, int idx2, int* type=NULL); \newline
2502 uchar* cvPtrND(const CvArr* arr, int* idx, int* type=NULL, int createNode=1, unsigned* precalcHashval=NULL);
2506 \cvarg{arr}{Input array}
2507 \cvarg{idx0}{The first zero-based component of the element index}
2508 \cvarg{idx1}{The second zero-based component of the element index}
2509 \cvarg{idx2}{The third zero-based component of the element index}
2510 \cvarg{idx}{Array of the element indices}
2511 \cvarg{type}{Optional output parameter: type of matrix elements}
2512 \cvarg{createNode}{Optional input parameter for sparse matrices. Non-zero value of the parameter means that the requested element is created if it does not exist already.}
2513 \cvarg{precalcHashval}{Optional input parameter for sparse matrices. If the pointer is not NULL, the function does not recalculate the node hash value, but takes it from the specified location. It is useful for speeding up pair-wise operations (TODO: provide an example)}
2516 The functions return a pointer to a specific array element. Number of array dimension should match to the number of indices passed to the function except for \texttt{cvPtr1D} function that can be used for sequential access to 1D, 2D or nD dense arrays.
2518 The functions can be used for sparse arrays as well - if the requested node does not exist they create it and set it to zero.
2520 All these as well as other functions accessing array elements (\cvCPyCross{Get}, \cvCPyCross{GetReal},
2521 \cvCPyCross{Set}, \cvCPyCross{SetReal}) raise an error in case if the element index is out of range.
2526 Initializes a random number generator state.
2528 \cvdefC{CvRNG cvRNG(int64 seed=-1);}
2529 \cvdefPy{RNG(seed=-1LL)-> CvRNG}
2532 \cvarg{seed}{64-bit value used to initiate a random sequence}
2535 The function initializes a random number generator
2536 and returns the state. The pointer to the state can be then passed to the
2537 \cvCPyCross{RandInt}, \cvCPyCross{RandReal} and \cvCPyCross{RandArr} functions. In the
2538 current implementation a multiply-with-carry generator is used.
2541 Fills an array with random numbers and updates the RNG state.
2543 \cvdefC{void cvRandArr(\par CvRNG* rng,\par CvArr* arr,\par int distType,\par CvScalar param1,\par CvScalar param2);}
2544 \cvdefPy{RandArr(rng,arr,distType,param1,param2)-> None}
2547 \cvarg{rng}{RNG state initialized by \cvCPyCross{RNG}}
2548 \cvarg{arr}{The destination array}
2549 \cvarg{distType}{Distribution type
2551 \cvarg{CV\_RAND\_UNI}{uniform distribution}
2552 \cvarg{CV\_RAND\_NORMAL}{normal or Gaussian distribution}
2554 \cvarg{param1}{The first parameter of the distribution. In the case of a uniform distribution it is the inclusive lower boundary of the random numbers range. In the case of a normal distribution it is the mean value of the random numbers.}
2555 \cvarg{param2}{The second parameter of the distribution. In the case of a uniform distribution it is the exclusive upper boundary of the random numbers range. In the case of a normal distribution it is the standard deviation of the random numbers.}
2558 The function fills the destination array with uniformly
2559 or normally distributed random numbers.
2562 In the example below, the function
2563 is used to add a few normally distributed floating-point numbers to
2564 random locations within a 2d array.
2567 /* let noisy_screen be the floating-point 2d array that is to be "crapped" */
2568 CvRNG rng_state = cvRNG(0xffffffff);
2569 int i, pointCount = 1000;
2570 /* allocate the array of coordinates of points */
2571 CvMat* locations = cvCreateMat(pointCount, 1, CV_32SC2);
2572 /* arr of random point values */
2573 CvMat* values = cvCreateMat(pointCount, 1, CV_32FC1);
2574 CvSize size = cvGetSize(noisy_screen);
2576 /* initialize the locations */
2577 cvRandArr(&rng_state, locations, CV_RAND_UNI, cvScalar(0,0,0,0),
2578 cvScalar(size.width,size.height,0,0));
2580 /* generate values */
2581 cvRandArr(&rng_state, values, CV_RAND_NORMAL,
2582 cvRealScalar(100), // average intensity
2583 cvRealScalar(30) // deviation of the intensity
2586 /* set the points */
2587 for(i = 0; i < pointCount; i++ )
2589 CvPoint pt = *(CvPoint*)cvPtr1D(locations, i, 0);
2590 float value = *(float*)cvPtr1D(values, i, 0);
2591 *((float*)cvPtr2D(noisy_screen, pt.y, pt.x, 0 )) += value;
2594 /* not to forget to release the temporary arrays */
2595 cvReleaseMat(&locations);
2596 cvReleaseMat(&values);
2598 /* RNG state does not need to be deallocated */
2603 Returns a 32-bit unsigned integer and updates RNG.
2605 \cvdefC{unsigned cvRandInt(CvRNG* rng);}
2606 \cvdefPy{RandInt(rng)-> unsigned}
2609 \cvarg{rng}{RNG state initialized by \texttt{RandInit} and, optionally, customized by \texttt{RandSetRange} (though, the latter function does not affect the discussed function outcome)}
2612 The function returns a uniformly-distributed random
2613 32-bit unsigned integer and updates the RNG state. It is similar to the rand()
2614 function from the C runtime library, but it always generates a 32-bit number
2615 whereas rand() returns a number in between 0 and \texttt{RAND\_MAX}
2616 which is $2^{16}$ or $2^{32}$, depending on the platform.
2618 The function is useful for generating scalar random numbers, such as
2619 points, patch sizes, table indices, etc., where integer numbers of a certain
2620 range can be generated using a modulo operation and floating-point numbers
2621 can be generated by scaling from 0 to 1 or any other specific range.
2624 Here is the example from the previous function discussion rewritten using
2625 \cvCPyCross{RandInt}:
2628 /* the input and the task is the same as in the previous sample. */
2629 CvRNG rnggstate = cvRNG(0xffffffff);
2630 int i, pointCount = 1000;
2631 /* ... - no arrays are allocated here */
2632 CvSize size = cvGetSize(noisygscreen);
2633 /* make a buffer for normally distributed numbers to reduce call overhead */
2634 #define bufferSize 16
2635 float normalValueBuffer[bufferSize];
2636 CvMat normalValueMat = cvMat(bufferSize, 1, CVg32F, normalValueBuffer);
2639 for(i = 0; i < pointCount; i++ )
2642 /* generate random point */
2643 pt.x = cvRandInt(&rnggstate ) % size.width;
2644 pt.y = cvRandInt(&rnggstate ) % size.height;
2646 if(valuesLeft <= 0 )
2648 /* fulfill the buffer with normally distributed numbers
2649 if the buffer is empty */
2650 cvRandArr(&rnggstate, &normalValueMat, CV\_RAND\_NORMAL,
2651 cvRealScalar(100), cvRealScalar(30));
2652 valuesLeft = bufferSize;
2654 *((float*)cvPtr2D(noisygscreen, pt.y, pt.x, 0 ) =
2655 normalValueBuffer[--valuesLeft];
2658 /* there is no need to deallocate normalValueMat because we have
2659 both the matrix header and the data on stack. It is a common and efficient
2660 practice of working with small, fixed-size matrices */
2664 \cvCPyFunc{RandReal}
2665 Returns a floating-point random number and updates RNG.
2667 \cvdefC{double cvRandReal(CvRNG* rng);}
2668 \cvdefPy{RandReal(rng)-> double}
2671 \cvarg{rng}{RNG state initialized by \cvCPyCross{RNG}}
2675 The function returns a uniformly-distributed random floating-point number between 0 and 1 (1 is not included).
2678 Reduces a matrix to a vector.
2680 \cvdefC{void cvReduce(const CvArr* src, CvArr* dst, int dim = -1, int op=CV\_REDUCE\_SUM);}
2681 \cvdefPy{Reduce(src,dst,dim=-1,op=CV\_REDUCE\_SUM)-> None}
2684 \cvarg{src}{The input matrix.}
2685 \cvarg{dst}{The output single-row/single-column vector that accumulates somehow all the matrix rows/columns.}
2686 \cvarg{dim}{The dimension index along which the matrix is reduced. 0 means that the matrix is reduced to a single row, 1 means that the matrix is reduced to a single column and -1 means that the dimension is chosen automatically by analysing the dst size.}
2687 \cvarg{op}{The reduction operation. It can take of the following values:
2689 \cvarg{CV\_REDUCE\_SUM}{The output is the sum of all of the matrix's rows/columns.}
2690 \cvarg{CV\_REDUCE\_AVG}{The output is the mean vector of all of the matrix's rows/columns.}
2691 \cvarg{CV\_REDUCE\_MAX}{The output is the maximum (column/row-wise) of all of the matrix's rows/columns.}
2692 \cvarg{CV\_REDUCE\_MIN}{The output is the minimum (column/row-wise) of all of the matrix's rows/columns.}
2696 The function reduces matrix to a vector by treating the matrix rows/columns as a set of 1D vectors and performing the specified operation on the vectors until a single row/column is obtained. For example, the function can be used to compute horizontal and vertical projections of an raster image. In the case of \texttt{CV\_REDUCE\_SUM} and \texttt{CV\_REDUCE\_AVG} the output may have a larger element bit-depth to preserve accuracy. And multi-channel arrays are also supported in these two reduction modes.
2699 \cvCPyFunc{ReleaseData}
2700 Releases array data.
2702 \cvdefC{void cvReleaseData(CvArr* arr);}
2705 \cvarg{arr}{Array header}
2708 The function releases the array data. In the case of \cross{CvMat} or \cross{CvMatND} it simply calls cvDecRefData(), that is the function can not deallocate external data. See also the note to \cvCPyCross{CreateData}.
2710 \cvCPyFunc{ReleaseImage}
2711 Deallocates the image header and the image data.
2713 \cvdefC{void cvReleaseImage(IplImage** image);}
2716 \cvarg{image}{Double pointer to the image header}
2719 This call is a shortened form of
2724 cvReleaseData(*image);
2725 cvReleaseImageHeader(image);
2730 \cvCPyFunc{ReleaseImageHeader}
2731 Deallocates an image header.
2733 \cvdefC{void cvReleaseImageHeader(IplImage** image);}
2736 \cvarg{image}{Double pointer to the image header}
2739 This call is an analogue of
2743 iplDeallocate(*image, IPL_IMAGE_HEADER | IPL_IMAGE_ROI);
2747 but it does not use IPL functions by default (see the \texttt{CV\_TURN\_ON\_IPL\_COMPATIBILITY} macro).
2750 \cvCPyFunc{ReleaseMat}
2751 Deallocates a matrix.
2753 \cvdefC{void cvReleaseMat(CvMat** mat);}
2756 \cvarg{mat}{Double pointer to the matrix}
2760 The function decrements the matrix data reference counter and deallocates matrix header. If the data reference counter is 0, it also deallocates the data.
2765 cvFree((void**)mat);
2769 \cvCPyFunc{ReleaseMatND}
2770 Deallocates a multi-dimensional array.
2772 \cvdefC{void cvReleaseMatND(CvMatND** mat);}
2775 \cvarg{mat}{Double pointer to the array}
2778 The function decrements the array data reference counter and releases the array header. If the reference counter reaches 0, it also deallocates the data.
2783 cvFree((void**)mat);
2786 \cvCPyFunc{ReleaseSparseMat}
2787 Deallocates sparse array.
2789 \cvdefC{void cvReleaseSparseMat(CvSparseMat** mat);}
2792 \cvarg{mat}{Double pointer to the array}
2795 The function releases the sparse array and clears the array pointer upon exit.
2800 Fill the destination array with repeated copies of the source array.
2802 \cvdefC{void cvRepeat(const CvArr* src, CvArr* dst);}
2803 \cvdefPy{Repeat(src,dst)-> None}
2806 \cvarg{src}{Source array, image or matrix}
2807 \cvarg{dst}{Destination array, image or matrix}
2810 The function fills the destination array with repeated copies of the source array:
2813 dst(i,j)=src(i mod rows(src), j mod cols(src))
2816 So the destination array may be as larger as well as smaller than the source array.
2818 \cvCPyFunc{ResetImageROI}
2819 Resets the image ROI to include the entire image and releases the ROI structure.
2821 \cvdefC{void cvResetImageROI(IplImage* image);}
2822 \cvdefPy{ResetImageROI(image)-> None}
2825 \cvarg{image}{A pointer to the image header}
2828 This produces a similar result to the following
2830 , but in addition it releases the ROI structure.
2833 cvSetImageROI(image, cvRect(0, 0, image->width, image->height ));
2834 cvSetImageCOI(image, 0);
2839 cv.SetImageROI(image, (0, 0, image.width, image.height))
2840 cv.SetImageCOI(image, 0)
2846 Changes shape of matrix/image without copying data.
2848 \cvdefC{CvMat* cvReshape(const CvArr* arr, CvMat* header, int newCn, int newRows=0);}
2849 \cvdefPy{Reshape(arr, newCn, newRows=0) -> cvmat}
2852 \cvarg{arr}{Input array}
2854 \cvarg{header}{Output header to be filled}
2856 \cvarg{newCn}{New number of channels. 'newCn = 0' means that the number of channels remains unchanged.}
2857 \cvarg{newRows}{New number of rows. 'newRows = 0' means that the number of rows remains unchanged unless it needs to be changed according to \texttt{newCn} value.}
2860 The function initializes the CvMat header so that it points to the same data as the original array but has a different shape - different number of channels, different number of rows, or both.
2863 The following example code creates one image buffer and two image headers, the first is for a 320x240x3 image and the second is for a 960x240x1 image:
2866 IplImage* color_img = cvCreateImage(cvSize(320,240), IPL_DEPTH_8U, 3);
2868 IplImage gray_img_hdr, *gray_img;
2869 cvReshape(color_img, &gray_mat_hdr, 1);
2870 gray_img = cvGetImage(&gray_mat_hdr, &gray_img_hdr);
2873 And the next example converts a 3x3 matrix to a single 1x9 vector:
2876 CvMat* mat = cvCreateMat(3, 3, CV_32F);
2877 CvMat row_header, *row;
2878 row = cvReshape(mat, &row_header, 0, 1);
2882 \cvCPyFunc{ReshapeMatND}
2883 Changes the shape of a multi-dimensional array without copying the data.
2885 \cvdefC{CvArr* cvReshapeMatND(const CvArr* arr,
2886 int sizeofHeader, CvArr* header,
2887 int newCn, int newDims, int* newSizes);}
2888 \cvdefPy{ReshapeMatND(arr, newCn, newDims) -> cvmat}
2892 #define cvReshapeND(arr, header, newCn, newDims, newSizes ) \
2893 cvReshapeMatND((arr), sizeof(*(header)), (header), \
2894 (newCn), (newDims), (newSizes))
2899 \cvarg{arr}{Input array}
2901 \cvarg{sizeofHeader}{Size of output header to distinguish between IplImage, CvMat and CvMatND output headers}
2902 \cvarg{header}{Output header to be filled}
2903 \cvarg{newCn}{New number of channels. $\texttt{newCn} = 0$ means that the number of channels remains unchanged.}
2904 \cvarg{newDims}{New number of dimensions. $\texttt{newDims} = 0$ means that the number of dimensions remains the same.}
2905 \cvarg{newSizes}{Array of new dimension sizes. Only $\texttt{newDims}-1$ values are used, because the total number of elements must remain the same.
2906 Thus, if $\texttt{newDims} = 1$, \texttt{newSizes} array is not used.}
2908 \cvarg{newDims}{List of new dimensions.}
2912 The function is an advanced version of \cvCPyCross{Reshape} that can work with multi-dimensional arrays as well (though it can work with ordinary images and matrices) and change the number of dimensions.
2915 Below are the two samples from the \cvCPyCross{Reshape} description rewritten using \cvCPyCross{ReshapeMatND}:
2919 IplImage* color_img = cvCreateImage(cvSize(320,240), IPL_DEPTH_8U, 3);
2920 IplImage gray_img_hdr, *gray_img;
2921 gray_img = (IplImage*)cvReshapeND(color_img, &gray_img_hdr, 1, 0, 0);
2925 /* second example is modified to convert 2x2x2 array to 8x1 vector */
2926 int size[] = { 2, 2, 2 };
2927 CvMatND* mat = cvCreateMatND(3, size, CV_32F);
2928 CvMat row_header, *row;
2929 row = (CvMat*)cvReshapeND(mat, &row_header, 0, 1, 0);
2935 \cvfunc{cvRound, cvFloor, cvCeil}\label{cvRound}
2937 Converts a floating-point number to an integer.
2940 int cvRound(double value);
2941 int cvFloor(double value);
2942 int cvCeil(double value);
2944 }\cvdefPy{Round, Floor, Ceil(value)-> int}
2947 \cvarg{value}{The input floating-point value}
2951 The functions convert the input floating-point number to an integer using one of the rounding
2952 modes. \texttt{Round} returns the nearest integer value to the
2953 argument. \texttt{Floor} returns the maximum integer value that is not
2954 larger than the argument. \texttt{Ceil} returns the minimum integer
2955 value that is not smaller than the argument. On some architectures the
2956 functions work much faster than the standard cast
2957 operations in C. If the absolute value of the argument is greater than
2958 $2^{31}$, the result is not determined. Special values ($\pm \infty$ , NaN)
2965 Converts a floating-point number to the nearest integer value.
2967 \cvdefPy{Round(value) -> int}
2970 \cvarg{value}{The input floating-point value}
2973 On some architectures this function is much faster than the standard cast
2974 operations. If the absolute value of the argument is greater than
2975 $2^{31}$, the result is not determined. Special values ($\pm \infty$ , NaN)
2980 Converts a floating-point number to the nearest integer value that is not larger than the argument.
2982 \cvdefPy{Floor(value) -> int}
2985 \cvarg{value}{The input floating-point value}
2988 On some architectures this function is much faster than the standard cast
2989 operations. If the absolute value of the argument is greater than
2990 $2^{31}$, the result is not determined. Special values ($\pm \infty$ , NaN)
2995 Converts a floating-point number to the nearest integer value that is not smaller than the argument.
2997 \cvdefPy{Ceil(value) -> int}
3000 \cvarg{value}{The input floating-point value}
3003 On some architectures this function is much faster than the standard cast
3004 operations. If the absolute value of the argument is greater than
3005 $2^{31}$, the result is not determined. Special values ($\pm \infty$ , NaN)
3011 \cvCPyFunc{ScaleAdd}
3012 Calculates the sum of a scaled array and another array.
3014 \cvdefC{void cvScaleAdd(const CvArr* src1, CvScalar scale, const CvArr* src2, CvArr* dst);}
3015 \cvdefPy{ScaleAdd(src1,scale,src2,dst)-> None}
3018 \cvarg{src1}{The first source array}
3019 \cvarg{scale}{Scale factor for the first array}
3020 \cvarg{src2}{The second source array}
3021 \cvarg{dst}{The destination array}
3024 The function calculates the sum of a scaled array and another array:
3027 \texttt{dst}(I)=\texttt{scale} \, \texttt{src1}(I) + \texttt{src2}(I)
3030 All array parameters should have the same type and the same size.
3033 Sets every element of an array to a given value.
3035 \cvdefC{void cvSet(CvArr* arr, CvScalar value, const CvArr* mask=NULL);}
3036 \cvdefPy{Set(arr,value,mask=NULL)-> None}
3039 \cvarg{arr}{The destination array}
3040 \cvarg{value}{Fill value}
3041 \cvarg{mask}{Operation mask, 8-bit single channel array; specifies elements of the destination array to be changed}
3045 The function copies the scalar \texttt{value} to every selected element of the destination array:
3048 \texttt{arr}(I)=\texttt{value} \quad \text{if} \quad \texttt{mask}(I) \ne 0
3051 If array \texttt{arr} is of \texttt{IplImage} type, then is ROI used, but COI must not be set.
3055 Change the particular array element.
3058 void cvSet1D(CvArr* arr, int idx0, CvScalar value); \newline
3059 void cvSet2D(CvArr* arr, int idx0, int idx1, CvScalar value); \newline
3060 void cvSet3D(CvArr* arr, int idx0, int idx1, int idx2, CvScalar value); \newline
3061 void cvSetND(CvArr* arr, int* idx, CvScalar value);
3065 \cvarg{arr}{Input array}
3066 \cvarg{idx0}{The first zero-based component of the element index}
3067 \cvarg{idx1}{The second zero-based component of the element index}
3068 \cvarg{idx2}{The third zero-based component of the element index}
3069 \cvarg{idx}{Array of the element indices}
3070 \cvarg{value}{The assigned value}
3073 The functions assign the new value to a particular array element. In the case of a sparse array the functions create the node if it does not exist yet.
3078 Set a specific array element.
3080 \cvdefPy{ Set1D(arr, idx, value) -> None }
3083 \cvarg{arr}{Input array}
3084 \cvarg{idx}{Zero-based element index}
3085 \cvarg{value}{The value to assign to the element}
3088 Sets a specific array element. Array must have dimension 1.
3091 Set a specific array element.
3093 \cvdefPy{ Set2D(arr, idx0, idx1, value) -> None }
3096 \cvarg{arr}{Input array}
3097 \cvarg{idx0}{Zero-based element row index}
3098 \cvarg{idx1}{Zero-based element column index}
3099 \cvarg{value}{The value to assign to the element}
3102 Sets a specific array element. Array must have dimension 2.
3105 Set a specific array element.
3107 \cvdefPy{ Set3D(arr, idx0, idx1, idx2, value) -> None }
3110 \cvarg{arr}{Input array}
3111 \cvarg{idx0}{Zero-based element index}
3112 \cvarg{idx1}{Zero-based element index}
3113 \cvarg{idx2}{Zero-based element index}
3114 \cvarg{value}{The value to assign to the element}
3117 Sets a specific array element. Array must have dimension 3.
3120 Set a specific array element.
3122 \cvdefPy{ SetND(arr, indices, value) -> None }
3125 \cvarg{arr}{Input array}
3126 \cvarg{indices}{List of zero-based element indices}
3127 \cvarg{value}{The value to assign to the element}
3130 Sets a specific array element. The length of array indices must be the same as the dimension of the array.
3134 Assigns user data to the array header.
3136 \cvdefC{void cvSetData(CvArr* arr, void* data, int step);}
3137 \cvdefPy{SetData(arr, data, step)-> None}
3140 \cvarg{arr}{Array header}
3141 \cvarg{data}{User data}
3142 \cvarg{step}{Full row length in bytes}
3145 The function assigns user data to the array header. Header should be initialized before using \texttt{cvCreate*Header}, \texttt{cvInit*Header} or \cvCPyCross{Mat} (in the case of matrix) function.
3147 \cvCPyFunc{SetIdentity}
3148 Initializes a scaled identity matrix.
3150 \cvdefC{void cvSetIdentity(CvArr* mat, CvScalar value=cvRealScalar(1));}
3151 \cvdefPy{SetIdentity(mat,value=1)-> None}
3154 \cvarg{mat}{The matrix to initialize (not necesserily square)}
3155 \cvarg{value}{The value to assign to the diagonal elements}
3158 The function initializes a scaled identity matrix:
3161 \texttt{arr}(i,j)=\fork{\texttt{value}}{ if $i=j$}{0}{otherwise}
3164 \cvCPyFunc{SetImageCOI}
3165 Sets the channel of interest in an IplImage.
3167 \cvdefC{void cvSetImageCOI(\par IplImage* image,\par int coi);}
3168 \cvdefPy{SetImageCOI(image, coi)-> None}
3171 \cvarg{image}{A pointer to the image header}
3172 \cvarg{coi}{The channel of interest. 0 - all channels are selected, 1 - first channel is selected, etc. Note that the channel indices become 1-based.}
3175 If the ROI is set to \texttt{NULL} and the coi is \textit{not} 0,
3176 the ROI is allocated. Most OpenCV functions do \textit{not} support
3177 the COI setting, so to process an individual image/matrix channel one
3178 may copy (via \cvCPyCross{Copy} or \cvCPyCross{Split}) the channel to a separate
3179 image/matrix, process it and then copy the result back (via \cvCPyCross{Copy}
3180 or \cvCPyCross{Merge}) if needed.
3182 \cvCPyFunc{SetImageROI}
3183 Sets an image Region Of Interest (ROI) for a given rectangle.
3185 \cvdefC{void cvSetImageROI(\par IplImage* image,\par CvRect rect);}
3186 \cvdefPy{SetImageROI(image, rect)-> None}
3189 \cvarg{image}{A pointer to the image header}
3190 \cvarg{rect}{The ROI rectangle}
3193 If the original image ROI was \texttt{NULL} and the \texttt{rect} is not the whole image, the ROI structure is allocated.
3195 Most OpenCV functions support the use of ROI and treat the image rectangle as a separate image. For example, all of the pixel coordinates are counted from the top-left (or bottom-left) corner of the ROI, not the original image.
3198 \cvCPyFunc{SetReal?D}
3199 Change a specific array element.
3202 void cvSetReal1D(CvArr* arr, int idx0, double value); \newline
3203 void cvSetReal2D(CvArr* arr, int idx0, int idx1, double value); \newline
3204 void cvSetReal3D(CvArr* arr, int idx0, int idx1, int idx2, double value); \newline
3205 void cvSetRealND(CvArr* arr, int* idx, double value);
3209 \cvarg{arr}{Input array}
3210 \cvarg{idx0}{The first zero-based component of the element index}
3211 \cvarg{idx1}{The second zero-based component of the element index}
3212 \cvarg{idx2}{The third zero-based component of the element index}
3213 \cvarg{idx}{Array of the element indices}
3214 \cvarg{value}{The assigned value}
3217 The functions assign a new value to a specific
3218 element of a single-channel array. If the array has multiple channels,
3219 a runtime error is raised. Note that the \cvCPyCross{Set*D} function can be used
3220 safely for both single-channel and multiple-channel arrays, though they
3223 In the case of a sparse array the functions create the node if it does not yet exist.
3227 \cvCPyFunc{SetReal1D}
3228 Set a specific array element.
3230 \cvdefPy{ SetReal1D(arr, idx, value) -> None }
3233 \cvarg{arr}{Input array}
3234 \cvarg{idx}{Zero-based element index}
3235 \cvarg{value}{The value to assign to the element}
3238 Sets a specific array element. Array must have dimension 1.
3240 \cvCPyFunc{SetReal2D}
3241 Set a specific array element.
3243 \cvdefPy{ SetReal2D(arr, idx0, idx1, value) -> None }
3246 \cvarg{arr}{Input array}
3247 \cvarg{idx0}{Zero-based element row index}
3248 \cvarg{idx1}{Zero-based element column index}
3249 \cvarg{value}{The value to assign to the element}
3252 Sets a specific array element. Array must have dimension 2.
3254 \cvCPyFunc{SetReal3D}
3255 Set a specific array element.
3257 \cvdefPy{ SetReal3D(arr, idx0, idx1, idx2, value) -> None }
3260 \cvarg{arr}{Input array}
3261 \cvarg{idx0}{Zero-based element index}
3262 \cvarg{idx1}{Zero-based element index}
3263 \cvarg{idx2}{Zero-based element index}
3264 \cvarg{value}{The value to assign to the element}
3267 Sets a specific array element. Array must have dimension 3.
3269 \cvCPyFunc{SetRealND}
3270 Set a specific array element.
3272 \cvdefPy{ SetRealND(arr, indices, value) -> None }
3275 \cvarg{arr}{Input array}
3276 \cvarg{indices}{List of zero-based element indices}
3277 \cvarg{value}{The value to assign to the element}
3280 Sets a specific array element. The length of array indices must be the same as the dimension of the array.
3286 \cvdefC{void cvSetZero(CvArr* arr);}
3287 \cvdefPy{SetZero(arr)-> None}
3291 #define cvZero cvSetZero
3296 \cvarg{arr}{Array to be cleared}
3299 The function clears the array. In the case of dense arrays (CvMat, CvMatND or IplImage), cvZero(array) is equivalent to cvSet(array,cvScalarAll(0),0).
3300 In the case of sparse arrays all the elements are removed.
3303 Solves a linear system or least-squares problem.
3305 \cvdefC{int cvSolve(const CvArr* src1, const CvArr* src2, CvArr* dst, int method=CV\_LU);}
3306 \cvdefPy{Solve(A,B,X,method=CV\_LU)-> None}
3309 \cvarg{A}{The source matrix}
3310 \cvarg{B}{The right-hand part of the linear system}
3311 \cvarg{X}{The output solution}
3312 \cvarg{method}{The solution (matrix inversion) method
3314 \cvarg{CV\_LU}{Gaussian elimination with optimal pivot element chosen}
3315 \cvarg{CV\_SVD}{Singular value decomposition (SVD) method}
3316 \cvarg{CV\_SVD\_SYM}{SVD method for a symmetric positively-defined matrix.}
3320 The function solves a linear system or least-squares problem (the latter is possible with SVD methods):
3323 \texttt{dst} = argmin_X||\texttt{src1} \, \texttt{X} - \texttt{src2}||
3326 If \texttt{CV\_LU} method is used, the function returns 1 if \texttt{src1} is non-singular and 0 otherwise; in the latter case \texttt{dst} is not valid.
3328 \cvCPyFunc{SolveCubic}
3329 Finds the real roots of a cubic equation.
3331 \cvdefC{void cvSolveCubic(const CvArr* coeffs, CvArr* roots);}
3332 \cvdefPy{SolveCubic(coeffs,roots)-> None}
3335 \cvarg{coeffs}{The equation coefficients, an array of 3 or 4 elements}
3336 \cvarg{roots}{The output array of real roots which should have 3 elements}
3339 The function finds the real roots of a cubic equation:
3341 If coeffs is a 4-element vector:
3344 \texttt{coeffs}[0] x^3 + \texttt{coeffs}[1] x^2 + \texttt{coeffs}[2] x + \texttt{coeffs}[3] = 0
3347 or if coeffs is 3-element vector:
3350 x^3 + \texttt{coeffs}[0] x^2 + \texttt{coeffs}[1] x + \texttt{coeffs}[2] = 0
3353 The function returns the number of real roots found. The roots are
3354 stored to \texttt{root} array, which is padded with zeros if there is
3358 Divides multi-channel array into several single-channel arrays or extracts a single channel from the array.
3360 \cvdefC{void cvSplit(const CvArr* src, CvArr* dst0, CvArr* dst1,
3361 CvArr* dst2, CvArr* dst3);}
3362 \cvdefPy{Split(src,dst0,dst1,dst2,dst3)-> None}
3365 \cvarg{src}{Source array}
3366 \cvarg{dst0}{Destination channel 0}
3367 \cvarg{dst1}{Destination channel 1}
3368 \cvarg{dst2}{Destination channel 2}
3369 \cvarg{dst3}{Destination channel 3}
3372 The function divides a multi-channel array into separate
3373 single-channel arrays. Two modes are available for the operation. If the
3374 source array has N channels then if the first N destination channels
3375 are not NULL, they all are extracted from the source array;
3376 if only a single destination channel of the first N is not NULL, this
3377 particular channel is extracted; otherwise an error is raised. The rest
3378 of the destination channels (beyond the first N) must always be NULL. For
3379 IplImage \cvCPyCross{Copy} with COI set can be also used to extract a single
3380 channel from the image.
3384 Calculates the square root.
3386 \cvdefC{float cvSqrt(float value);}
3387 \cvdefPy{Sqrt(value)-> float}
3390 \cvarg{value}{The input floating-point value}
3394 The function calculates the square root of the argument. If the argument is negative, the result is not determined.
3397 Computes the per-element difference between two arrays.
3399 \cvdefC{void cvSub(const CvArr* src1, const CvArr* src2, CvArr* dst, const CvArr* mask=NULL);}
3400 \cvdefPy{Sub(src1,src2,dst,mask=NULL)-> None}
3403 \cvarg{src1}{The first source array}
3404 \cvarg{src2}{The second source array}
3405 \cvarg{dst}{The destination array}
3406 \cvarg{mask}{Operation mask, 8-bit single channel array; specifies elements of the destination array to be changed}
3410 The function subtracts one array from another one:
3413 dst(I)=src1(I)-src2(I) if mask(I)!=0
3416 All the arrays must have the same type, except the mask, and the same size (or ROI size).
3417 For types that have limited range this operation is saturating.
3420 Computes the difference between a scalar and an array.
3422 \cvdefC{void cvSubRS(const CvArr* src, CvScalar value, CvArr* dst, const CvArr* mask=NULL);}
3423 \cvdefPy{SubRS(src,value,dst,mask=NULL)-> None}
3426 \cvarg{src}{The first source array}
3427 \cvarg{value}{Scalar to subtract from}
3428 \cvarg{dst}{The destination array}
3429 \cvarg{mask}{Operation mask, 8-bit single channel array; specifies elements of the destination array to be changed}
3432 The function subtracts every element of source array from a scalar:
3435 dst(I)=value-src(I) if mask(I)!=0
3438 All the arrays must have the same type, except the mask, and the same size (or ROI size).
3439 For types that have limited range this operation is saturating.
3442 Computes the difference between an array and a scalar.
3444 \cvdefC{void cvSubS(const CvArr* src, CvScalar value, CvArr* dst, const CvArr* mask=NULL);}
3445 \cvdefPy{SubS(src,value,dst,mask=NULL)-> None}
3448 \cvarg{src}{The source array}
3449 \cvarg{value}{Subtracted scalar}
3450 \cvarg{dst}{The destination array}
3451 \cvarg{mask}{Operation mask, 8-bit single channel array; specifies elements of the destination array to be changed}
3454 The function subtracts a scalar from every element of the source array:
3457 dst(I)=src(I)-value if mask(I)!=0
3460 All the arrays must have the same type, except the mask, and the same size (or ROI size).
3461 For types that have limited range this operation is saturating.
3465 Adds up array elements.
3467 \cvdefC{CvScalar cvSum(const CvArr* arr);}
3468 \cvdefPy{Sum(arr)-> CvScalar}
3471 \cvarg{arr}{The array}
3475 The function calculates the sum \texttt{S} of array elements, independently for each channel:
3477 \[ \sum_I \texttt{arr}(I)_c \]
3479 If the array is \texttt{IplImage} and COI is set, the function processes the selected channel only and stores the sum to the first scalar component.
3483 Performs singular value back substitution.
3486 void cvSVBkSb(\par const CvArr* W,\par const CvArr* U,\par const CvArr* V,\par const CvArr* B,\par CvArr* X,\par int flags);}
3487 \cvdefPy{SVBkSb(W,U,V,B,X,flags)-> None}
3490 \cvarg{W}{Matrix or vector of singular values}
3491 \cvarg{U}{Left orthogonal matrix (tranposed, perhaps)}
3492 \cvarg{V}{Right orthogonal matrix (tranposed, perhaps)}
3493 \cvarg{B}{The matrix to multiply the pseudo-inverse of the original matrix \texttt{A} by. This is an optional parameter. If it is omitted then it is assumed to be an identity matrix of an appropriate size (so that \texttt{X} will be the reconstructed pseudo-inverse of \texttt{A}).}
3494 \cvarg{X}{The destination matrix: result of back substitution}
3495 \cvarg{flags}{Operation flags, should match exactly to the \texttt{flags} passed to \cvCPyCross{SVD}}
3498 The function calculates back substitution for decomposed matrix \texttt{A} (see \cvCPyCross{SVD} description) and matrix \texttt{B}:
3501 \texttt{X} = \texttt{V} \texttt{W}^{-1} \texttt{U}^T \texttt{B}
3509 {1/W_{(i,i)}}{if $W_{(i,i)} > \epsilon \sum_i{W_{(i,i)}}$ }
3513 and $\epsilon$ is a small number that depends on the matrix data type.
3515 This function together with \cvCPyCross{SVD} is used inside \cvCPyCross{Invert}
3516 and \cvCPyCross{Solve}, and the possible reason to use these (svd and bksb)
3517 "low-level" function, is to avoid allocation of temporary matrices inside
3518 the high-level counterparts (inv and solve).
3521 Performs singular value decomposition of a real floating-point matrix.
3523 \cvdefC{void cvSVD(\par CvArr* A, \par CvArr* W, \par CvArr* U=NULL, \par CvArr* V=NULL, \par int flags=0);}
3524 \cvdefPy{SVD(A,W, U = None, V = None, flags=0)-> None}
3527 \cvarg{A}{Source $\texttt{M} \times \texttt{N}$ matrix}
3528 \cvarg{W}{Resulting singular value diagonal matrix ($\texttt{M} \times \texttt{N}$ or $\min(\texttt{M}, \texttt{N}) \times \min(\texttt{M}, \texttt{N})$) or $\min(\texttt{M},\texttt{N}) \times 1$ vector of the singular values}
3529 \cvarg{U}{Optional left orthogonal matrix, $\texttt{M} \times \min(\texttt{M}, \texttt{N})$ (when \texttt{CV\_SVD\_U\_T} is not set), or $\min(\texttt{M},\texttt{N}) \times \texttt{M}$ (when \texttt{CV\_SVD\_U\_T} is set), or $\texttt{M} \times \texttt{M}$ (regardless of \texttt{CV\_SVD\_U\_T} flag).}
3530 \cvarg{V}{Optional right orthogonal matrix, $\texttt{N} \times \min(\texttt{M}, \texttt{N})$ (when \texttt{CV\_SVD\_V\_T} is not set), or $\min(\texttt{M},\texttt{N}) \times \texttt{N}$ (when \texttt{CV\_SVD\_V\_T} is set), or $\texttt{N} \times \texttt{N}$ (regardless of \texttt{CV\_SVD\_V\_T} flag).}
3531 \cvarg{flags}{Operation flags; can be 0 or a combination of the following values:
3533 \cvarg{CV\_SVD\_MODIFY\_A}{enables modification of matrix \texttt{A} during the operation. It speeds up the processing.}
3534 \cvarg{CV\_SVD\_U\_T}{means that the transposed matrix \texttt{U} is returned. Specifying the flag speeds up the processing.}
3535 \cvarg{CV\_SVD\_V\_T}{means that the transposed matrix \texttt{V} is returned. Specifying the flag speeds up the processing.}
3539 The function decomposes matrix \texttt{A} into the product of a diagonal matrix and two
3541 orthogonal matrices:
3547 where $W$ is a diagonal matrix of singular values that can be coded as a
3548 1D vector of singular values and $U$ and $V$. All the singular values
3549 are non-negative and sorted (together with $U$ and $V$ columns)
3550 in descending order.
3552 An SVD algorithm is numerically robust and its typical applications include:
3555 \item accurate eigenvalue problem solution when matrix \texttt{A}
3556 is a square, symmetric, and positively defined matrix, for example, when
3557 it is a covariance matrix. $W$ in this case will be a vector/matrix
3558 of the eigenvalues, and $U = V$ will be a matrix of the eigenvectors.
3559 \item accurate solution of a poor-conditioned linear system.
3560 \item least-squares solution of an overdetermined linear system. This and the preceeding is done by using the \cvCPyCross{Solve} function with the \texttt{CV\_SVD} method.
3561 \item accurate calculation of different matrix characteristics such as the matrix rank (the number of non-zero singular values), condition number (ratio of the largest singular value to the smallest one), and determinant (absolute value of the determinant is equal to the product of singular values).
3565 Returns the trace of a matrix.
3567 \cvdefC{CvScalar cvTrace(const CvArr* mat);}
3568 \cvdefPy{Trace(mat)-> CvScalar}
3571 \cvarg{mat}{The source matrix}
3575 The function returns the sum of the diagonal elements of the matrix \texttt{src1}.
3577 \[ tr(\texttt{mat}) = \sum_i \texttt{mat}(i,i) \]
3579 \cvCPyFunc{Transform}
3581 Performs matrix transformation of every array element.
3583 \cvdefC{void cvTransform(const CvArr* src, CvArr* dst, const CvMat* transmat, const CvMat* shiftvec=NULL);}
3584 \cvdefPy{Transform(src,dst,transmat,shiftvec=NULL)-> None}
3587 \cvarg{src}{The first source array}
3588 \cvarg{dst}{The destination array}
3589 \cvarg{transmat}{Transformation matrix}
3590 \cvarg{shiftvec}{Optional shift vector}
3593 The function performs matrix transformation of every element of array \texttt{src} and stores the results in \texttt{dst}:
3596 dst(I) = transmat \cdot src(I) + shiftvec % or dst(I),,k,,=sum,,j,,(transmat(k,j)*src(I),,j,,) + shiftvec(k)
3599 That is, every element of an \texttt{N}-channel array \texttt{src} is
3600 considered as an \texttt{N}-element vector which is transformed using
3601 a $\texttt{M} \times \texttt{N}$ matrix \texttt{transmat} and shift
3602 vector \texttt{shiftvec} into an element of \texttt{M}-channel array
3603 \texttt{dst}. There is an option to embedd \texttt{shiftvec} into
3604 \texttt{transmat}. In this case \texttt{transmat} should be a $\texttt{M}
3605 \times (N+1)$ matrix and the rightmost column is treated as the shift
3608 Both source and destination arrays should have the same depth and the
3609 same size or selected ROI size. \texttt{transmat} and \texttt{shiftvec}
3610 should be real floating-point matrices.
3612 The function may be used for geometrical transformation of n dimensional
3613 point set, arbitrary linear color space transformation, shuffling the
3614 channels and so forth.
3616 \cvCPyFunc{Transpose}
3617 Transposes a matrix.
3619 \cvdefC{void cvTranspose(const CvArr* src, CvArr* dst);}
3620 \cvdefPy{Transpose(src,dst)-> None}
3623 \cvarg{src}{The source matrix}
3624 \cvarg{dst}{The destination matrix}
3627 The function transposes matrix \texttt{src1}:
3629 \[ \texttt{dst}(i,j) = \texttt{src}(j,i) \]
3631 Note that no complex conjugation is done in the case of a complex
3632 matrix. Conjugation should be done separately: look at the sample code
3633 in \cvCPyCross{XorS} for an example.
3636 Performs per-element bit-wise "exclusive or" operation on two arrays.
3638 \cvdefC{void cvXor(const CvArr* src1, const CvArr* src2, CvArr* dst, const CvArr* mask=NULL);}
3639 \cvdefPy{Xor(src1,src2,dst,mask=NULL)-> None}
3642 \cvarg{src1}{The first source array}
3643 \cvarg{src2}{The second source array}
3644 \cvarg{dst}{The destination array}
3645 \cvarg{mask}{Operation mask, 8-bit single channel array; specifies elements of the destination array to be changed}
3648 The function calculates per-element bit-wise logical conjunction of two arrays:
3651 dst(I)=src1(I)^src2(I) if mask(I)!=0
3654 In the case of floating-point arrays their bit representations are used for the operation. All the arrays must have the same type, except the mask, and the same size.
3657 Performs per-element bit-wise "exclusive or" operation on an array and a scalar.
3659 \cvdefC{void cvXorS(const CvArr* src, CvScalar value, CvArr* dst, const CvArr* mask=NULL);}
3660 \cvdefPy{XorS(src,value,dst,mask=NULL)-> None}
3663 \cvarg{src}{The source array}
3664 \cvarg{value}{Scalar to use in the operation}
3665 \cvarg{dst}{The destination array}
3666 \cvarg{mask}{Operation mask, 8-bit single channel array; specifies elements of the destination array to be changed}
3670 The function XorS calculates per-element bit-wise conjunction of an array and a scalar:
3673 dst(I)=src(I)^value if mask(I)!=0
3676 Prior to the actual operation, the scalar is converted to the same type as that of the array(s). In the case of floating-point arrays their bit representations are used for the operation. All the arrays must have the same type, except the mask, and the same size
3679 The following sample demonstrates how to conjugate complex vector by switching the most-significant bit of imaging part:
3683 float a[] = { 1, 0, 0, 1, -1, 0, 0, -1 }; /* 1, j, -1, -j */
3684 CvMat A = cvMat(4, 1, CV\_32FC2, &a);
3685 int i, negMask = 0x80000000;
3686 cvXorS(&A, cvScalar(0, *(float*)&negMask, 0, 0 ), &A, 0);
3687 for(i = 0; i < 4; i++ )
3688 printf("(\%.1f, \%.1f) ", a[i*2], a[i*2+1]);
3692 The code should print:
3695 (1.0,0.0) (0.0,-1.0) (-1.0,0.0) (0.0,1.0)
3700 Returns the particular element of single-channel floating-point matrix.
3702 \cvdefC{double cvmGet(const CvMat* mat, int row, int col);}
3703 \cvdefPy{mGet(mat,row,col)-> double}
3706 \cvarg{mat}{Input matrix}
3707 \cvarg{row}{The zero-based index of row}
3708 \cvarg{col}{The zero-based index of column}
3711 The function is a fast replacement for \cvCPyCross{GetReal2D}
3712 in the case of single-channel floating-point matrices. It is faster because
3713 it is inline, it does fewer checks for array type and array element type,
3714 and it checks for the row and column ranges only in debug mode.
3717 Returns a specific element of a single-channel floating-point matrix.
3719 \cvdefC{void cvmSet(CvMat* mat, int row, int col, double value);}
3720 \cvdefPy{mSet(mat,row,col,value)-> None}
3723 \cvarg{mat}{The matrix}
3724 \cvarg{row}{The zero-based index of row}
3725 \cvarg{col}{The zero-based index of column}
3726 \cvarg{value}{The new value of the matrix element}
3730 The function is a fast replacement for \cvCPyCross{SetReal2D}
3731 in the case of single-channel floating-point matrices. It is faster because
3732 it is inline, it does fewer checks for array type and array element type,
3733 and it checks for the row and column ranges only in debug mode.
3737 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3741 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3746 Computes absolute value of each matrix element
3748 \cvdefCpp{MatExpr<...> abs(const Mat\& src);\newline
3749 MatExpr<...> abs(const MatExpr<...>\& src);}
3752 \cvarg{src}{matrix or matrix expression}
3755 \texttt{abs} is a meta-function that is expanded to one of \cvCppCross{absdiff} forms:
3758 \item \texttt{C = abs(A-B)} is equivalent to \texttt{absdiff(A, B, C)} and
3759 \item \texttt{C = abs(A)} is equivalent to \texttt{absdiff(A, Scalar::all(0), C)}.
3760 \item \texttt{C = Mat\_<Vec<uchar,\emph{n}> >(abs(A*$\alpha$ + $\beta$))} is equivalent to \texttt{convertScaleAbs(A, C, alpha, beta)}
3763 The output matrix will have the same size and the same type as the input one
3764 (except for the last case, where \texttt{C} will be \texttt{depth=CV\_8U}).
3766 See also: \cross{Matrix Expressions}, \cvCppCross{absdiff}, \hyperref[cppfunc.saturatecast]{saturate\_cast}
3769 Computes per-element absolute difference between 2 arrays or between array and a scalar.
3771 \cvdefCpp{void absdiff(const Mat\& src1, const Mat\& src2, Mat\& dst);\newline
3772 void absdiff(const Mat\& src1, const Scalar\& sc, Mat\& dst);\newline
3773 void absdiff(const MatND\& src1, const MatND\& src2, MatND\& dst);\newline
3774 void absdiff(const MatND\& src1, const Scalar\& sc, MatND\& dst);}
3777 \cvarg{src1}{The first input array}
3778 \cvarg{src2}{The second input array; Must be the same size and same type as \texttt{src1}}
3779 \cvarg{sc}{Scalar; the second input parameter}
3780 \cvarg{dst}{The destination array; it will have the same size and same type as \texttt{src1}; see \texttt{Mat::create}}
3783 The functions \texttt{absdiff} compute:
3785 \item absolute difference between two arrays
3786 \[\texttt{dst}(I) = \texttt{saturate}(|\texttt{src1}(I) - \texttt{src2}(I)|)\]
3787 \item or absolute difference between array and a scalar:
3788 \[\texttt{dst}(I) = \texttt{saturate}(|\texttt{src1}(I) - \texttt{sc}|)\]
3790 where \texttt{I} is multi-dimensional index of array elements.
3791 in the case of multi-channel arrays each channel is processed independently.
3793 See also: \cvCppCross{abs}, \hyperref[cppfunc.saturatecast]{saturate\_cast}
3796 Computes the per-element sum of two arrays or an array and a scalar.
3798 \cvdefCpp{void add(const Mat\& src1, const Mat\& src2, Mat\& dst);\newline
3799 void add(const Mat\& src1, const Mat\& src2, \par Mat\& dst, const Mat\& mask);\newline
3800 void add(const Mat\& src1, const Scalar\& sc, \par Mat\& dst, const Mat\& mask=Mat());\newline
3801 void add(const MatND\& src1, const MatND\& src2, MatND\& dst);\newline
3802 void add(const MatND\& src1, const MatND\& src2, \par MatND\& dst, const MatND\& mask);\newline
3803 void add(const MatND\& src1, const Scalar\& sc, \par MatND\& dst, const MatND\& mask=MatND());}
3806 \cvarg{src1}{The first source array}
3807 \cvarg{src2}{The second source array. It must have the same size and same type as \texttt{src1}}
3808 \cvarg{sc}{Scalar; the second input parameter}
3809 \cvarg{dst}{The destination array; it will have the same size and same type as \texttt{src1}; see \texttt{Mat::create}}
3810 \cvarg{mask}{The optional operation mask, 8-bit single channel array;
3811 specifies elements of the destination array to be changed}
3814 The functions \texttt{add} compute:
3816 \item the sum of two arrays:
3817 \[\texttt{dst}(I) = \texttt{saturate}(\texttt{src1}(I) + \texttt{src2}(I))\quad\texttt{if mask}(I)\ne0\]
3818 \item or the sum of array and a scalar:
3819 \[\texttt{dst}(I) = \texttt{saturate}(\texttt{src1}(I) + \texttt{sc})\quad\texttt{if mask}(I)\ne0\]
3821 where \texttt{I} is multi-dimensional index of array elements.
3823 The first function in the above list can be replaced with matrix expressions:
3826 dst += src1; // equivalent to add(dst, src1, dst);
3829 in the case of multi-channel arrays each channel is processed independently.
3831 See also: \cvCppCross{subtract}, \cvCppCross{addWeighted}, \cvCppCross{scaleAdd}, \cvCppCross{convertScale},
3832 \cross{Matrix Expressions}, \hyperref[cppfunc.saturatecast]{saturate\_cast}.
3834 \cvCppFunc{addWeighted}
3835 Computes the weighted sum of two arrays.
3837 \cvdefCpp{void addWeighted(const Mat\& src1, double alpha, const Mat\& src2,\par
3838 double beta, double gamma, Mat\& dst);\newline
3839 void addWeighted(const MatND\& src1, double alpha, const MatND\& src2,\par
3840 double beta, double gamma, MatND\& dst);
3844 \cvarg{src1}{The first source array}
3845 \cvarg{alpha}{Weight for the first array elements}
3846 \cvarg{src2}{The second source array; must have the same size and same type as \texttt{src1}}
3847 \cvarg{beta}{Weight for the second array elements}
3848 \cvarg{dst}{The destination array; it will have the same size and same type as \texttt{src1}}
3849 \cvarg{gamma}{Scalar, added to each sum}
3852 The functions \texttt{addWeighted} calculate the weighted sum of two arrays as follows:
3853 \[\texttt{dst}(I)=\texttt{saturate}(\texttt{src1}(I)*\texttt{alpha} + \texttt{src2}(I)*\texttt{beta} + \texttt{gamma})\]
3854 where \texttt{I} is multi-dimensional index of array elements.
3856 The first function can be replaced with a matrix expression:
3858 dst = src1*alpha + src2*beta + gamma;
3861 In the case of multi-channel arrays each channel is processed independently.
3863 See also: \cvCppCross{add}, \cvCppCross{subtract}, \cvCppCross{scaleAdd}, \cvCppCross{convertScale},
3864 \cross{Matrix Expressions}, \hyperref[cppfunc.saturatecast]{saturate\_cast}.
3866 \cvfunc{bitwise\_and}\label{cppfunc.bitwise.and}
3867 Calculates per-element bit-wise conjunction of two arrays and an array and a scalar.
3869 \cvdefCpp{void bitwise\_and(const Mat\& src1, const Mat\& src2,\par Mat\& dst, const Mat\& mask=Mat());\newline
3870 void bitwise\_and(const Mat\& src1, const Scalar\& sc,\par Mat\& dst, const Mat\& mask=Mat());\newline
3871 void bitwise\_and(const MatND\& src1, const MatND\& src2,\par MatND\& dst, const MatND\& mask=MatND());\newline
3872 void bitwise\_and(const MatND\& src1, const Scalar\& sc,\par MatND\& dst, const MatND\& mask=MatND());}
3875 \cvarg{src1}{The first source array}
3876 \cvarg{src2}{The second source array. It must have the same size and same type as \texttt{src1}}
3877 \cvarg{sc}{Scalar; the second input parameter}
3878 \cvarg{dst}{The destination array; it will have the same size and same type as \texttt{src1}; see \texttt{Mat::create}}
3879 \cvarg{mask}{The optional operation mask, 8-bit single channel array;
3880 specifies elements of the destination array to be changed}
3883 The functions \texttt{bitwise\_and} compute per-element bit-wise logical conjunction:
3886 \[\texttt{dst}(I) = \texttt{src1}(I) \wedge \texttt{src2}(I)\quad\texttt{if mask}(I)\ne0\]
3887 \item or array and a scalar:
3888 \[\texttt{dst}(I) = \texttt{src1}(I) \wedge \texttt{sc}\quad\texttt{if mask}(I)\ne0\]
3891 In the case of floating-point arrays their machine-specific bit representations (usually IEEE754-compliant) are used for the operation, and in the case of multi-channel arrays each channel is processed independently.
3893 See also: \hyperref[cppfunc.bitwise.and]{bitwise\_and}, \hyperref[cppfunc.bitwise.not]{bitwise\_not}, \hyperref[cppfunc.bitwise.xor]{bitwise\_xor}
3895 \cvfunc{bitwise\_not}\label{cppfunc.bitwise.not}
3896 Inverts every bit of array
3898 \cvdefCpp{void bitwise\_not(const Mat\& src, Mat\& dst);\newline
3899 void bitwise\_not(const MatND\& src, MatND\& dst);}
3901 \cvarg{src1}{The source array}
3902 \cvarg{dst}{The destination array; it is reallocated to be of the same size and
3903 the same type as \texttt{src}; see \texttt{Mat::create}}
3904 \cvarg{mask}{The optional operation mask, 8-bit single channel array;
3905 specifies elements of the destination array to be changed}
3908 The functions \texttt{bitwise\_not} compute per-element bit-wise inversion of the source array:
3909 \[\texttt{dst}(I) = \neg\texttt{src}(I)\]
3911 In the case of floating-point source array its machine-specific bit representation (usually IEEE754-compliant) is used for the operation. in the case of multi-channel arrays each channel is processed independently.
3913 See also: \hyperref[cppfunc.bitwise.and]{bitwise\_and}, \hyperref[cppfunc.bitwise.or]{bitwise\_or}, \hyperref[cppfunc.bitwise.xor]{bitwise\_xor}
3916 \cvfunc{bitwise\_or}\label{cppfunc.bitwise.or}
3917 Calculates per-element bit-wise disjunction of two arrays and an array and a scalar.
3919 \cvdefCpp{void bitwise\_or(const Mat\& src1, const Mat\& src2,\par Mat\& dst, const Mat\& mask=Mat());\newline
3920 void bitwise\_or(const Mat\& src1, const Scalar\& sc,\par Mat\& dst, const Mat\& mask=Mat());\newline
3921 void bitwise\_or(const MatND\& src1, const MatND\& src2,\par MatND\& dst, const MatND\& mask=MatND());\newline
3922 void bitwise\_or(const MatND\& src1, const Scalar\& sc,\par MatND\& dst, const MatND\& mask=MatND());}
3924 \cvarg{src1}{The first source array}
3925 \cvarg{src2}{The second source array. It must have the same size and same type as \texttt{src1}}
3926 \cvarg{sc}{Scalar; the second input parameter}
3927 \cvarg{dst}{The destination array; it is reallocated to be of the same size and
3928 the same type as \texttt{src1}; see \texttt{Mat::create}}
3929 \cvarg{mask}{The optional operation mask, 8-bit single channel array;
3930 specifies elements of the destination array to be changed}
3933 The functions \texttt{bitwise\_or} compute per-element bit-wise logical disjunction
3936 \[\texttt{dst}(I) = \texttt{src1}(I) \vee \texttt{src2}(I)\quad\texttt{if mask}(I)\ne0\]
3937 \item or array and a scalar:
3938 \[\texttt{dst}(I) = \texttt{src1}(I) \vee \texttt{sc}\quad\texttt{if mask}(I)\ne0\]
3941 In the case of floating-point arrays their machine-specific bit representations (usually IEEE754-compliant) are used for the operation. in the case of multi-channel arrays each channel is processed independently.
3943 See also: \hyperref[cppfunc.bitwise.and]{bitwise\_and}, \hyperref[cppfunc.bitwise.not]{bitwise\_not}, \hyperref[cppfunc.bitwise.or]{bitwise\_or}
3945 \cvfunc{bitwise\_xor}\label{cppfunc.bitwise.xor}
3946 Calculates per-element bit-wise "exclusive or" operation on two arrays and an array and a scalar.
3948 \cvdefCpp{void bitwise\_xor(const Mat\& src1, const Mat\& src2,\par Mat\& dst, const Mat\& mask=Mat());\newline
3949 void bitwise\_xor(const Mat\& src1, const Scalar\& sc,\par Mat\& dst, const Mat\& mask=Mat());\newline
3950 void bitwise\_xor(const MatND\& src1, const MatND\& src2,\par MatND\& dst, const MatND\& mask=MatND());\newline
3951 void bitwise\_xor(const MatND\& src1, const Scalar\& sc,\par MatND\& dst, const MatND\& mask=MatND());}
3953 \cvarg{src1}{The first source array}
3954 \cvarg{src2}{The second source array. It must have the same size and same type as \texttt{src1}}
3955 \cvarg{sc}{Scalar; the second input parameter}
3956 \cvarg{dst}{The destination array; it is reallocated to be of the same size and
3957 the same type as \texttt{src1}; see \texttt{Mat::create}}
3958 \cvarg{mask}{The optional operation mask, 8-bit single channel array;
3959 specifies elements of the destination array to be changed}
3962 The functions \texttt{bitwise\_xor} compute per-element bit-wise logical "exclusive or" operation
3966 \[\texttt{dst}(I) = \texttt{src1}(I) \oplus \texttt{src2}(I)\quad\texttt{if mask}(I)\ne0\]
3967 \item or array and a scalar:
3968 \[\texttt{dst}(I) = \texttt{src1}(I) \oplus \texttt{sc}\quad\texttt{if mask}(I)\ne0\]
3971 In the case of floating-point arrays their machine-specific bit representations (usually IEEE754-compliant) are used for the operation. in the case of multi-channel arrays each channel is processed independently.
3973 See also: \hyperref[cppfunc.bitwise.and]{bitwise\_and}, \hyperref[cppfunc.bitwise.not]{bitwise\_not}, \hyperref[cppfunc.bitwise.or]{bitwise\_or}
3975 \cvCppFunc{calcCovarMatrix}
3976 Calculates covariation matrix of a set of vectors
3978 \cvdefCpp{void calcCovarMatrix( const Mat* samples, int nsamples,\par
3979 Mat\& covar, Mat\& mean,\par
3980 int flags, int ctype=CV\_64F);\newline
3981 void calcCovarMatrix( const Mat\& samples, Mat\& covar, Mat\& mean,\par
3982 int flags, int ctype=CV\_64F);}
3984 \cvarg{samples}{The samples, stored as separate matrices, or as rows or columns of a single matrix}
3985 \cvarg{nsamples}{The number of samples when they are stored separately}
3986 \cvarg{covar}{The output covariance matrix; it will have type=\texttt{ctype} and square size}
3987 \cvarg{mean}{The input or output (depending on the flags) array - the mean (average) vector of the input vectors}
3988 \cvarg{flags}{The operation flags, a combination of the following values
3990 \cvarg{CV\_COVAR\_SCRAMBLED}{The output covariance matrix is calculated as:
3992 \texttt{scale} \cdot [ \texttt{vects} [0]- \texttt{mean} ,\texttt{vects} [1]- \texttt{mean} ,...]^T \cdot [\texttt{vects} [0]-\texttt{mean} ,\texttt{vects} [1]-\texttt{mean} ,...]
3994 that is, the covariance matrix will be $\texttt{nsamples} \times \texttt{nsamples}$.
3995 Such an unusual covariance matrix is used for fast PCA
3996 of a set of very large vectors (see, for example, the EigenFaces technique
3997 for face recognition). Eigenvalues of this "scrambled" matrix will
3998 match the eigenvalues of the true covariance matrix and the "true"
3999 eigenvectors can be easily calculated from the eigenvectors of the
4000 "scrambled" covariance matrix.}
4001 \cvarg{CV\_COVAR\_NORMAL}{The output covariance matrix is calculated as:
4003 \texttt{scale} \cdot [ \texttt{vects} [0]- \texttt{mean} ,\texttt{vects} [1]- \texttt{mean} ,...] \cdot [\texttt{vects} [0]-\texttt{mean} ,\texttt{vects} [1]-\texttt{mean} ,...]^T
4005 that is, \texttt{covar} will be a square matrix
4006 of the same size as the total number of elements in each
4007 input vector. One and only one of \texttt{CV\_COVAR\_SCRAMBLED} and
4008 \texttt{CV\_COVAR\_NORMAL} must be specified}
4009 \cvarg{CV\_COVAR\_USE\_AVG}{If the flag is specified, the function does not calculate \texttt{mean} from the input vectors, but, instead, uses the passed \texttt{mean} vector. This is useful if \texttt{mean} has been pre-computed or known a-priori, or if the covariance matrix is calculated by parts - in this case, \texttt{mean} is not a mean vector of the input sub-set of vectors, but rather the mean vector of the whole set.}
4010 \cvarg{CV\_COVAR\_SCALE}{If the flag is specified, the covariance matrix is scaled. In the "normal" mode \texttt{scale} is \texttt{1./nsamples}; in the "scrambled" mode \texttt{scale} is the reciprocal of the total number of elements in each input vector. By default (if the flag is not specified) the covariance matrix is not scaled (i.e. \texttt{scale=1}).}
4012 \cvarg{CV\_COVAR\_ROWS}{[Only useful in the second variant of the function] The flag means that all the input vectors are stored as rows of the \texttt{samples} matrix. \texttt{mean} should be a single-row vector in this case.}
4013 \cvarg{CV\_COVAR\_COLS}{[Only useful in the second variant of the function] The flag means that all the input vectors are stored as columns of the \texttt{samples} matrix. \texttt{mean} should be a single-column vector in this case.}
4018 The functions \texttt{calcCovarMatrix} calculate the covariance matrix
4019 and, optionally, the mean vector of the set of input vectors.
4021 See also: \cvCppCross{PCA}, \cvCppCross{mulTransposed}, \cvCppCross{Mahalanobis}
4023 \cvCppFunc{cartToPolar}
4024 Calculates the magnitude and angle of 2d vectors.
4026 \cvdefCpp{void cartToPolar(const Mat\& x, const Mat\& y,\par
4027 Mat\& magnitude, Mat\& angle,\par
4028 bool angleInDegrees=false);}
4030 \cvarg{x}{The array of x-coordinates; must be single-precision or double-precision floating-point array}
4031 \cvarg{y}{The array of y-coordinates; it must have the same size and same type as \texttt{x}}
4032 \cvarg{magnitude}{The destination array of magnitudes of the same size and same type as \texttt{x}}
4033 \cvarg{angle}{The destination array of angles of the same size and same type as \texttt{x}.
4034 The angles are measured in radians $(0$ to $2 \pi )$ or in degrees (0 to 360 degrees).}
4035 \cvarg{angleInDegrees}{The flag indicating whether the angles are measured in radians, which is default mode, or in degrees}
4038 The function \texttt{cartToPolar} calculates either the magnitude, angle, or both of every 2d vector (x(I),y(I)):
4042 \texttt{magnitude}(I)=\sqrt{\texttt{x}(I)^2+\texttt{y}(I)^2},\\
4043 \texttt{angle}(I)=\texttt{atan2}(\texttt{y}(I), \texttt{x}(I))[\cdot180/\pi]
4047 The angles are calculated with $\sim\,0.3^\circ$ accuracy. For the (0,0) point, the angle is set to 0.
4049 \cvCppFunc{checkRange}
4050 Checks every element of an input array for invalid values.
4052 \cvdefCpp{bool checkRange(const Mat\& src, bool quiet=true, Point* pos=0,\par
4053 double minVal=-DBL\_MAX, double maxVal=DBL\_MAX);\newline
4054 bool checkRange(const MatND\& src, bool quiet=true, int* pos=0,\par
4055 double minVal=-DBL\_MAX, double maxVal=DBL\_MAX);}
4057 \cvarg{src}{The array to check}
4058 \cvarg{quiet}{The flag indicating whether the functions quietly return false when the array elements are out of range, or they throw an exception.}
4059 \cvarg{pos}{The optional output parameter, where the position of the first outlier is stored. In the second function \texttt{pos}, when not NULL, must be a pointer to array of \texttt{src.dims} elements}
4060 \cvarg{minVal}{The inclusive lower boundary of valid values range}
4061 \cvarg{maxVal}{The exclusive upper boundary of valid values range}
4064 The functions \texttt{checkRange} check that every array element is
4065 neither NaN nor $\pm \infty $. When \texttt{minVal < -DBL\_MAX} and \texttt{maxVal < DBL\_MAX}, then the functions also check that
4066 each value is between \texttt{minVal} and \texttt{maxVal}. in the case of multi-channel arrays each channel is processed independently.
4067 If some values are out of range, position of the first outlier is stored in \texttt{pos} (when $\texttt{pos}\ne0$), and then the functions either return false (when \texttt{quiet=true}) or throw an exception.
4071 Performs per-element comparison of two arrays or an array and scalar value.
4073 \cvdefCpp{void compare(const Mat\& src1, const Mat\& src2, Mat\& dst, int cmpop);\newline
4074 void compare(const Mat\& src1, double value, \par Mat\& dst, int cmpop);\newline
4075 void compare(const MatND\& src1, const MatND\& src2, \par MatND\& dst, int cmpop);\newline
4076 void compare(const MatND\& src1, double value, \par MatND\& dst, int cmpop);}
4078 \cvarg{src1}{The first source array}
4079 \cvarg{src2}{The second source array; must have the same size and same type as \texttt{src1}}
4080 \cvarg{value}{The scalar value to compare each array element with}
4081 \cvarg{dst}{The destination array; will have the same size as \texttt{src1} and type=\texttt{CV\_8UC1}}
4082 \cvarg{cmpop}{The flag specifying the relation between the elements to be checked
4084 \cvarg{CMP\_EQ}{$\texttt{src1}(I) = \texttt{src2}(I)$ or $\texttt{src1}(I) = \texttt{value}$}
4085 \cvarg{CMP\_GT}{$\texttt{src1}(I) > \texttt{src2}(I)$ or $\texttt{src1}(I) > \texttt{value}$}
4086 \cvarg{CMP\_GE}{$\texttt{src1}(I) \geq \texttt{src2}(I)$ or $\texttt{src1}(I) \geq \texttt{value}$}
4087 \cvarg{CMP\_LT}{$\texttt{src1}(I) < \texttt{src2}(I)$ or $\texttt{src1}(I) < \texttt{value}$}
4088 \cvarg{CMP\_LE}{$\texttt{src1}(I) \leq \texttt{src2}(I)$ or $\texttt{src1}(I) \leq \texttt{value}$}
4089 \cvarg{CMP\_NE}{$\texttt{src1}(I) \ne \texttt{src2}(I)$ or $\texttt{src1}(I) \ne \texttt{value}$}
4093 The functions \texttt{compare} compare each element of \texttt{src1} with the corresponding element of \texttt{src2}
4094 or with real scalar \texttt{value}. When the comparison result is true, the corresponding element of destination array is set to 255, otherwise it is set to 0:
4096 \item \texttt{dst(I) = src1(I) cmpop src2(I) ? 255 : 0}
4097 \item \texttt{dst(I) = src1(I) cmpop value ? 255 : 0}
4100 The comparison operations can be replaced with the equivalent matrix expressions:
4103 Mat dst1 = src1 >= src2;
4104 Mat dst2 = src1 < 8;
4108 See also: \cvCppCross{checkRange}, \cvCppCross{min}, \cvCppCross{max}, \cvCppCross{threshold}, \cross{Matrix Expressions}
4110 \cvCppFunc{completeSymm}
4111 Copies the lower or the upper half of a square matrix to another half.
4113 \cvdefCpp{void completeSymm(Mat\& mtx, bool lowerToUpper=false);}
4115 \cvarg{mtx}{Input-output floating-point square matrix}
4116 \cvarg{lowerToUpper}{If true, the lower half is copied to the upper half, otherwise the upper half is copied to the lower half}
4119 The function \texttt{completeSymm} copies the lower half of a square matrix to its another half; the matrix diagonal remains unchanged:
4122 \item $\texttt{mtx}_{ij}=\texttt{mtx}_{ji}$ for $i > j$ if \texttt{lowerToUpper=false}
4123 \item $\texttt{mtx}_{ij}=\texttt{mtx}_{ji}$ for $i < j$ if \texttt{lowerToUpper=true}
4126 See also: \cvCppCross{flip}, \cvCppCross{transpose}
4128 \cvCppFunc{convertScaleAbs}
4129 Scales, computes absolute values and converts the result to 8-bit.
4131 \cvdefCpp{void convertScaleAbs(const Mat\& src, Mat\& dst, double alpha=1, double beta=0);}
4133 \cvarg{src}{The source array}
4134 \cvarg{dst}{The destination array}
4135 \cvarg{alpha}{The optional scale factor}
4136 \cvarg{beta}{The optional delta added to the scaled values}
4139 On each element of the input array the function \texttt{convertScaleAbs} performs 3 operations sequentially: scaling, taking absolute value, conversion to unsigned 8-bit type:
4140 \[\texttt{dst}(I)=\texttt{saturate\_cast<uchar>}(|\texttt{src}(I)*\texttt{alpha} + \texttt{beta}|)\]
4142 in the case of multi-channel arrays the function processes each channel independently. When the output is not 8-bit, the operation can be emulated by calling \texttt{Mat::convertTo} method (or by using matrix expressions) and then by computing absolute value of the result, for example:
4145 Mat_<float> A(30,30);
4146 randu(A, Scalar(-100), Scalar(100));
4147 Mat_<float> B = A*5 + 3;
4149 // Mat_<float> B = abs(A*5+3) will also do the job,
4150 // but it will allocate a temporary matrix
4153 See also: \cvCppCross{Mat::convertTo}, \cvCppCross{abs}
4155 \cvCppFunc{countNonZero}
4156 Counts non-zero array elements.
4158 \cvdefCpp{int countNonZero( const Mat\& mtx );\newline
4159 int countNonZero( const MatND\& mtx );}
4161 \cvarg{mtx}{Single-channel array}
4164 The function \texttt{cvCountNonZero} returns the number of non-zero elements in mtx:
4166 \[ \sum_{I:\;\texttt{mtx}(I)\ne0} 1 \]
4168 See also: \cvCppCross{mean}, \cvCppCross{meanStdDev}, \cvCppCross{norm}, \cvCppCross{minMaxLoc}, \cvCppCross{calcCovarMatrix}
4170 \cvCppFunc{cubeRoot}
4171 Computes cube root of the argument
4173 \cvdefCpp{float cubeRoot(float val);}
4175 \cvarg{val}{The function argument}
4178 The function \texttt{cubeRoot} computes $\sqrt[3]{\texttt{val}}$.
4179 Negative arguments are handled correctly, \emph{NaN} and $\pm\infty$ are not handled.
4180 The accuracy approaches the maximum possible accuracy for single-precision data.
4182 \cvCppFunc{cvarrToMat}
4183 Converts CvMat, IplImage or CvMatND to cv::Mat.
4185 \cvdefCpp{Mat cvarrToMat(const CvArr* src, bool copyData=false, bool allowND=true, int coiMode=0);}
4187 \cvarg{src}{The source \texttt{CvMat}, \texttt{IplImage} or \texttt{CvMatND}}
4188 \cvarg{copyData}{When it is false (default value), no data is copied, only the new header is created.
4189 In this case the original array should not be deallocated while the new matrix header is used. The the parameter is true, all the data is copied, then user may deallocate the original array right after the conversion}
4190 \cvarg{allowND}{When it is true (default value), then \texttt{CvMatND} is converted to \texttt{Mat} if it's possible
4191 (e.g. then the data is contiguous). If it's not possible, or when the parameter is false, the function will report an error}
4192 \cvarg{coiMode}{The parameter specifies how the IplImage COI (when set) is handled.
4194 \item If \texttt{coiMode=0}, the function will report an error if COI is set.
4195 \item If \texttt{coiMode=1}, the function will never report an error; instead it returns the header to the whole original image and user will have to check and process COI manually, see \cvCppCross{extractImageCOI}.
4196 % \item If \texttt{coiMode=2}, the function will extract the COI into the separate matrix. \emph{This is also done when the COI is set and }\texttt{copyData=true}}
4200 The function \texttt{cvarrToMat} converts \cross{CvMat}, \cross{IplImage} or \cross{CvMatND} header to \cvCppCross{Mat} header, and optionally duplicates the underlying data. The constructed header is returned by the function.
4202 When \texttt{copyData=false}, the conversion is done really fast (in O(1) time) and the newly created matrix header will have \texttt{refcount=0}, which means that no reference counting is done for the matrix data, and user has to preserve the data until the new header is destructed. Otherwise, when \texttt{copyData=true}, the new buffer will be allocated and managed as if you created a new matrix from scratch and copy the data there. That is,
4203 \texttt{cvarrToMat(src, true) $\sim$ cvarrToMat(src, false).clone()} (assuming that COI is not set). The function provides uniform way of supporting \cross{CvArr} paradigm in the code that is migrated to use new-style data structures internally. The reverse transformation, from \cvCppCross{Mat} to \cross{CvMat} or \cross{IplImage} can be done by simple assignment:
4206 CvMat* A = cvCreateMat(10, 10, CV_32F);
4208 IplImage A1; cvGetImage(A, &A1);
4209 Mat B = cvarrToMat(A);
4210 Mat B1 = cvarrToMat(&A1);
4213 // now A, A1, B, B1, C and C1 are different headers
4214 // for the same 10x10 floating-point array.
4215 // note, that you will need to use "&"
4216 // to pass C & C1 to OpenCV functions, e.g:
4217 printf("%g", cvDet(&C1));
4220 Normally, the function is used to convert an old-style 2D array (\cross{CvMat} or \cross{IplImage}) to \texttt{Mat}, however, the function can also take \cross{CvMatND} on input and create \cvCppCross{Mat} for it, if it's possible. And for \texttt{CvMatND A} it is possible if and only if \texttt{A.dim[i].size*A.dim.step[i] == A.dim.step[i-1]} for all or for all but one \texttt{i, 0 < i < A.dims}. That is, the matrix data should be continuous or it should be representable as a sequence of continuous matrices. By using this function in this way, you can process \cross{CvMatND} using arbitrary element-wise function. But for more complex operations, such as filtering functions, it will not work, and you need to convert \cross{CvMatND} to \cvCppCross{MatND} using the corresponding constructor of the latter.
4222 The last parameter, \texttt{coiMode}, specifies how to react on an image with COI set: by default it's 0, and then the function reports an error when an image with COI comes in. And \texttt{coiMode=1} means that no error is signaled - user has to check COI presence and handle it manually. The modern structures, such as \cvCppCross{Mat} and \cvCppCross{MatND} do not support COI natively. To process individual channel of an new-style array, you will need either to organize loop over the array (e.g. using matrix iterators) where the channel of interest will be processed, or extract the COI using \cvCppCross{mixChannels} (for new-style arrays) or \cvCppCross{extractImageCOI} (for old-style arrays), process this individual channel and insert it back to the destination array if need (using \cvCppCross{mixChannel} or \cvCppCross{insertImageCOI}, respectively).
4224 See also: \cvCppCross{cvGetImage}, \cvCppCross{cvGetMat}, \cvCppCross{cvGetMatND}, \cvCppCross{extractImageCOI}, \cvCppCross{insertImageCOI}, \cvCppCross{mixChannels}
4228 Performs a forward or inverse discrete cosine transform of 1D or 2D array
4230 \cvdefCpp{void dct(const Mat\& src, Mat\& dst, int flags=0);}
4232 \cvarg{src}{The source floating-point array}
4233 \cvarg{dst}{The destination array; will have the same size and same type as \texttt{src}}
4234 \cvarg{flags}{Transformation flags, a combination of the following values
4236 \cvarg{DCT\_INVERSE}{do an inverse 1D or 2D transform instead of the default forward transform.}
4237 \cvarg{DCT\_ROWS}{do a forward or inverse transform of every individual row of the input matrix. This flag allows user to transform multiple vectors simultaneously and can be used to decrease the overhead (which is sometimes several times larger than the processing itself), to do 3D and higher-dimensional transforms and so forth.}
4241 The function \texttt{dct} performs a forward or inverse discrete cosine transform (DCT) of a 1D or 2D floating-point array:
4243 Forward Cosine transform of 1D vector of $N$ elements:
4244 \[Y = C^{(N)} \cdot X\]
4246 \[C^{(N)}_{jk}=\sqrt{\alpha_j/N}\cos\left(\frac{\pi(2k+1)j}{2N}\right)\]
4247 and $\alpha_0=1$, $\alpha_j=2$ for $j > 0$.
4249 Inverse Cosine transform of 1D vector of N elements:
4250 \[X = \left(C^{(N)}\right)^{-1} \cdot Y = \left(C^{(N)}\right)^T \cdot Y\]
4251 (since $C^{(N)}$ is orthogonal matrix, $C^{(N)} \cdot \left(C^{(N)}\right)^T = I$)
4253 Forward Cosine transform of 2D $M \times N$ matrix:
4254 \[Y = C^{(N)} \cdot X \cdot \left(C^{(N)}\right)^T\]
4256 Inverse Cosine transform of 2D vector of $M \times N$ elements:
4257 \[X = \left(C^{(N)}\right)^T \cdot X \cdot C^{(N)}\]
4259 The function chooses the mode of operation by looking at the flags and size of the input array:
4261 \item if \texttt{(flags \& DCT\_INVERSE) == 0}, the function does forward 1D or 2D transform, otherwise it is inverse 1D or 2D transform.
4262 \item if \texttt{(flags \& DCT\_ROWS) $\ne$ 0}, the function performs 1D transform of each row.
4263 \item otherwise, if the array is a single column or a single row, the function performs 1D transform
4264 \item otherwise it performs 2D transform.
4267 \textbf{Important note}: currently cv::dct supports even-size arrays (2, 4, 6 ...). For data analysis and approximation you can pad the array when necessary.
4269 Also, the function's performance depends very much, and not monotonically, on the array size, see \cvCppCross{getOptimalDFTSize}. In the current implementation DCT of a vector of size \texttt{N} is computed via DFT of a vector of size \texttt{N/2}, thus the optimal DCT size $\texttt{N}^*\geq\texttt{N}$ can be computed as:
4272 size_t getOptimalDCTSize(size_t N) { return 2*getOptimalDFTSize((N+1)/2); }
4275 See also: \cvCppCross{dft}, \cvCppCross{getOptimalDFTSize}, \cvCppCross{idct}
4279 Performs a forward or inverse Discrete Fourier transform of 1D or 2D floating-point array.
4281 \cvdefCpp{void dft(const Mat\& src, Mat\& dst, int flags=0, int nonzeroRows=0);}
4283 \cvarg{src}{The source array, real or complex}
4284 \cvarg{dst}{The destination array, which size and type depends on the \texttt{flags}}
4285 \cvarg{flags}{Transformation flags, a combination of the following values
4287 \cvarg{DFT\_INVERSE}{do an inverse 1D or 2D transform instead of the default forward transform.}
4288 \cvarg{DFT\_SCALE}{scale the result: divide it by the number of array elements. Normally, it is combined with \texttt{DFT\_INVERSE}}.
4289 \cvarg{DFT\_ROWS}{do a forward or inverse transform of every individual row of the input matrix. This flag allows the user to transform multiple vectors simultaneously and can be used to decrease the overhead (which is sometimes several times larger than the processing itself), to do 3D and higher-dimensional transforms and so forth.}
4290 \cvarg{DFT\_COMPLEX\_OUTPUT}{then the function performs forward transformation of 1D or 2D real array, the result, though being a complex array, has complex-conjugate symmetry (\emph{CCS}), see the description below. Such an array can be packed into real array of the same size as input, which is the fastest option and which is what the function does by default. However, you may wish to get the full complex array (for simpler spectrum analysis etc.). Pass the flag to tell the function to produce full-size complex output array.}
4291 \cvarg{DFT\_REAL\_OUTPUT}{then the function performs inverse transformation of 1D or 2D complex array, the result is normally a complex array of the same size. However, if the source array has conjugate-complex symmetry (for example, it is a result of forward transformation with \texttt{DFT\_COMPLEX\_OUTPUT} flag), then the output is real array. While the function itself does not check whether the input is symmetrical or not, you can pass the flag and then the function will assume the symmetry and produce the real output array. Note that when the input is packed real array and inverse transformation is executed, the function treats the input as packed complex-conjugate symmetrical array, so the output will also be real array}
4293 \cvarg{nonzeroRows}{When the parameter $\ne 0$, the function assumes that only the first \texttt{nonzeroRows} rows of the input array (\texttt{DFT\_INVERSE} is not set) or only the first \texttt{nonzeroRows} of the output array (\texttt{DFT\_INVERSE} is set) contain non-zeros, thus the function can handle the rest of the rows more efficiently and thus save some time. This technique is very useful for computing array cross-correlation or convolution using DFT}
4296 Forward Fourier transform of 1D vector of N elements:
4297 \[Y = F^{(N)} \cdot X,\]
4298 where $F^{(N)}_{jk}=\exp(-2\pi i j k/N)$ and $i=\sqrt{-1}$
4300 Inverse Fourier transform of 1D vector of N elements:
4303 X'= \left(F^{(N)}\right)^{-1} \cdot Y = \left(F^{(N)}\right)^* \cdot y \\
4307 where $F^*=\left(\textrm{Re}(F^{(N)})-\textrm{Im}(F^{(N)})\right)^T$
4309 Forward Fourier transform of 2D vector of $M \times N$ elements:
4310 \[Y = F^{(M)} \cdot X \cdot F^{(N)}\]
4312 Inverse Fourier transform of 2D vector of $M \times N$ elements:
4315 X'= \left(F^{(M)}\right)^* \cdot Y \cdot \left(F^{(N)}\right)^*\\
4316 X = \frac{1}{M \cdot N} \cdot X'
4320 In the case of real (single-channel) data, the packed format called \emph{CCS} (complex-conjugate-symmetrical) that was borrowed from IPL and used to represent the result of a forward Fourier transform or input for an inverse Fourier transform:
4323 Re Y_{0,0} & Re Y_{0,1} & Im Y_{0,1} & Re Y_{0,2} & Im Y_{0,2} & \cdots & Re Y_{0,N/2-1} & Im Y_{0,N/2-1} & Re Y_{0,N/2} \\
4324 Re Y_{1,0} & Re Y_{1,1} & Im Y_{1,1} & Re Y_{1,2} & Im Y_{1,2} & \cdots & Re Y_{1,N/2-1} & Im Y_{1,N/2-1} & Re Y_{1,N/2} \\
4325 Im Y_{1,0} & Re Y_{2,1} & Im Y_{2,1} & Re Y_{2,2} & Im Y_{2,2} & \cdots & Re Y_{2,N/2-1} & Im Y_{2,N/2-1} & Im Y_{1,N/2} \\
4327 Re Y_{M/2-1,0} & Re Y_{M-3,1} & Im Y_{M-3,1} & \hdotsfor{3} & Re Y_{M-3,N/2-1} & Im Y_{M-3,N/2-1}& Re Y_{M/2-1,N/2} \\
4328 Im Y_{M/2-1,0} & Re Y_{M-2,1} & Im Y_{M-2,1} & \hdotsfor{3} & Re Y_{M-2,N/2-1} & Im Y_{M-2,N/2-1}& Im Y_{M/2-1,N/2} \\
4329 Re Y_{M/2,0} & Re Y_{M-1,1} & Im Y_{M-1,1} & \hdotsfor{3} & Re Y_{M-1,N/2-1} & Im Y_{M-1,N/2-1}& Re Y_{M/2,N/2}
4333 in the case of 1D transform of real vector, the output will look as the first row of the above matrix.
4335 So, the function chooses the operation mode depending on the flags and size of the input array:
4337 \item if \texttt{DFT\_ROWS} is set or the input array has single row or single column then the function performs 1D forward or inverse transform (of each row of a matrix when \texttt{DFT\_ROWS} is set, otherwise it will be 2D transform.
4338 \item if input array is real and \texttt{DFT\_INVERSE} is not set, the function does forward 1D or 2D transform:
4340 \item when \texttt{DFT\_COMPLEX\_OUTPUT} is set then the output will be complex matrix of the same size as input.
4341 \item otherwise the output will be a real matrix of the same size as input. in the case of 2D transform it will use the packed format as shown above; in the case of single 1D transform it will look as the first row of the above matrix; in the case of multiple 1D transforms (when using \texttt{DCT\_ROWS} flag) each row of the output matrix will look like the first row of the above matrix.
4343 \item otherwise, if the input array is complex and either \texttt{DFT\_INVERSE} or \texttt{DFT\_REAL\_OUTPUT} are not set then the output will be a complex array of the same size as input and the function will perform the forward or inverse 1D or 2D transform of the whole input array or each row of the input array independently, depending on the flags \texttt{DFT\_INVERSE} and \texttt{DFT\_ROWS}.
4344 \item otherwise, i.e. when \texttt{DFT\_INVERSE} is set, the input array is real, or it is complex but \texttt{DFT\_REAL\_OUTPUT} is set, the output will be a real array of the same size as input, and the function will perform 1D or 2D inverse transformation of the whole input array or each individual row, depending on the flags \texttt{DFT\_INVERSE} and \texttt{DFT\_ROWS}.
4347 The scaling is done after the transformation if \texttt{DFT\_SCALE} is set.
4349 Unlike \cvCppCross{dct}, the function supports arrays of arbitrary size, but only those arrays are processed efficiently, which sizes can be factorized in a product of small prime numbers (2, 3 and 5 in the current implementation). Such an efficient DFT size can be computed using \cvCppCross{getOptimalDFTSize} method.
4351 Here is the sample on how to compute DFT-based convolution of two 2D real arrays:
4353 void convolveDFT(const Mat& A, const Mat& B, Mat& C)
4355 // reallocate the output array if needed
4356 C.create(abs(A.rows - B.rows)+1, abs(A.cols - B.cols)+1, A.type());
4358 // compute the size of DFT transform
4359 dftSize.width = getOptimalDFTSize(A.cols + B.cols - 1);
4360 dftSize.height = getOptimalDFTSize(A.rows + B.rows - 1);
4362 // allocate temporary buffers and initialize them with 0's
4363 Mat tempA(dftSize, A.type(), Scalar::all(0));
4364 Mat tempB(dftSize, B.type(), Scalar::all(0));
4366 // copy A and B to the top-left corners of tempA and tempB, respectively
4367 Mat roiA(tempA, Rect(0,0,A.cols,A.rows));
4369 Mat roiB(tempB, Rect(0,0,B.cols,B.rows));
4372 // now transform the padded A & B in-place;
4373 // use "nonzeroRows" hint for faster processing
4374 dft(tempA, tempA, 0, A.rows);
4375 dft(tempB, tempB, 0, B.rows);
4377 // multiply the spectrums;
4378 // the function handles packed spectrum representations well
4379 mulSpectrums(tempA, tempB, tempA);
4381 // transform the product back from the frequency domain.
4382 // Even though all the result rows will be non-zero,
4383 // we need only the first C.rows of them, and thus we
4384 // pass nonzeroRows == C.rows
4385 dft(tempA, tempA, DFT_INVERSE + DFT_SCALE, C.rows);
4387 // now copy the result back to C.
4388 tempA(Rect(0, 0, C.cols, C.rows)).copyTo(C);
4390 // all the temporary buffers will be deallocated automatically
4394 What can be optimized in the above sample?
4396 \item since we passed $\texttt{nonzeroRows} \ne 0$ to the forward transform calls and
4397 since we copied \texttt{A}/\texttt{B} to the top-left corners of \texttt{tempA}/\texttt{tempB}, respectively,
4398 it's not necessary to clear the whole \texttt{tempA} and \texttt{tempB};
4399 it is only necessary to clear the \texttt{tempA.cols - A.cols} (\texttt{tempB.cols - B.cols})
4400 rightmost columns of the matrices.
4401 \item this DFT-based convolution does not have to be applied to the whole big arrays,
4402 especially if \texttt{B} is significantly smaller than \texttt{A} or vice versa.
4403 Instead, we can compute convolution by parts. For that we need to split the destination array
4404 \texttt{C} into multiple tiles and for each tile estimate, which parts of \texttt{A} and \texttt{B}
4405 are required to compute convolution in this tile. If the tiles in \texttt{C} are too small,
4406 the speed will decrease a lot, because of repeated work - in the ultimate case, when each tile in \texttt{C} is a single pixel,
4407 the algorithm becomes equivalent to the naive convolution algorithm.
4408 If the tiles are too big, the temporary arrays \texttt{tempA} and \texttt{tempB} become too big
4409 and there is also slowdown because of bad cache locality. So there is optimal tile size somewhere in the middle.
4410 \item if the convolution is done by parts, since different tiles in \texttt{C} can be computed in parallel, the loop can be threaded.
4413 All of the above improvements have been implemented in \cvCppCross{matchTemplate} and \cvCppCross{filter2D}, therefore, by using them, you can get even better performance than with the above theoretically optimal implementation (though, those two functions actually compute cross-correlation, not convolution, so you will need to "flip" the kernel or the image around the center using \cvCppCross{flip}).
4415 See also: \cvCppCross{dct}, \cvCppCross{getOptimalDFTSize}, \cvCppCross{mulSpectrums}, \cvCppCross{filter2D}, \cvCppCross{matchTemplate}, \cvCppCross{flip}, \cvCppCross{cartToPolar}, \cvCppCross{magnitude}, \cvCppCross{phase}
4419 Performs per-element division of two arrays or a scalar by an array.
4421 \cvdefCpp{void divide(const Mat\& src1, const Mat\& src2, \par Mat\& dst, double scale=1);\newline
4422 void divide(double scale, const Mat\& src2, Mat\& dst);\newline
4423 void divide(const MatND\& src1, const MatND\& src2, \par MatND\& dst, double scale=1);\newline
4424 void divide(double scale, const MatND\& src2, MatND\& dst);}
4426 \cvarg{src1}{The first source array}
4427 \cvarg{src2}{The second source array; should have the same size and same type as \texttt{src1}}
4428 \cvarg{scale}{Scale factor}
4429 \cvarg{dst}{The destination array; will have the same size and same type as \texttt{src2}}
4432 The functions \texttt{divide} divide one array by another:
4433 \[\texttt{dst(I) = saturate(src1(I)*scale/src2(I))} \]
4435 or a scalar by array, when there is no \texttt{src1}:
4436 \[\texttt{dst(I) = saturate(scale/src2(I))} \]
4438 The result will have the same type as \texttt{src1}. When \texttt{src2(I)=0}, \texttt{dst(I)=0} too.
4440 See also: \cvCppCross{multiply}, \cvCppCross{add}, \cvCppCross{subtract}, \cross{Matrix Expressions}
4442 \cvCppFunc{determinant}
4444 Returns determinant of a square floating-point matrix.
4446 \cvdefCpp{double determinant(const Mat\& mtx);}
4448 \cvarg{mtx}{The input matrix; must have \texttt{CV\_32FC1} or \texttt{CV\_64FC1} type and square size}
4451 The function \texttt{determinant} computes and returns determinant of the specified matrix. For small matrices (\texttt{mtx.cols=mtx.rows<=3})
4452 the direct method is used; for larger matrices the function uses LU factorization.
4454 For symmetric positive-determined matrices, it is also possible to compute \cvCppCross{SVD}: $\texttt{mtx}=U \cdot W \cdot V^T$ and then calculate the determinant as a product of the diagonal elements of $W$.
4456 See also: \cvCppCross{SVD}, \cvCppCross{trace}, \cvCppCross{invert}, \cvCppCross{solve}, \cross{Matrix Expressions}
4459 Computes eigenvalues and eigenvectors of a symmetric matrix.
4461 \cvdefCpp{bool eigen(const Mat\& src, Mat\& eigenvalues, \par int lowindex=-1, int highindex=-1);\newline
4462 bool eigen(const Mat\& src, Mat\& eigenvalues, \par Mat\& eigenvectors, int lowindex=-1,\par
4465 \cvarg{src}{The input matrix; must have \texttt{CV\_32FC1} or \texttt{CV\_64FC1} type, square size and be symmetric: $\texttt{src}^T=\texttt{src}$}
4466 \cvarg{eigenvalues}{The output vector of eigenvalues of the same type as \texttt{src}; The eigenvalues are stored in the descending order.}
4467 \cvarg{eigenvectors}{The output matrix of eigenvectors; It will have the same size and the same type as \texttt{src}; The eigenvectors are stored as subsequent matrix rows, in the same order as the corresponding eigenvalues}
4468 \cvarg{lowindex}{Optional index of largest eigenvalue/-vector to calculate.
4470 \cvarg{highindex}{Optional index of smallest eigenvalue/-vector to calculate.
4474 The functions \texttt{eigen} compute just eigenvalues, or eigenvalues and eigenvectors of symmetric matrix \texttt{src}:
4477 src*eigenvectors(i,:)' = eigenvalues(i)*eigenvectors(i,:)' (in MATLAB notation)
4480 If either low- or highindex is supplied the other is required, too.
4481 Indexing is 0-based. Example: To calculate the largest eigenvector/-value set
4482 lowindex = highindex = 0.
4483 For legacy reasons this function always returns a square matrix the same size
4484 as the source matrix with eigenvectors and a vector the length of the source
4485 matrix with eigenvalues. The selected eigenvectors/-values are always in the
4486 first highindex - lowindex + 1 rows.
4488 See also: \cvCppCross{SVD}, \cvCppCross{completeSymm}, \cvCppCross{PCA}
4491 Calculates the exponent of every array element.
4493 \cvdefCpp{void exp(const Mat\& src, Mat\& dst);\newline
4494 void exp(const MatND\& src, MatND\& dst);}
4496 \cvarg{src}{The source array}
4497 \cvarg{dst}{The destination array; will have the same size and same type as \texttt{src}}
4500 The function \texttt{exp} calculates the exponent of every element of the input array:
4503 \texttt{dst} [I] = e^{\texttt{src}}(I)
4506 The maximum relative error is about $7 \times 10^{-6}$ for single-precision and less than $10^{-10}$ for double-precision. Currently, the function converts denormalized values to zeros on output. Special values (NaN, $\pm \infty$) are not handled.
4508 See also: \cvCppCross{log}, \cvCppCross{cartToPolar}, \cvCppCross{polarToCart}, \cvCppCross{phase}, \cvCppCross{pow}, \cvCppCross{sqrt}, \cvCppCross{magnitude}
4510 \cvCppFunc{extractImageCOI}
4512 Extract the selected image channel
4514 \cvdefCpp{void extractImageCOI(const CvArr* src, Mat\& dst, int coi=-1);}
4516 \cvarg{src}{The source array. It should be a pointer to \cross{CvMat} or \cross{IplImage}}
4517 \cvarg{dst}{The destination array; will have single-channel, and the same size and the same depth as \texttt{src}}
4518 \cvarg{coi}{If the parameter is \texttt{>=0}, it specifies the channel to extract;
4519 If it is \texttt{<0}, \texttt{src} must be a pointer to \texttt{IplImage} with valid COI set - then the selected COI is extracted.}
4522 The function \texttt{extractImageCOI} is used to extract image COI from an old-style array and put the result to the new-style C++ matrix. As usual, the destination matrix is reallocated using \texttt{Mat::create} if needed.
4524 To extract a channel from a new-style matrix, use \cvCppCross{mixChannels} or \cvCppCross{split}
4526 See also: \cvCppCross{mixChannels}, \cvCppCross{split}, \cvCppCross{merge}, \cvCppCross{cvarrToMat}, \cvCppCross{cvSetImageCOI}, \cvCppCross{cvGetImageCOI}
4529 \cvCppFunc{fastAtan2}
4530 Calculates the angle of a 2D vector in degrees
4532 \cvdefCpp{float fastAtan2(float y, float x);}
4534 \cvarg{x}{x-coordinate of the vector}
4535 \cvarg{y}{y-coordinate of the vector}
4538 The function \texttt{fastAtan2} calculates the full-range angle of an input 2D vector. The angle is
4539 measured in degrees and varies from $0^\circ$ to $360^\circ$. The accuracy is about $0.3^\circ$.
4542 Flips a 2D array around vertical, horizontal or both axes.
4544 \cvdefCpp{void flip(const Mat\& src, Mat\& dst, int flipCode);}
4546 \cvarg{src}{The source array}
4547 \cvarg{dst}{The destination array; will have the same size and same type as \texttt{src}}
4548 \cvarg{flipCode}{Specifies how to flip the array:
4549 0 means flipping around the x-axis, positive (e.g., 1) means flipping around y-axis, and negative (e.g., -1) means flipping around both axes. See also the discussion below for the formulas.}
4552 The function \texttt{flip} flips the array in one of three different ways (row and column indices are 0-based):
4555 \texttt{dst}_{ij} = \forkthree
4556 {\texttt{src}_{\texttt{src.rows}-i-1,j}}{if \texttt{flipCode} = 0}
4557 {\texttt{src}_{i,\texttt{src.cols}-j-1}}{if \texttt{flipCode} > 0}
4558 {\texttt{src}_{\texttt{src.rows}-i-1,\texttt{src.cols}-j-1}}{if \texttt{flipCode} < 0}
4561 The example scenarios of function use are:
4563 \item vertical flipping of the image ($\texttt{flipCode} = 0$) to switch between top-left and bottom-left image origin, which is a typical operation in video processing in Windows.
4564 \item horizontal flipping of the image with subsequent horizontal shift and absolute difference calculation to check for a vertical-axis symmetry ($\texttt{flipCode} > 0$)
4565 \item simultaneous horizontal and vertical flipping of the image with subsequent shift and absolute difference calculation to check for a central symmetry ($\texttt{flipCode} < 0$)
4566 \item reversing the order of 1d point arrays ($\texttt{flipCode} > 0$ or $\texttt{flipCode} = 0$)
4569 See also: \cvCppCross{transpose}, \cvCppCross{repeat}, \cvCppCross{completeSymm}
4572 Performs generalized matrix multiplication.
4574 \cvdefCpp{void gemm(const Mat\& src1, const Mat\& src2, double alpha,\par
4575 const Mat\& src3, double beta, Mat\& dst, int flags=0);}
4577 \cvarg{src1}{The first multiplied input matrix; should have \texttt{CV\_32FC1}, \texttt{CV\_64FC1}, \texttt{CV\_32FC2} or \texttt{CV\_64FC2} type}
4578 \cvarg{src2}{The second multiplied input matrix; should have the same type as \texttt{src1}}
4579 \cvarg{alpha}{The weight of the matrix product}
4580 \cvarg{src3}{The third optional delta matrix added to the matrix product; should have the same type as \texttt{src1} and \texttt{src2}}
4581 \cvarg{beta}{The weight of \texttt{src3}}
4582 \cvarg{dst}{The destination matrix; It will have the proper size and the same type as input matrices}
4583 \cvarg{flags}{Operation flags:
4585 \cvarg{GEMM\_1\_T}{transpose \texttt{src1}}
4586 \cvarg{GEMM\_2\_T}{transpose \texttt{src2}}
4587 \cvarg{GEMM\_3\_T}{transpose \texttt{src3}}
4591 The function performs generalized matrix multiplication and similar to the corresponding functions \texttt{*gemm} in BLAS level 3.
4592 For example, \texttt{gemm(src1, src2, alpha, src3, beta, dst, GEMM\_1\_T + GEMM\_3\_T)} corresponds to
4594 \texttt{dst} = \texttt{alpha} \cdot \texttt{src1} ^T \cdot \texttt{src2} + \texttt{beta} \cdot \texttt{src3} ^T
4597 The function can be replaced with a matrix expression, e.g. the above call can be replaced with:
4599 dst = alpha*src1.t()*src2 + beta*src3.t();
4602 See also: \cvCppCross{mulTransposed}, \cvCppCross{transform}, \cross{Matrix Expressions}
4605 \cvCppFunc{getConvertElem}
4606 Returns conversion function for a single pixel
4608 \cvdefCpp{ConvertData getConvertElem(int fromType, int toType);\newline
4609 ConvertScaleData getConvertScaleElem(int fromType, int toType);\newline
4610 typedef void (*ConvertData)(const void* from, void* to, int cn);\newline
4611 typedef void (*ConvertScaleData)(const void* from, void* to,\par
4612 int cn, double alpha, double beta);}
4614 \cvarg{fromType}{The source pixel type}
4615 \cvarg{toType}{The destination pixel type}
4616 \cvarg{from}{Callback parameter: pointer to the input pixel}
4617 \cvarg{to}{Callback parameter: pointer to the output pixel}
4618 \cvarg{cn}{Callback parameter: the number of channels; can be arbitrary, 1, 100, 100000, ...}
4619 \cvarg{alpha}{ConvertScaleData callback optional parameter: the scale factor}
4620 \cvarg{beta}{ConvertScaleData callback optional parameter: the delta or offset}
4623 The functions \texttt{getConvertElem} and \texttt{getConvertScaleElem} return pointers to the functions for converting individual pixels from one type to another. While the main function purpose is to convert single pixels (actually, for converting sparse matrices from one type to another), you can use them to convert the whole row of a dense matrix or the whole matrix at once, by setting \texttt{cn = matrix.cols*matrix.rows*matrix.channels()} if the matrix data is continuous.
4625 See also: \cvCppCross{Mat::convertTo}, \cvCppCross{MatND::convertTo}, \cvCppCross{SparseMat::convertTo}
4628 \cvCppFunc{getOptimalDFTSize}
4629 Returns optimal DFT size for a given vector size.
4631 \cvdefCpp{int getOptimalDFTSize(int vecsize);}
4633 \cvarg{vecsize}{Vector size}
4636 DFT performance is not a monotonic function of a vector size, therefore, when you compute convolution of two arrays or do a spectral analysis of array, it usually makes sense to pad the input data with zeros to get a bit larger array that can be transformed much faster than the original one.
4637 Arrays, which size is a power-of-two (2, 4, 8, 16, 32, ...) are the fastest to process, though, the arrays, which size is a product of 2's, 3's and 5's (e.g. 300 = 5*5*3*2*2), are also processed quite efficiently.
4639 The function \texttt{getOptimalDFTSize} returns the minimum number \texttt{N} that is greater than or equal to \texttt{vecsize}, such that the DFT
4640 of a vector of size \texttt{N} can be computed efficiently. In the current implementation $N=2^p \times 3^q \times 5^r$, for some $p$, $q$, $r$.
4642 The function returns a negative number if \texttt{vecsize} is too large (very close to \texttt{INT\_MAX}).
4644 While the function cannot be used directly to estimate the optimal vector size for DCT transform (since the current DCT implementation supports only even-size vectors), it can be easily computed as \texttt{getOptimalDFTSize((vecsize+1)/2)*2}.
4646 See also: \cvCppCross{dft}, \cvCppCross{dct}, \cvCppCross{idft}, \cvCppCross{idct}, \cvCppCross{mulSpectrums}
4649 Computes inverse Discrete Cosine Transform of a 1D or 2D array
4651 \cvdefCpp{void idct(const Mat\& src, Mat\& dst, int flags=0);}
4653 \cvarg{src}{The source floating-point single-channel array}
4654 \cvarg{dst}{The destination array. Will have the same size and same type as \texttt{src}}
4655 \cvarg{flags}{The operation flags.}
4658 \texttt{idct(src, dst, flags)} is equivalent to \texttt{dct(src, dst, flags | DCT\_INVERSE)}.
4659 See \cvCppCross{dct} for details.
4661 See also: \cvCppCross{dct}, \cvCppCross{dft}, \cvCppCross{idft}, \cvCppCross{getOptimalDFTSize}
4665 Computes inverse Discrete Fourier Transform of a 1D or 2D array
4667 \cvdefCpp{void idft(const Mat\& src, Mat\& dst, int flags=0, int outputRows=0);}
4669 \cvarg{src}{The source floating-point real or complex array}
4670 \cvarg{dst}{The destination array, which size and type depends on the \texttt{flags}}
4671 \cvarg{flags}{The operation flags. See \cvCppCross{dft}}
4672 \cvarg{nonzeroRows}{The number of \texttt{dst} rows to compute.
4673 The rest of the rows will have undefined content.
4674 See the convolution sample in \cvCppCross{dft} description}
4677 \texttt{idft(src, dst, flags)} is equivalent to \texttt{dct(src, dst, flags | DFT\_INVERSE)}.
4678 See \cvCppCross{dft} for details.
4679 Note, that none of \texttt{dft} and \texttt{idft} scale the result by default.
4680 Thus, you should pass \texttt{DFT\_SCALE} to one of \texttt{dft} or \texttt{idft}
4681 explicitly to make these transforms mutually inverse.
4683 See also: \cvCppCross{dft}, \cvCppCross{dct}, \cvCppCross{idct}, \cvCppCross{mulSpectrums}, \cvCppCross{getOptimalDFTSize}
4687 Checks if array elements lie between the elements of two other arrays.
4689 \cvdefCpp{void inRange(const Mat\& src, const Mat\& lowerb,\par
4690 const Mat\& upperb, Mat\& dst);\newline
4691 void inRange(const Mat\& src, const Scalar\& lowerb,\par
4692 const Scalar\& upperb, Mat\& dst);\newline
4693 void inRange(const MatND\& src, const MatND\& lowerb,\par
4694 const MatND\& upperb, MatND\& dst);\newline
4695 void inRange(const MatND\& src, const Scalar\& lowerb,\par
4696 const Scalar\& upperb, MatND\& dst);}
4698 \cvarg{src}{The first source array}
4699 \cvarg{lowerb}{The inclusive lower boundary array of the same size and type as \texttt{src}}
4700 \cvarg{upperb}{The exclusive upper boundary array of the same size and type as \texttt{src}}
4701 \cvarg{dst}{The destination array, will have the same size as \texttt{src} and \texttt{CV\_8U} type}
4704 The functions \texttt{inRange} do the range check for every element of the input array:
4707 \texttt{dst}(I)=\texttt{lowerb}(I)_0 \leq \texttt{src}(I)_0 < \texttt{upperb}(I)_0
4710 for single-channel arrays,
4714 \texttt{lowerb}(I)_0 \leq \texttt{src}(I)_0 < \texttt{upperb}(I)_0 \land
4715 \texttt{lowerb}(I)_1 \leq \texttt{src}(I)_1 < \texttt{upperb}(I)_1
4718 for two-channel arrays and so forth.
4719 \texttt{dst}(I) is set to 255 (all \texttt{1}-bits) if \texttt{src}(I) is within the specified range and 0 otherwise.
4723 Finds the inverse or pseudo-inverse of a matrix
4725 \cvdefCpp{double invert(const Mat\& src, Mat\& dst, int method=DECOMP\_LU);}
4727 \cvarg{src}{The source floating-point $M \times N$ matrix}
4728 \cvarg{dst}{The destination matrix; will have $N \times M$ size and the same type as \texttt{src}}
4729 \cvarg{flags}{The inversion method :
4731 \cvarg{DECOMP\_LU}{Gaussian elimination with optimal pivot element chosen}
4732 \cvarg{DECOMP\_SVD}{Singular value decomposition (SVD) method}
4733 \cvarg{DECOMP\_CHOLESKY}{Cholesky decomposion. The matrix must be symmetrical and positively defined}
4737 The function \texttt{invert} inverts matrix \texttt{src} and stores the result in \texttt{dst}.
4738 When the matrix \texttt{src} is singular or non-square, the function computes the pseudo-inverse matrix, i.e. the matrix \texttt{dst}, such that $\|\texttt{src} \cdot \texttt{dst} - I\|$ is minimal.
4740 In the case of \texttt{DECOMP\_LU} method, the function returns the \texttt{src} determinant (\texttt{src} must be square). If it is 0, the matrix is not inverted and \texttt{dst} is filled with zeros.
4742 In the case of \texttt{DECOMP\_SVD} method, the function returns the inversed condition number of \texttt{src} (the ratio of the smallest singular value to the largest singular value) and 0 if \texttt{src} is singular. The SVD method calculates a pseudo-inverse matrix if \texttt{src} is singular.
4744 Similarly to \texttt{DECOMP\_LU}, the method \texttt{DECOMP\_CHOLESKY} works only with non-singular square matrices. In this case the function stores the inverted matrix in \texttt{dst} and returns non-zero, otherwise it returns 0.
4746 See also: \cvCppCross{solve}, \cvCppCross{SVD}
4750 Calculates the natural logarithm of every array element.
4752 \cvdefCpp{void log(const Mat\& src, Mat\& dst);\newline
4753 void log(const MatND\& src, MatND\& dst);}
4755 \cvarg{src}{The source array}
4756 \cvarg{dst}{The destination array; will have the same size and same type as \texttt{src}}
4759 The function \texttt{log} calculates the natural logarithm of the absolute value of every element of the input array:
4762 \texttt{dst}(I) = \fork
4763 {\log |\texttt{src}(I)|}{if $\texttt{src}(I) \ne 0$ }
4764 {\texttt{C}}{otherwise}
4767 Where \texttt{C} is a large negative number (about -700 in the current implementation).
4768 The maximum relative error is about $7 \times 10^{-6}$ for single-precision input and less than $10^{-10}$ for double-precision input. Special values (NaN, $\pm \infty$) are not handled.
4770 See also: \cvCppCross{exp}, \cvCppCross{cartToPolar}, \cvCppCross{polarToCart}, \cvCppCross{phase}, \cvCppCross{pow}, \cvCppCross{sqrt}, \cvCppCross{magnitude}
4774 Performs a look-up table transform of an array.
4776 \cvdefCpp{void LUT(const Mat\& src, const Mat\& lut, Mat\& dst);}
4778 \cvarg{src}{Source array of 8-bit elements}
4779 \cvarg{lut}{Look-up table of 256 elements. In the case of multi-channel source array, the table should either have a single channel (in this case the same table is used for all channels) or the same number of channels as in the source array}
4780 \cvarg{dst}{Destination array; will have the same size and the same number of channels as \texttt{src}, and the same depth as \texttt{lut}}
4783 The function \texttt{LUT} fills the destination array with values from the look-up table. Indices of the entries are taken from the source array. That is, the function processes each element of \texttt{src} as follows:
4786 \texttt{dst}(I) \leftarrow \texttt{lut(src(I) + d)}
4793 {0}{if \texttt{src} has depth \texttt{CV\_8U}}
4794 {128}{if \texttt{src} has depth \texttt{CV\_8S}}
4797 See also: \cvCppCross{convertScaleAbs}, \texttt{Mat::convertTo}
4799 \cvCppFunc{magnitude}
4800 Calculates magnitude of 2D vectors.
4802 \cvdefCpp{void magnitude(const Mat\& x, const Mat\& y, Mat\& magnitude);}
4804 \cvarg{x}{The floating-point array of x-coordinates of the vectors}
4805 \cvarg{y}{The floating-point array of y-coordinates of the vectors; must have the same size as \texttt{x}}
4806 \cvarg{dst}{The destination array; will have the same size and same type as \texttt{x}}
4809 The function \texttt{magnitude} calculates magnitude of 2D vectors formed from the corresponding elements of \texttt{x} and \texttt{y} arrays:
4812 \texttt{dst}(I) = \sqrt{\texttt{x}(I)^2 + \texttt{y}(I)^2}
4815 See also: \cvCppCross{cartToPolar}, \cvCppCross{polarToCart}, \cvCppCross{phase}, \cvCppCross{sqrt}
4818 \cvCppFunc{Mahalanobis}
4819 Calculates the Mahalanobis distance between two vectors.
4821 \cvdefCpp{double Mahalanobis(const Mat\& vec1, const Mat\& vec2, \par const Mat\& icovar);}
4823 \cvarg{vec1}{The first 1D source vector}
4824 \cvarg{vec2}{The second 1D source vector}
4825 \cvarg{icovar}{The inverse covariance matrix}
4828 The function \texttt{cvMahalonobis} calculates and returns the weighted distance between two vectors:
4831 d(\texttt{vec1},\texttt{vec2})=\sqrt{\sum_{i,j}{\texttt{icovar(i,j)}\cdot(\texttt{vec1}(I)-\texttt{vec2}(I))\cdot(\texttt{vec1(j)}-\texttt{vec2(j)})}}
4834 The covariance matrix may be calculated using the \cvCppCross{calcCovarMatrix} function and then inverted using the \cvCppCross{invert} function (preferably using DECOMP\_SVD method, as the most accurate).
4838 Calculates per-element maximum of two arrays or array and a scalar
4840 \cvdefCpp{Mat\_Expr<...> max(const Mat\& src1, const Mat\& src2);\newline
4841 Mat\_Expr<...> max(const Mat\& src1, double value);\newline
4842 Mat\_Expr<...> max(double value, const Mat\& src1);\newline
4843 void max(const Mat\& src1, const Mat\& src2, Mat\& dst);\newline
4844 void max(const Mat\& src1, double value, Mat\& dst);\newline
4845 void max(const MatND\& src1, const MatND\& src2, MatND\& dst);\newline
4846 void max(const MatND\& src1, double value, MatND\& dst);}
4848 \cvarg{src1}{The first source array}
4849 \cvarg{src2}{The second source array of the same size and type as \texttt{src1}}
4850 \cvarg{value}{The real scalar value}
4851 \cvarg{dst}{The destination array; will have the same size and type as \texttt{src1}}
4854 The functions \texttt{max} compute per-element maximum of two arrays:
4855 \[\texttt{dst}(I)=\max(\texttt{src1}(I), \texttt{src2}(I))\]
4856 or array and a scalar:
4857 \[\texttt{dst}(I)=\max(\texttt{src1}(I), \texttt{value})\]
4859 In the second variant, when the source array is multi-channel, each channel is compared with \texttt{value} independently.
4861 The first 3 variants of the function listed above are actually a part of \cross{Matrix Expressions}, they return the expression object that can be further transformed, or assigned to a matrix, or passed to a function etc.
4863 See also: \cvCppCross{min}, \cvCppCross{compare}, \cvCppCross{inRange}, \cvCppCross{minMaxLoc}, \cross{Matrix Expressions}
4866 Calculates average (mean) of array elements
4868 \cvdefCpp{Scalar mean(const Mat\& mtx);\newline
4869 Scalar mean(const Mat\& mtx, const Mat\& mask);\newline
4870 Scalar mean(const MatND\& mtx);\newline
4871 Scalar mean(const MatND\& mtx, const MatND\& mask);}
4873 \cvarg{mtx}{The source array; it should have 1 to 4 channels (so that the result can be stored in \cvCppCross{Scalar})}
4874 \cvarg{mask}{The optional operation mask}
4877 The functions \texttt{mean} compute mean value \texttt{M} of array elements, independently for each channel, and return it:
4881 N = \sum_{I:\;\texttt{mask}(I)\ne 0} 1\\
4882 M_c = \left(\sum_{I:\;\texttt{mask}(I)\ne 0}{\texttt{mtx}(I)_c}\right)/N
4886 When all the mask elements are 0's, the functions return \texttt{Scalar::all(0)}.
4888 See also: \cvCppCross{countNonZero}, \cvCppCross{meanStdDev}, \cvCppCross{norm}, \cvCppCross{minMaxLoc}
4890 \cvCppFunc{meanStdDev}
4891 Calculates mean and standard deviation of array elements
4893 \cvdefCpp{void meanStdDev(const Mat\& mtx, Scalar\& mean, \par Scalar\& stddev, const Mat\& mask=Mat());\newline
4894 void meanStdDev(const MatND\& mtx, Scalar\& mean, \par Scalar\& stddev, const MatND\& mask=MatND());}
4896 \cvarg{mtx}{The source array; it should have 1 to 4 channels (so that the results can be stored in \cvCppCross{Scalar}'s)}
4897 \cvarg{mean}{The output parameter: computed mean value}
4898 \cvarg{stddev}{The output parameter: computed standard deviation}
4899 \cvarg{mask}{The optional operation mask}
4902 The functions \texttt{meanStdDev} compute the mean and the standard deviation \texttt{M} of array elements, independently for each channel, and return it via the output parameters:
4906 N = \sum_{I, \texttt{mask}(I) \ne 0} 1\\
4907 \texttt{mean}_c = \frac{\sum_{ I: \; \texttt{mask}(I) \ne 0} \texttt{src}(I)_c}{N}\\
4908 \texttt{stddev}_c = \sqrt{\sum_{ I: \; \texttt{mask}(I) \ne 0} \left(\texttt{src}(I)_c - \texttt{mean}_c\right)^2}
4912 When all the mask elements are 0's, the functions return \texttt{mean=stddev=Scalar::all(0)}.
4913 Note that the computed standard deviation is only the diagonal of the complete normalized covariance matrix. If the full matrix is needed, you can reshape the multi-channel array $M \times N$ to the single-channel array $M*N \times \texttt{mtx.channels}()$ (only possible when the matrix is continuous) and then pass the matrix to \cvCppCross{calcCovarMatrix}.
4915 See also: \cvCppCross{countNonZero}, \cvCppCross{mean}, \cvCppCross{norm}, \cvCppCross{minMaxLoc}, \cvCppCross{calcCovarMatrix}
4919 Composes a multi-channel array from several single-channel arrays.
4921 \cvdefCpp{void merge(const Mat* mv, size\_t count, Mat\& dst);\newline
4922 void merge(const vector<Mat>\& mv, Mat\& dst);\newline
4923 void merge(const MatND* mv, size\_t count, MatND\& dst);\newline
4924 void merge(const vector<MatND>\& mv, MatND\& dst);}
4926 \cvarg{mv}{The source array or vector of the single-channel matrices to be merged. All the matrices in \texttt{mv} must have the same size and the same type}
4927 \cvarg{count}{The number of source matrices when \texttt{mv} is a plain C array; must be greater than zero}
4928 \cvarg{dst}{The destination array; will have the same size and the same depth as \texttt{mv[0]}, the number of channels will match the number of source matrices}
4931 The functions \texttt{merge} merge several single-channel arrays (or rather interleave their elements) to make a single multi-channel array.
4933 \[\texttt{dst}(I)_c = \texttt{mv}[c](I)\]
4935 The function \cvCppCross{split} does the reverse operation and if you need to merge several multi-channel images or shuffle channels in some other advanced way, use \cvCppCross{mixChannels}
4937 See also: \cvCppCross{mixChannels}, \cvCppCross{split}, \cvCppCross{reshape}
4940 Calculates per-element minimum of two arrays or array and a scalar
4942 \cvdefCpp{Mat\_Expr<...> min(const Mat\& src1, const Mat\& src2);\newline
4943 Mat\_Expr<...> min(const Mat\& src1, double value);\newline
4944 Mat\_Expr<...> min(double value, const Mat\& src1);\newline
4945 void min(const Mat\& src1, const Mat\& src2, Mat\& dst);\newline
4946 void min(const Mat\& src1, double value, Mat\& dst);\newline
4947 void min(const MatND\& src1, const MatND\& src2, MatND\& dst);\newline
4948 void min(const MatND\& src1, double value, MatND\& dst);}
4950 \cvarg{src1}{The first source array}
4951 \cvarg{src2}{The second source array of the same size and type as \texttt{src1}}
4952 \cvarg{value}{The real scalar value}
4953 \cvarg{dst}{The destination array; will have the same size and type as \texttt{src1}}
4956 The functions \texttt{min} compute per-element minimum of two arrays:
4957 \[\texttt{dst}(I)=\min(\texttt{src1}(I), \texttt{src2}(I))\]
4958 or array and a scalar:
4959 \[\texttt{dst}(I)=\min(\texttt{src1}(I), \texttt{value})\]
4961 In the second variant, when the source array is multi-channel, each channel is compared with \texttt{value} independently.
4963 The first 3 variants of the function listed above are actually a part of \cross{Matrix Expressions}, they return the expression object that can be further transformed, or assigned to a matrix, or passed to a function etc.
4965 See also: \cvCppCross{max}, \cvCppCross{compare}, \cvCppCross{inRange}, \cvCppCross{minMaxLoc}, \cross{Matrix Expressions}
4967 \cvCppFunc{minMaxLoc}
4968 Finds global minimum and maximum in a whole array or sub-array
4970 \cvdefCpp{void minMaxLoc(const Mat\& src, double* minVal,\par
4971 double* maxVal=0, Point* minLoc=0,\par
4972 Point* maxLoc=0, const Mat\& mask=Mat());\newline
4973 void minMaxLoc(const MatND\& src, double* minVal,\par
4974 double* maxVal, int* minIdx=0, int* maxIdx=0,\par
4975 const MatND\& mask=MatND());\newline
4976 void minMaxLoc(const SparseMat\& src, double* minVal,\par
4977 double* maxVal, int* minIdx=0, int* maxIdx=0);}
4979 \cvarg{src}{The source single-channel array}
4980 \cvarg{minVal}{Pointer to returned minimum value; \texttt{NULL} if not required}
4981 \cvarg{maxVal}{Pointer to returned maximum value; \texttt{NULL} if not required}
4982 \cvarg{minLoc}{Pointer to returned minimum location (in 2D case); \texttt{NULL} if not required}
4983 \cvarg{maxLoc}{Pointer to returned maximum location (in 2D case); \texttt{NULL} if not required}
4984 \cvarg{minIdx}{Pointer to returned minimum location (in nD case);
4985 \texttt{NULL} if not required, otherwise must point to an array of \texttt{src.dims} elements and the coordinates of minimum element in each dimensions will be stored sequentially there.}
4986 \cvarg{maxIdx}{Pointer to returned maximum location (in nD case); \texttt{NULL} if not required}
4987 \cvarg{mask}{The optional mask used to select a sub-array}
4990 The functions \texttt{ninMaxLoc} find minimum and maximum element values
4991 and their positions. The extremums are searched across the whole array, or,
4992 if \texttt{mask} is not an empty array, in the specified array region.
4994 The functions do not work with multi-channel arrays. If you need to find minimum or maximum elements across all the channels, use \cvCppCross{reshape} first to reinterpret the array as single-channel. Or you may extract the particular channel using \cvCppCross{extractImageCOI} or \cvCppCross{mixChannels} or \cvCppCross{split}.
4996 in the case of a sparse matrix the minimum is found among non-zero elements only.
4998 See also: \cvCppCross{max}, \cvCppCross{min}, \cvCppCross{compare}, \cvCppCross{inRange}, \cvCppCross{extractImageCOI}, \cvCppCross{mixChannels}, \cvCppCross{split}, \cvCppCross{reshape}.
5000 \cvCppFunc{mixChannels}
5001 Copies specified channels from input arrays to the specified channels of output arrays
5003 \cvdefCpp{void mixChannels(const Mat* srcv, int nsrc, Mat* dstv, int ndst,\par
5004 const int* fromTo, size\_t npairs);\newline
5005 void mixChannels(const MatND* srcv, int nsrc, MatND* dstv, int ndst,\par
5006 const int* fromTo, size\_t npairs);\newline
5007 void mixChannels(const vector<Mat>\& srcv, vector<Mat>\& dstv,\par
5008 const int* fromTo, int npairs);\newline
5009 void mixChannels(const vector<MatND>\& srcv, vector<MatND>\& dstv,\par
5010 const int* fromTo, int npairs);}
5012 \cvarg{srcv}{The input array or vector of matrices.
5013 All the matrices must have the same size and the same depth}
5014 \cvarg{nsrc}{The number of elements in \texttt{srcv}}
5015 \cvarg{dstv}{The output array or vector of matrices.
5016 All the matrices \emph{must be allocated}, their size and depth must be the same as in \texttt{srcv[0]}}
5017 \cvarg{ndst}{The number of elements in \texttt{dstv}}
5018 \cvarg{fromTo}{The array of index pairs, specifying which channels are copied and where.
5019 \texttt{fromTo[k*2]} is the 0-based index of the input channel in \texttt{srcv} and
5020 \texttt{fromTo[k*2+1]} is the index of the output channel in \texttt{dstv}. Here the continuous channel numbering is used, that is,
5021 the first input image channels are indexed from \texttt{0} to \texttt{srcv[0].channels()-1},
5022 the second input image channels are indexed from \texttt{srcv[0].channels()} to
5023 \texttt{srcv[0].channels() + srcv[1].channels()-1} etc., and the same scheme is used for the output image channels.
5024 As a special case, when \texttt{fromTo[k*2]} is negative, the corresponding output channel is filled with zero.
5026 \texttt{npairs}{The number of pairs. In the latter case the parameter is not passed explicitly, but computed as \texttt{srcv.size()} (=\texttt{dstv.size()})}
5029 The functions \texttt{mixChannels} provide an advanced mechanism for shuffling image channels. \cvCppCross{split} and \cvCppCross{merge} and some forms of \cvCppCross{cvtColor} are partial cases of \texttt{mixChannels}.
5031 As an example, this code splits a 4-channel RGBA image into a 3-channel
5032 BGR (i.e. with R and B channels swapped) and separate alpha channel image:
5035 Mat rgba( 100, 100, CV_8UC4, Scalar(1,2,3,4) );
5036 Mat bgr( rgba.rows, rgba.cols, CV_8UC3 );
5037 Mat alpha( rgba.rows, rgba.cols, CV_8UC1 );
5039 // forming array of matrices is quite efficient operations,
5040 // because the matrix data is not copied, only the headers
5041 Mat out[] = { bgr, alpha };
5042 // rgba[0] -> bgr[2], rgba[1] -> bgr[1],
5043 // rgba[2] -> bgr[0], rgba[3] -> alpha[0]
5044 int from_to[] = { 0,2, 1,1, 2,0, 3,3 };
5045 mixChannels( &rgba, 1, out, 2, from_to, 4 );
5048 Note that, unlike many other new-style C++ functions in OpenCV (see the introduction section and \cvCppCross{Mat::create}),
5049 \texttt{mixChannels} requires the destination arrays be pre-allocated before calling the function.
5051 See also: \cvCppCross{split}, \cvCppCross{merge}, \cvCppCross{cvtColor}
5054 \cvCppFunc{mulSpectrums}
5055 Performs per-element multiplication of two Fourier spectrums.
5057 \cvdefCpp{void mulSpectrums(const Mat\& src1, const Mat\& src2, Mat\& dst,\par
5058 int flags, bool conj=false);}
5060 \cvarg{src1}{The first source array}
5061 \cvarg{src2}{The second source array; must have the same size and the same type as \texttt{src1}}
5062 \cvarg{dst}{The destination array; will have the same size and the same type as \texttt{src1}}
5063 \cvarg{flags}{The same flags as passed to \cvCppCross{dft}; only the flag \texttt{DFT\_ROWS} is checked for}
5064 \cvarg{conj}{The optional flag that conjugate the second source array before the multiplication (true) or not (false)}
5067 The function \texttt{mulSpectrums} performs per-element multiplication of the two CCS-packed or complex matrices that are results of a real or complex Fourier transform.
5069 The function, together with \cvCppCross{dft} and \cvCppCross{idft}, may be used to calculate convolution (pass \texttt{conj=false}) or correlation (pass \texttt{conj=false}) of two arrays rapidly. When the arrays are complex, they are simply multiplied (per-element) with optional conjugation of the second array elements. When the arrays are real, they assumed to be CCS-packed (see \cvCppCross{dft} for details).
5071 \cvCppFunc{multiply}
5072 Calculates the per-element scaled product of two arrays
5074 \cvdefCpp{void multiply(const Mat\& src1, const Mat\& src2, \par Mat\& dst, double scale=1);\newline
5075 void multiply(const MatND\& src1, const MatND\& src2, \par MatND\& dst, double scale=1);}
5077 \cvarg{src1}{The first source array}
5078 \cvarg{src2}{The second source array of the same size and the same type as \texttt{src1}}
5079 \cvarg{dst}{The destination array; will have the same size and the same type as \texttt{src1}}
5080 \cvarg{scale}{The optional scale factor}
5083 The function \texttt{multiply} calculates the per-element product of two arrays:
5086 \texttt{dst}(I)=\texttt{saturate}(\texttt{scale} \cdot \texttt{src1}(I) \cdot \texttt{src2}(I))
5089 There is also \cross{Matrix Expressions}-friendly variant of the first function, see \cvCppCross{Mat::mul}.
5091 If you are looking for a matrix product, not per-element product, see \cvCppCross{gemm}.
5093 See also: \cvCppCross{add}, \cvCppCross{substract}, \cvCppCross{divide}, \cross{Matrix Expressions}, \cvCppCross{scaleAdd}, \cvCppCross{addWeighted}, \cvCppCross{accumulate}, \cvCppCross{accumulateProduct}, \cvCppCross{accumulateSquare}, \cvCppCross{Mat::convertTo}
5095 \cvCppFunc{mulTransposed}
5096 Calculates the product of a matrix and its transposition.
5098 \cvdefCpp{void mulTransposed( const Mat\& src, Mat\& dst, bool aTa,\par
5099 const Mat\& delta=Mat(),\par
5100 double scale=1, int rtype=-1 );}
5102 \cvarg{src}{The source matrix}
5103 \cvarg{dst}{The destination square matrix}
5104 \cvarg{aTa}{Specifies the multiplication ordering; see the description below}
5105 \cvarg{delta}{The optional delta matrix, subtracted from \texttt{src} before the multiplication. When the matrix is empty (\texttt{delta=Mat()}), it's assumed to be zero, i.e. nothing is subtracted, otherwise if it has the same size as \texttt{src}, then it's simply subtracted, otherwise it is "repeated" (see \cvCppCross{repeat}) to cover the full \texttt{src} and then subtracted. Type of the delta matrix, when it's not empty, must be the same as the type of created destination matrix, see the \texttt{rtype} description}
5106 \cvarg{scale}{The optional scale factor for the matrix product}
5107 \cvarg{rtype}{When it's negative, the destination matrix will have the same type as \texttt{src}. Otherwise, it will have \texttt{type=CV\_MAT\_DEPTH(rtype)}, which should be either \texttt{CV\_32F} or \texttt{CV\_64F}}
5110 The function \texttt{mulTransposed} calculates the product of \texttt{src} and its transposition:
5112 \texttt{dst}=\texttt{scale} (\texttt{src}-\texttt{delta})^T (\texttt{src}-\texttt{delta})
5114 if \texttt{aTa=true}, and
5117 \texttt{dst}=\texttt{scale} (\texttt{src}-\texttt{delta}) (\texttt{src}-\texttt{delta})^T
5120 otherwise. The function is used to compute covariance matrix and with zero delta can be used as a faster substitute for general matrix product $A*B$ when $B=A^T$.
5122 See also: \cvCppCross{calcCovarMatrix}, \cvCppCross{gemm}, \cvCppCross{repeat}, \cvCppCross{reduce}
5126 Calculates absolute array norm, absolute difference norm, or relative difference norm.
5128 \cvdefCpp{double norm(const Mat\& src1, int normType=NORM\_L2);\newline
5129 double norm(const Mat\& src1, const Mat\& src2, int normType=NORM\_L2);\newline
5130 double norm(const Mat\& src1, int normType, const Mat\& mask);\newline
5131 double norm(const Mat\& src1, const Mat\& src2, \par int normType, const Mat\& mask);\newline
5132 double norm(const MatND\& src1, int normType=NORM\_L2, \par const MatND\& mask=MatND());\newline
5133 double norm(const MatND\& src1, const MatND\& src2,\par
5134 int normType=NORM\_L2, const MatND\& mask=MatND());\newline
5135 double norm( const SparseMat\& src, int normType );}
5137 \cvarg{src1}{The first source array}
5138 \cvarg{src2}{The second source array of the same size and the same type as \texttt{src1}}
5139 \cvarg{normType}{Type of the norm; see the discussion below}
5140 \cvarg{mask}{The optional operation mask}
5143 The functions \texttt{norm} calculate the absolute norm of \texttt{src1} (when there is no \texttt{src2}):
5146 {\|\texttt{src1}\|_{L_{\infty}} = \max_I |\texttt{src1}(I)|}{if $\texttt{normType} = \texttt{NORM\_INF}$}
5147 {\|\texttt{src1}\|_{L_1} = \sum_I |\texttt{src1}(I)|}{if $\texttt{normType} = \texttt{NORM\_L1}$}
5148 {\|\texttt{src1}\|_{L_2} = \sqrt{\sum_I \texttt{src1}(I)^2}}{if $\texttt{normType} = \texttt{NORM\_L2}$}
5151 or an absolute or relative difference norm if \texttt{src2} is there:
5154 {\|\texttt{src1}-\texttt{src2}\|_{L_{\infty}} = \max_I |\texttt{src1}(I) - \texttt{src2}(I)|}{if $\texttt{normType} = \texttt{NORM\_INF}$}
5155 {\|\texttt{src1}-\texttt{src2}\|_{L_1} = \sum_I |\texttt{src1}(I) - \texttt{src2}(I)|}{if $\texttt{normType} = \texttt{NORM\_L1}$}
5156 {\|\texttt{src1}-\texttt{src2}\|_{L_2} = \sqrt{\sum_I (\texttt{src1}(I) - \texttt{src2}(I))^2}}{if $\texttt{normType} = \texttt{NORM\_L2}$}
5163 {\frac{\|\texttt{src1}-\texttt{src2}\|_{L_{\infty}} }{\|\texttt{src2}\|_{L_{\infty}} }}{if $\texttt{normType} = \texttt{NORM\_RELATIVE\_INF}$}
5164 {\frac{\|\texttt{src1}-\texttt{src2}\|_{L_1} }{\|\texttt{src2}\|_{L_1}}}{if $\texttt{normType} = \texttt{NORM\_RELATIVE\_L1}$}
5165 {\frac{\|\texttt{src1}-\texttt{src2}\|_{L_2} }{\|\texttt{src2}\|_{L_2}}}{if $\texttt{normType} = \texttt{NORM\_RELATIVE\_L2}$}
5168 The functions \texttt{norm} return the calculated norm.
5170 When there is \texttt{mask} parameter, and it is not empty (then it should have type \texttt{CV\_8U} and the same size as \texttt{src1}), the norm is computed only over the specified by the mask region.
5172 A multiple-channel source arrays are treated as a single-channel, that is, the results for all channels are combined.
5175 \cvCppFunc{normalize}
5176 Normalizes array's norm or the range
5178 \cvdefCpp{void normalize( const Mat\& src, Mat\& dst, \par double alpha=1, double beta=0,\par
5179 int normType=NORM\_L2, int rtype=-1, \par const Mat\& mask=Mat());\newline
5180 void normalize( const MatND\& src, MatND\& dst, \par double alpha=1, double beta=0,\par
5181 int normType=NORM\_L2, int rtype=-1, \par const MatND\& mask=MatND());\newline
5182 void normalize( const SparseMat\& src, SparseMat\& dst, \par double alpha, int normType );}
5184 \cvarg{src}{The source array}
5185 \cvarg{dst}{The destination array; will have the same size as \texttt{src}}
5186 \cvarg{alpha}{The norm value to normalize to or the lower range boundary in the case of range normalization}
5187 \cvarg{beta}{The upper range boundary in the case of range normalization; not used for norm normalization}
5188 \cvarg{normType}{The normalization type, see the discussion}
5189 \cvarg{rtype}{When the parameter is negative, the destination array will have the same type as \texttt{src}, otherwise it will have the same number of channels as \texttt{src} and the depth\texttt{=CV\_MAT\_DEPTH(rtype)}}
5190 \cvarg{mask}{The optional operation mask}
5193 The functions \texttt{normalize} scale and shift the source array elements, so that
5194 \[\|\texttt{dst}\|_{L_p}=\texttt{alpha}\]
5195 (where $p=\infty$, 1 or 2) when \texttt{normType=NORM\_INF}, \texttt{NORM\_L1} or \texttt{NORM\_L2},
5197 \[\min_I \texttt{dst}(I)=\texttt{alpha},\,\,\max_I \texttt{dst}(I)=\texttt{beta}\]
5198 when \texttt{normType=NORM\_MINMAX} (for dense arrays only).
5200 The optional mask specifies the sub-array to be normalize, that is, the norm or min-n-max are computed over the sub-array and then this sub-array is modified to be normalized. If you want to only use the mask to compute the norm or min-max, but modify the whole array, you can use \cvCppCross{norm} and \cvCppCross{Mat::convertScale}/\cvCppCross{MatND::convertScale}/cross{SparseMat::convertScale} separately.
5202 in the case of sparse matrices, only the non-zero values are analyzed and transformed. Because of this, the range transformation for sparse matrices is not allowed, since it can shift the zero level.
5204 See also: \cvCppCross{norm}, \cvCppCross{Mat::convertScale}, \cvCppCross{MatND::convertScale}, \cvCppCross{SparseMat::convertScale}
5208 Class for Principal Component Analysis
5214 // default constructor
5216 // computes PCA for a set of vectors stored as data rows or columns.
5217 PCA(const Mat& data, const Mat& mean, int flags, int maxComponents=0);newline
5218 // computes PCA for a set of vectors stored as data rows or columns
5219 PCA& operator()(const Mat& data, const Mat& mean, int flags, int maxComponents=0);newline
5220 // projects vector into the principal components space
5221 Mat project(const Mat& vec) const;newline
5222 void project(const Mat& vec, Mat& result) const;newline
5223 // reconstructs the vector from its PC projection
5224 Mat backProject(const Mat& vec) const;newline
5225 void backProject(const Mat& vec, Mat& result) const;newline
5227 // eigenvectors of the PC space, stored as the matrix rows
5228 Mat eigenvectors;newline
5229 // the corresponding eigenvalues; not used for PCA compression/decompression
5230 Mat eigenvalues;newline
5231 // mean vector, subtracted from the projected vector
5232 // or added to the reconstructed vector
5237 The class \texttt{PCA} is used to compute the special basis for a set of vectors. The basis will consist of eigenvectors of the covariance matrix computed from the input set of vectors. And also the class \texttt{PCA} can transform vectors to/from the new coordinate space, defined by the basis. Usually, in this new coordinate system each vector from the original set (and any linear combination of such vectors) can be quite accurately approximated by taking just the first few its components, corresponding to the eigenvectors of the largest eigenvalues of the covariance matrix. Geometrically it means that we compute projection of the vector to a subspace formed by a few eigenvectors corresponding to the dominant eigenvalues of the covariation matrix. And usually such a projection is very close to the original vector. That is, we can represent the original vector from a high-dimensional space with a much shorter vector consisting of the projected vector's coordinates in the subspace. Such a transformation is also known as Karhunen-Loeve Transform, or KLT. See \url{http://en.wikipedia.org/wiki/Principal\_component\_analysis}
5239 The following sample is the function that takes two matrices. The first one stores the set of vectors (a row per vector) that is used to compute PCA, the second one stores another "test" set of vectors (a row per vector) that are first compressed with PCA, then reconstructed back and then the reconstruction error norm is computed and printed for each vector.
5241 PCA compressPCA(const Mat& pcaset, int maxComponents,
5242 const Mat& testset, Mat& compressed)
5244 PCA pca(pcaset, // pass the data
5245 Mat(), // we do not have a pre-computed mean vector,
5246 // so let the PCA engine to compute it
5247 CV_PCA_DATA_AS_ROW, // indicate that the vectors
5248 // are stored as matrix rows
5249 // (use CV_PCA_DATA_AS_COL if the vectors are
5250 // the matrix columns)
5251 maxComponents // specify, how many principal components to retain
5253 // if there is no test data, just return the computed basis, ready-to-use
5256 CV_Assert( testset.cols == pcaset.cols );
5258 compressed.create(testset.rows, maxComponents, testset.type());
5261 for( int i = 0; i < testset.rows; i++ )
5263 Mat vec = testset.row(i), coeffs = compressed.row(i);
5264 // compress the vector, the result will be stored
5265 // in the i-th row of the output matrix
5266 pca.project(vec, coeffs);
5267 // and then reconstruct it
5268 pca.backProject(coeffs, reconstructed);
5269 // and measure the error
5270 printf("%d. diff = %g\n", i, norm(vec, reconstructed, NORM_L2));
5276 See also: \cvCppCross{calcCovarMatrix}, \cvCppCross{mulTransposed}, \cvCppCross{SVD}, \cvCppCross{dft}, \cvCppCross{dct}
5278 \cvCppFunc{perspectiveTransform}
5279 Performs perspective matrix transformation of vectors.
5281 \cvdefCpp{void perspectiveTransform(const Mat\& src, \par Mat\& dst, const Mat\& mtx );}
5283 \cvarg{src}{The source two-channel or three-channel floating-point array;
5284 each element is 2D/3D vector to be transformed}
5285 \cvarg{dst}{The destination array; it will have the same size and same type as \texttt{src}}
5286 \cvarg{mtx}{$3\times 3$ or $4 \times 4$ transformation matrix}
5289 The function \texttt{perspectiveTransform} transforms every element of \texttt{src},
5290 by treating it as 2D or 3D vector, in the following way (here 3D vector transformation is shown; in the case of 2D vector transformation the $z$ component is omitted):
5292 \[ (x, y, z) \rightarrow (x'/w, y'/w, z'/w) \]
5297 (x', y', z', w') = \texttt{mat} \cdot
5298 \begin{bmatrix} x & y & z & 1 \end{bmatrix}
5302 \[ w = \fork{w'}{if $w' \ne 0$}{\infty}{otherwise} \]
5304 Note that the function transforms a sparse set of 2D or 3D vectors. If you want to transform an image using perspective transformation, use \cvCppCross{warpPerspective}. If you have an inverse task, i.e. want to compute the most probable perspective transformation out of several pairs of corresponding points, you can use \cvCppCross{getPerspectiveTransform} or \cvCppCross{findHomography}.
5306 See also: \cvCppCross{transform}, \cvCppCross{warpPerspective}, \cvCppCross{getPerspectiveTransform}, \cvCppCross{findHomography}
5309 Calculates the rotation angle of 2d vectors
5311 \cvdefCpp{void phase(const Mat\& x, const Mat\& y, Mat\& angle,\par
5312 bool angleInDegrees=false);}
5314 \cvarg{x}{The source floating-point array of x-coordinates of 2D vectors}
5315 \cvarg{y}{The source array of y-coordinates of 2D vectors; must have the same size and the same type as \texttt{x}}
5316 \cvarg{angle}{The destination array of vector angles; it will have the same size and same type as \texttt{x}}
5317 \cvarg{angleInDegrees}{When it is true, the function will compute angle in degrees, otherwise they will be measured in radians}
5320 The function \texttt{phase} computes the rotation angle of each 2D vector that is formed from the corresponding elements of \texttt{x} and \texttt{y}:
5322 \[\texttt{angle}(I) = \texttt{atan2}(\texttt{y}(I), \texttt{x}(I))\]
5324 The angle estimation accuracy is $\sim\,0.3^\circ$, when \texttt{x(I)=y(I)=0}, the corresponding \texttt{angle}(I) is set to $0$.
5328 \cvCppFunc{polarToCart}
5329 Computes x and y coordinates of 2D vectors from their magnitude and angle.
5331 \cvdefCpp{void polarToCart(const Mat\& magnitude, const Mat\& angle,\par
5332 Mat\& x, Mat\& y, bool angleInDegrees=false);}
5334 \cvarg{magnitude}{The source floating-point array of magnitudes of 2D vectors. It can be an empty matrix (\texttt{=Mat()}) - in this case the function assumes that all the magnitudes are =1. If it's not empty, it must have the same size and same type as \texttt{angle}}
5335 \cvarg{angle}{The source floating-point array of angles of the 2D vectors}
5336 \cvarg{x}{The destination array of x-coordinates of 2D vectors; will have the same size and the same type as \texttt{angle}}
5337 \cvarg{y}{The destination array of y-coordinates of 2D vectors; will have the same size and the same type as \texttt{angle}}
5338 \cvarg{angleInDegrees}{When it is true, the input angles are measured in degrees, otherwise they are measured in radians}
5341 The function \texttt{polarToCart} computes the cartesian coordinates of each 2D vector represented by the corresponding elements of \texttt{magnitude} and \texttt{angle}:
5345 \texttt{x}(I) = \texttt{magnitude}(I)\cos(\texttt{angle}(I))\\
5346 \texttt{y}(I) = \texttt{magnitude}(I)\sin(\texttt{angle}(I))\\
5350 The relative accuracy of the estimated coordinates is $\sim\,10^{-6}$.
5352 See also: \cvCppCross{cartToPolar}, \cvCppCross{magnitude}, \cvCppCross{phase}, \cvCppCross{exp}, \cvCppCross{log}, \cvCppCross{pow}, \cvCppCross{sqrt}
5355 Raises every array element to a power.
5357 \cvdefCpp{void pow(const Mat\& src, double p, Mat\& dst);\newline
5358 void pow(const MatND\& src, double p, MatND\& dst);}
5360 \cvarg{src}{The source array}
5361 \cvarg{p}{The exponent of power}
5362 \cvarg{dst}{The destination array; will have the same size and the same type as \texttt{src}}
5365 The function \texttt{pow} raises every element of the input array to \texttt{p}:
5368 \texttt{dst}(I) = \fork
5369 {\texttt{src}(I)^p}{if \texttt{p} is integer}
5370 {|\texttt{src}(I)|^p}{otherwise}
5373 That is, for a non-integer power exponent the absolute values of input array elements are used. However, it is possible to get true values for negative values using some extra operations, as the following example, computing the 5th root of array \texttt{src}, shows:
5377 pow(src, 1./5, dst);
5378 subtract(Scalar::all(0), dst, dst, mask);
5381 For some values of \texttt{p}, such as integer values, 0.5, and -0.5, specialized faster algorithms are used.
5383 See also: \cvCppCross{sqrt}, \cvCppCross{exp}, \cvCppCross{log}, \cvCppCross{cartToPolar}, \cvCppCross{polarToCart}
5386 Generates a single uniformly-distributed random number or array of random numbers
5388 \cvdefCpp{template<typename \_Tp> \_Tp randu();\newline
5389 void randu(Mat\& mtx, const Scalar\& low, const Scalar\& high);}
5391 \cvarg{mtx}{The output array of random numbers. The array must be pre-allocated and have 1 to 4 channels}
5392 \cvarg{low}{The inclusive lower boundary of the generated random numbers}
5393 \cvarg{high}{The exclusive upper boundary of the generated random numbers}
5396 The template functions \texttt{randu} generate and return the next uniformly-distributed random value of the specified type. \texttt{randu<int>()} is equivalent to \texttt{(int)theRNG();} etc. See \cvCppCross{RNG} description.
5398 The second non-template variant of the function fills the matrix \texttt{mtx} with uniformly-distributed random numbers from the specified range:
5400 \[\texttt{low}_c \leq \texttt{mtx}(I)_c < \texttt{high}_c\]
5402 See also: \cvCppCross{RNG}, \cvCppCross{randn}, \cvCppCross{theRNG}.
5405 Fills array with normally distributed random numbers
5407 \cvdefCpp{void randn(Mat\& mtx, const Scalar\& mean, const Scalar\& stddev);}
5409 \cvarg{mtx}{The output array of random numbers. The array must be pre-allocated and have 1 to 4 channels}
5410 \cvarg{mean}{The mean value (expectation) of the generated random numbers}
5411 \cvarg{stddev}{The standard deviation of the generated random numbers}
5414 The function \texttt{randn} fills the matrix \texttt{mtx} with normally distributed random numbers with the specified mean and standard deviation. \hyperref[cppfunc.saturatecast]{saturate\_cast} is applied to the generated numbers (i.e. the values are clipped)
5416 See also: \cvCppCross{RNG}, \cvCppCross{randu}
5418 \cvCppFunc{randShuffle}
5419 Shuffles the array elements randomly
5421 \cvdefCpp{void randShuffle(Mat\& mtx, double iterFactor=1., RNG* rng=0);}
5423 \cvarg{mtx}{The input/output numerical 1D array}
5424 \cvarg{iterFactor}{The scale factor that determines the number of random swap operations. See the discussion}
5425 \cvarg{rng}{The optional random number generator used for shuffling. If it is zero, \cvCppCross{theRNG}() is used instead}
5428 The function \texttt{randShuffle} shuffles the specified 1D array by randomly choosing pairs of elements and swapping them. The number of such swap operations will be \texttt{mtx.rows*mtx.cols*iterFactor}
5430 See also: \cvCppCross{RNG}, \cvCppCross{sort}
5433 Reduces a matrix to a vector
5435 \cvdefCpp{void reduce(const Mat\& mtx, Mat\& vec, \par int dim, int reduceOp, int dtype=-1);}
5437 \cvarg{mtx}{The source 2D matrix}
5438 \cvarg{vec}{The destination vector. Its size and type is defined by \texttt{dim} and \texttt{dtype} parameters}
5439 \cvarg{dim}{The dimension index along which the matrix is reduced. 0 means that the matrix is reduced to a single row and 1 means that the matrix is reduced to a single column}
5440 \cvarg{reduceOp}{The reduction operation, one of:
5442 \cvarg{CV\_REDUCE\_SUM}{The output is the sum of all of the matrix's rows/columns.}
5443 \cvarg{CV\_REDUCE\_AVG}{The output is the mean vector of all of the matrix's rows/columns.}
5444 \cvarg{CV\_REDUCE\_MAX}{The output is the maximum (column/row-wise) of all of the matrix's rows/columns.}
5445 \cvarg{CV\_REDUCE\_MIN}{The output is the minimum (column/row-wise) of all of the matrix's rows/columns.}
5447 \cvarg{dtype}{When it is negative, the destination vector will have the same type as the source matrix, otherwise, its type will be \texttt{CV\_MAKE\_TYPE(CV\_MAT\_DEPTH(dtype), mtx.channels())}}
5450 The function \texttt{reduce} reduces matrix to a vector by treating the matrix rows/columns as a set of 1D vectors and performing the specified operation on the vectors until a single row/column is obtained. For example, the function can be used to compute horizontal and vertical projections of an raster image. In the case of \texttt{CV\_REDUCE\_SUM} and \texttt{CV\_REDUCE\_AVG} the output may have a larger element bit-depth to preserve accuracy. And multi-channel arrays are also supported in these two reduction modes.
5452 See also: \cvCppCross{repeat}
5455 Fill the destination array with repeated copies of the source array.
5457 \cvdefCpp{void repeat(const Mat\& src, int ny, int nx, Mat\& dst);\newline
5458 Mat repeat(const Mat\& src, int ny, int nx);}
5460 \cvarg{src}{The source array to replicate}
5461 \cvarg{dst}{The destination array; will have the same type as \texttt{src}}
5462 \cvarg{ny}{How many times the \texttt{src} is repeated along the vertical axis}
5463 \cvarg{nx}{How many times the \texttt{src} is repeated along the horizontal axis}
5466 The functions \cvCppCross{repeat} duplicate the source array one or more times along each of the two axes:
5468 \[\texttt{dst}_{ij}=\texttt{src}_{i\mod\texttt{src.rows},\;j\mod\texttt{src.cols}}\]
5470 The second variant of the function is more convenient to use with \cross{Matrix Expressions}
5472 See also: \cvCppCross{reduce}, \cross{Matrix Expressions}
5475 \cvfunc{saturate\_cast}\label{cppfunc.saturatecast}
5477 \subsection{saturate\_cast}\label{cppfunc.saturatecast}
5479 Template function for accurate conversion from one primitive type to another
5481 \cvdefCpp{template<typename \_Tp> inline \_Tp saturate\_cast(unsigned char v);\newline
5482 template<typename \_Tp> inline \_Tp saturate\_cast(signed char v);\newline
5483 template<typename \_Tp> inline \_Tp saturate\_cast(unsigned short v);\newline
5484 template<typename \_Tp> inline \_Tp saturate\_cast(signed short v);\newline
5485 template<typename \_Tp> inline \_Tp saturate\_cast(int v);\newline
5486 template<typename \_Tp> inline \_Tp saturate\_cast(unsigned int v);\newline
5487 template<typename \_Tp> inline \_Tp saturate\_cast(float v);\newline
5488 template<typename \_Tp> inline \_Tp saturate\_cast(double v);}
5491 \cvarg{v}{The function parameter}
5494 The functions \texttt{saturate\_cast} resembles the standard C++ cast operations, such as \texttt{static\_cast<T>()} etc. They perform an efficient and accurate conversion from one primitive type to another, see the introduction. "saturate" in the name means that when the input value \texttt{v} is out of range of the target type, the result will not be formed just by taking low bits of the input, but instead the value will be clipped. For example:
5497 uchar a = saturate_cast<uchar>(-100); // a = 0 (UCHAR_MIN)
5498 short b = saturate_cast<short>(33333.33333); // b = 32767 (SHRT_MAX)
5501 Such clipping is done when the target type is \texttt{unsigned char, signed char, unsigned short or signed short} - for 32-bit integers no clipping is done.
5503 When the parameter is floating-point value and the target type is an integer (8-, 16- or 32-bit), the floating-point value is first rounded to the nearest integer and then clipped if needed (when the target type is 8- or 16-bit).
5505 This operation is used in most simple or complex image processing functions in OpenCV.
5507 See also: \cvCppCross{add}, \cvCppCross{subtract}, \cvCppCross{multiply}, \cvCppCross{divide}, \cvCppCross{Mat::convertTo}
5509 \cvCppFunc{scaleAdd}
5510 Calculates the sum of a scaled array and another array.
5512 \cvdefCpp{void scaleAdd(const Mat\& src1, double scale, \par const Mat\& src2, Mat\& dst);\newline
5513 void scaleAdd(const MatND\& src1, double scale, \par const MatND\& src2, MatND\& dst);}
5515 \cvarg{src1}{The first source array}
5516 \cvarg{scale}{Scale factor for the first array}
5517 \cvarg{src2}{The second source array; must have the same size and the same type as \texttt{src1}}
5518 \cvarg{dst}{The destination array; will have the same size and the same type as \texttt{src1}}
5521 The function \texttt{cvScaleAdd} is one of the classical primitive linear algebra operations, known as \texttt{DAXPY} or \texttt{SAXPY} in \href{http://en.wikipedia.org/wiki/Basic_Linear_Algebra_Subprograms}{BLAS}. It calculates the sum of a scaled array and another array:
5524 \texttt{dst}(I)=\texttt{scale} \cdot \texttt{src1}(I) + \texttt{src2}(I)
5527 The function can also be emulated with a matrix expression, for example:
5530 Mat A(3, 3, CV_64F);
5532 A.row(0) = A.row(1)*2 + A.row(2);
5535 See also: \cvCppCross{add}, \cvCppCross{addWeighted}, \cvCppCross{subtract}, \cvCppCross{Mat::dot}, \cvCppCross{Mat::convertTo}, \cross{Matrix Expressions}
5537 \cvCppFunc{setIdentity}
5538 Initializes a scaled identity matrix
5540 \cvdefCpp{void setIdentity(Mat\& dst, const Scalar\& value=Scalar(1));}
5542 \cvarg{dst}{The matrix to initialize (not necessarily square)}
5543 \cvarg{value}{The value to assign to the diagonal elements}
5546 The function \cvCppCross{setIdentity} initializes a scaled identity matrix:
5549 \texttt{dst}(i,j)=\fork{\texttt{value}}{ if $i=j$}{0}{otherwise}
5552 The function can also be emulated using the matrix initializers and the matrix expressions:
5554 Mat A = Mat::eye(4, 3, CV_32F)*5;
5555 // A will be set to [[5, 0, 0], [0, 5, 0], [0, 0, 5], [0, 0, 0]]
5558 See also: \cvCppCross{Mat::zeros}, \cvCppCross{Mat::ones}, \cross{Matrix Expressions},
5559 \cvCppCross{Mat::setTo}, \cvCppCross{Mat::operator=},
5562 Solves one or more linear systems or least-squares problems.
5564 \cvdefCpp{bool solve(const Mat\& src1, const Mat\& src2, \par Mat\& dst, int flags=DECOMP\_LU);}
5566 \cvarg{src1}{The input matrix on the left-hand side of the system}
5567 \cvarg{src2}{The input matrix on the right-hand side of the system}
5568 \cvarg{dst}{The output solution}
5569 \cvarg{flags}{The solution (matrix inversion) method
5571 \cvarg{DECOMP\_LU}{Gaussian elimination with optimal pivot element chosen}
5572 \cvarg{DECOMP\_CHOLESKY}{Cholesky $LL^T$ factorization; the matrix \texttt{src1} must be symmetrical and positively defined}
5573 \cvarg{DECOMP\_EIG}{Eigenvalue decomposition; the matrix \texttt{src1} must be symmetrical}
5574 \cvarg{DECOMP\_SVD}{Singular value decomposition (SVD) method; the system can be over-defined and/or the matrix \texttt{src1} can be singular}
5575 \cvarg{DECOMP\_QR}{QR factorization; the system can be over-defined and/or the matrix \texttt{src1} can be singular}
5576 \cvarg{DECOMP\_NORMAL}{While all the previous flags are mutually exclusive, this flag can be used together with any of the previous. It means that the normal equations $\texttt{src1}^T\cdot\texttt{src1}\cdot\texttt{dst}=\texttt{src1}^T\texttt{src2}$ are solved instead of the original system $\texttt{src1}\cdot\texttt{dst}=\texttt{src2}$}
5580 The function \texttt{solve} solves a linear system or least-squares problem (the latter is possible with SVD or QR methods, or by specifying the flag \texttt{DECOMP\_NORMAL}):
5583 \texttt{dst} = \arg \min_X\|\texttt{src1}\cdot\texttt{X} - \texttt{src2}\|
5586 If \texttt{DECOMP\_LU} or \texttt{DECOMP\_CHOLESKY} method is used, the function returns 1 if \texttt{src1} (or $\texttt{src1}^T\texttt{src1}$) is non-singular and 0 otherwise; in the latter case \texttt{dst} is not valid. Other methods find some pseudo-solution in the case of singular left-hand side part.
5588 Note that if you want to find unity-norm solution of an under-defined singular system $\texttt{src1}\cdot\texttt{dst}=0$, the function \texttt{solve} will not do the work. Use \cvCppCross{SVD::solveZ} instead.
5590 See also: \cvCppCross{invert}, \cvCppCross{SVD}, \cvCppCross{eigen}
5592 \cvCppFunc{solveCubic}
5593 Finds the real roots of a cubic equation.
5595 \cvdefCpp{void solveCubic(const Mat\& coeffs, Mat\& roots);}
5597 \cvarg{coeffs}{The equation coefficients, an array of 3 or 4 elements}
5598 \cvarg{roots}{The destination array of real roots which will have 1 or 3 elements}
5601 The function \texttt{solveCubic} finds the real roots of a cubic equation:
5603 (if coeffs is a 4-element vector)
5606 \texttt{coeffs}[0] x^3 + \texttt{coeffs}[1] x^2 + \texttt{coeffs}[2] x + \texttt{coeffs}[3] = 0
5609 or (if coeffs is 3-element vector):
5612 x^3 + \texttt{coeffs}[0] x^2 + \texttt{coeffs}[1] x + \texttt{coeffs}[2] = 0
5615 The roots are stored to \texttt{roots} array.
5617 \cvCppFunc{solvePoly}
5618 Finds the real or complex roots of a polynomial equation
5620 \cvdefCpp{void solvePoly(const Mat\& coeffs, Mat\& roots, \par int maxIters=20, int fig=100);}
5622 \cvarg{coeffs}{The array of polynomial coefficients}
5623 \cvarg{roots}{The destination (complex) array of roots}
5624 \cvarg{maxIters}{The maximum number of iterations the algorithm does}
5628 The function \texttt{solvePoly} finds real and complex roots of a polynomial equation:
5630 \texttt{coeffs}[0] x^{n} + \texttt{coeffs}[1] x^{n-1} + ... + \texttt{coeffs}[n-1] x + \texttt{coeffs}[n] = 0
5634 Sorts each row or each column of a matrix
5636 \cvdefCpp{void sort(const Mat\& src, Mat\& dst, int flags);}
5638 \cvarg{src}{The source single-channel array}
5639 \cvarg{dst}{The destination array of the same size and the same type as \texttt{src}}
5640 \cvarg{flags}{The operation flags, a combination of the following values:
5642 \cvarg{CV\_SORT\_EVERY\_ROW}{Each matrix row is sorted independently}
5643 \cvarg{CV\_SORT\_EVERY\_COLUMN}{Each matrix column is sorted independently. This flag and the previous one are mutually exclusive}
5644 \cvarg{CV\_SORT\_ASCENDING}{Each matrix row is sorted in the ascending order}
5645 \cvarg{CV\_SORT\_DESCENDING}{Each matrix row is sorted in the descending order. This flag and the previous one are also mutually exclusive}
5649 The function \texttt{sort} sorts each matrix row or each matrix column in ascending or descending order. If you want to sort matrix rows or columns lexicographically, you can use STL \texttt{std::sort} generic function with the proper comparison predicate.
5651 See also: \cvCppCross{sortIdx}, \cvCppCross{randShuffle}
5654 Sorts each row or each column of a matrix
5656 \cvdefCpp{void sortIdx(const Mat\& src, Mat\& dst, int flags);}
5658 \cvarg{src}{The source single-channel array}
5659 \cvarg{dst}{The destination integer array of the same size as \texttt{src}}
5660 \cvarg{flags}{The operation flags, a combination of the following values:
5662 \cvarg{CV\_SORT\_EVERY\_ROW}{Each matrix row is sorted independently}
5663 \cvarg{CV\_SORT\_EVERY\_COLUMN}{Each matrix column is sorted independently. This flag and the previous one are mutually exclusive}
5664 \cvarg{CV\_SORT\_ASCENDING}{Each matrix row is sorted in the ascending order}
5665 \cvarg{CV\_SORT\_DESCENDING}{Each matrix row is sorted in the descending order. This flag and the previous one are also mutually exclusive}
5669 The function \texttt{sortIdx} sorts each matrix row or each matrix column in ascending or descending order. Instead of reordering the elements themselves, it stores the indices of sorted elements in the destination array. For example:
5672 Mat A = Mat::eye(3,3,CV_32F), B;
5673 sortIdx(A, B, CV_SORT_EVERY_ROW + CV_SORT_ASCENDING);
5674 // B will probably contain
5675 // (because of equal elements in A some permutations are possible):
5676 // [[1, 2, 0], [0, 2, 1], [0, 1, 2]]
5679 See also: \cvCppCross{sort}, \cvCppCross{randShuffle}
5682 Divides multi-channel array into several single-channel arrays
5684 \cvdefCpp{void split(const Mat\& mtx, Mat* mv);\newline
5685 void split(const Mat\& mtx, vector<Mat>\& mv);\newline
5686 void split(const MatND\& mtx, MatND* mv);\newline
5687 void split(const MatND\& mtx, vector<MatND>\& mv);}
5689 \cvarg{mtx}{The source multi-channel array}
5690 \cvarg{mv}{The destination array or vector of arrays; The number of arrays must match \texttt{mtx.channels()}. The arrays themselves will be reallocated if needed}
5693 The functions \texttt{split} split multi-channel array into separate single-channel arrays:
5695 \[ \texttt{mv}[c](I) = \texttt{mtx}(I)_c \]
5697 If you need to extract a single-channel or do some other sophisticated channel permutation, use \cvCppCross{mixChannels}
5699 See also: \cvCppCross{merge}, \cvCppCross{mixChannels}, \cvCppCross{cvtColor}
5702 Calculates square root of array elements
5704 \cvdefCpp{void sqrt(const Mat\& src, Mat\& dst);\newline
5705 void sqrt(const MatND\& src, MatND\& dst);}
5707 \cvarg{src}{The source floating-point array}
5708 \cvarg{dst}{The destination array; will have the same size and the same type as \texttt{src}}
5711 The functions \texttt{sqrt} calculate square root of each source array element. in the case of multi-channel arrays each channel is processed independently. The function accuracy is approximately the same as of the built-in \texttt{std::sqrt}.
5713 See also: \cvCppCross{pow}, \cvCppCross{magnitude}
5715 \cvCppFunc{subtract}
5716 Calculates per-element difference between two arrays or array and a scalar
5718 \cvdefCpp{void subtract(const Mat\& src1, const Mat\& src2, Mat\& dst);\newline
5719 void subtract(const Mat\& src1, const Mat\& src2, \par Mat\& dst, const Mat\& mask);\newline
5720 void subtract(const Mat\& src1, const Scalar\& sc, \par Mat\& dst, const Mat\& mask=Mat());\newline
5721 void subtract(const Scalar\& sc, const Mat\& src2, \par Mat\& dst, const Mat\& mask=Mat());\newline
5722 void subtract(const MatND\& src1, const MatND\& src2, MatND\& dst);\newline
5723 void subtract(const MatND\& src1, const MatND\& src2, \par MatND\& dst, const MatND\& mask);\newline
5724 void subtract(const MatND\& src1, const Scalar\& sc, \par MatND\& dst, const MatND\& mask=MatND());\newline
5725 void subtract(const Scalar\& sc, const MatND\& src2, \par MatND\& dst, const MatND\& mask=MatND());}
5727 \cvarg{src1}{The first source array}
5728 \cvarg{src2}{The second source array. It must have the same size and same type as \texttt{src1}}
5729 \cvarg{sc}{Scalar; the first or the second input parameter}
5730 \cvarg{dst}{The destination array; it will have the same size and same type as \texttt{src1}; see \texttt{Mat::create}}
5731 \cvarg{mask}{The optional operation mask, 8-bit single channel array;
5732 specifies elements of the destination array to be changed}
5735 The functions \texttt{subtract} compute
5738 \item the difference between two arrays
5739 \[\texttt{dst}(I) = \texttt{saturate}(\texttt{src1}(I) - \texttt{src2}(I))\quad\texttt{if mask}(I)\ne0\]
5740 \item the difference between array and a scalar:
5741 \[\texttt{dst}(I) = \texttt{saturate}(\texttt{src1}(I) - \texttt{sc})\quad\texttt{if mask}(I)\ne0\]
5742 \item the difference between scalar and an array:
5743 \[\texttt{dst}(I) = \texttt{saturate}(\texttt{sc} - \texttt{src2}(I))\quad\texttt{if mask}(I)\ne0\]
5746 where \texttt{I} is multi-dimensional index of array elements.
5748 The first function in the above list can be replaced with matrix expressions:
5751 dst -= src2; // equivalent to subtract(dst, src2, dst);
5754 See also: \cvCppCross{add}, \cvCppCross{addWeighted}, \cvCppCross{scaleAdd}, \cvCppCross{convertScale},
5755 \cross{Matrix Expressions}, \hyperref[cppfunc.saturatecast]{saturate\_cast}.
5758 Class for computing Singular Value Decomposition
5764 enum { MODIFY_A=1, NO_UV=2, FULL_UV=4 };newline
5765 // default empty constructor
5767 // decomposes m into u, w and vt: m = u*w*vt;newline
5768 // u and vt are orthogonal, w is diagonal
5769 SVD( const Mat& m, int flags=0 );newline
5770 // decomposes m into u, w and vt.
5771 SVD& operator ()( const Mat& m, int flags=0 );newline
5773 // finds such vector x, norm(x)=1, so that m*x = 0,
5774 // where m is singular matrix
5775 static void solveZ( const Mat& m, Mat& dst );newline
5776 // does back-subsitution:
5777 // dst = vt.t()*inv(w)*u.t()*rhs ~ inv(m)*rhs
5778 void backSubst( const Mat& rhs, Mat& dst ) const;newline
5784 The class \texttt{SVD} is used to compute Singular Value Decomposition of a floating-point matrix and then use it to solve least-square problems, under-determined linear systems, invert matrices, compute condition numbers etc.
5785 For a bit faster operation you can pass \texttt{flags=SVD::MODIFY\_A|...} to modify the decomposed matrix when it is not necessarily to preserve it. If you want to compute condition number of a matrix or absolute value of its determinant - you do not need \texttt{u} and \texttt{vt}, so you can pass \texttt{flags=SVD::NO\_UV|...}. Another flag \texttt{FULL\_UV} indicates that full-size \texttt{u} and \texttt{vt} must be computed, which is not necessary most of the time.
5787 See also: \cvCppCross{invert}, \cvCppCross{solve}, \cvCppCross{eigen}, \cvCppCross{determinant}
5790 Calculates sum of array elements
5792 \cvdefCpp{Scalar sum(const Mat\& mtx);\newline
5793 Scalar sum(const MatND\& mtx);}
5795 \cvarg{mtx}{The source array; must have 1 to 4 channels}
5798 The functions \texttt{sum} calculate and return the sum of array elements, independently for each channel.
5800 See also: \cvCppCross{countNonZero}, \cvCppCross{mean}, \cvCppCross{meanStdDev}, \cvCppCross{norm}, \cvCppCross{minMaxLoc}, \cvCppCross{reduce}
5803 Returns the default random number generator
5805 \cvdefCpp{RNG\& theRNG();}
5807 The function \texttt{theRNG} returns the default random number generator. For each thread there is separate random number generator, so you can use the function safely in multi-thread environments. If you just need to get a single random number using this generator or initialize an array, you can use \cvCppCross{randu} or \cvCppCross{randn} instead. But if you are going to generate many random numbers inside a loop, it will be much faster to use this function to retrieve the generator and then use \texttt{RNG::operator \_Tp()}.
5809 See also: \cvCppCross{RNG}, \cvCppCross{randu}, \cvCppCross{randn}
5812 Returns the trace of a matrix
5814 \cvdefCpp{Scalar trace(const Mat\& mtx);}
5816 \cvarg{mtx}{The source matrix}
5819 The function \texttt{trace} returns the sum of the diagonal elements of the matrix \texttt{mtx}.
5821 \[ \mathrm{tr}(\texttt{mtx}) = \sum_i \texttt{mtx}(i,i) \]
5824 \cvCppFunc{transform}
5825 Performs matrix transformation of every array element.
5827 \cvdefCpp{void transform(const Mat\& src, \par Mat\& dst, const Mat\& mtx );}
5829 \cvarg{src}{The source array; must have as many channels (1 to 4) as \texttt{mtx.cols} or \texttt{mtx.cols-1}}
5830 \cvarg{dst}{The destination array; will have the same size and depth as \texttt{src} and as many channels as \texttt{mtx.rows}}
5831 \cvarg{mtx}{The transformation matrix}
5834 The function \texttt{transform} performs matrix transformation of every element of array \texttt{src} and stores the results in \texttt{dst}:
5837 \texttt{dst}(I) = \texttt{mtx} \cdot \texttt{src}(I)
5839 (when \texttt{mtx.cols=src.channels()}), or
5842 \texttt{dst}(I) = \texttt{mtx} \cdot [\texttt{src}(I); 1]
5844 (when \texttt{mtx.cols=src.channels()+1})
5846 That is, every element of an \texttt{N}-channel array \texttt{src} is
5847 considered as \texttt{N}-element vector, which is transformed using
5848 a $\texttt{M} \times \texttt{N}$ or $\texttt{M} \times \texttt{N+1}$ matrix \texttt{mtx} into
5849 an element of \texttt{M}-channel array \texttt{dst}.
5851 The function may be used for geometrical transformation of $N$-dimensional
5852 points, arbitrary linear color space transformation (such as various kinds of RGB$\rightarrow$YUV transforms), shuffling the image channels and so forth.
5854 See also: \cvCppCross{perspectiveTransform}, \cvCppCross{getAffineTransform}, \cvCppCross{estimateRigidTransform}, \cvCppCross{warpAffine}, \cvCppCross{warpPerspective}
5856 \cvCppFunc{transpose}
5859 \cvdefCpp{void transpose(const Mat\& src, Mat\& dst);}
5861 \cvarg{src}{The source array}
5862 \cvarg{dst}{The destination array of the same type as \texttt{src}}
5865 The function \cvCppCross{transpose} transposes the matrix \texttt{src}:
5867 \[ \texttt{dst}(i,j) = \texttt{src}(j,i) \]
5869 Note that no complex conjugation is done in the case of a complex
5870 matrix, it should be done separately if needed.