1 \section{Basic Structures}
3 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
7 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
10 \label{CvPoint}\cvclass{CvPoint}
11 2D point with integer coordinates (usually zero-based).
15 typedef struct CvPoint
24 \cvarg{x}{x-coordinate}
25 \cvarg{y}{y-coordinate}
30 inline CvPoint cvPoint( int x, int y );
32 /* Conversion from CvPoint2D32f */
33 inline CvPoint cvPointFrom32f( CvPoint2D32f point );
36 2D point, represented as a tuple \texttt{(x, y)}, where x and y are integers.
39 \label{CvPoint2D32f}\cvclass{CvPoint2D32f}
40 2D point with floating-point coordinates
44 typedef struct CvPoint2D32f
53 \cvarg{x}{x-coordinate}
54 \cvarg{y}{y-coordinate}
59 inline CvPoint2D32f cvPoint2D32f( double x, double y );
61 /* Conversion from CvPoint */
62 inline CvPoint2D32f cvPointTo32f( CvPoint point );
65 2D point, represented as a tuple \texttt{(x, y)}, where x and y are floats.
69 \label{CvPoint3D32f}\cvclass{CvPoint3D32f}
70 3D point with floating-point coordinates
74 typedef struct CvPoint3D32f
84 \cvarg{x}{x-coordinate}
85 \cvarg{y}{y-coordinate}
86 \cvarg{z}{z-coordinate}
91 inline CvPoint3D32f cvPoint3D32f( double x, double y, double z );
94 3D point, represented as a tuple \texttt{(x, y, z)}, where x, y and z are floats.
97 \label{CvPoint2D64f}\cvclass{CvPoint2D64f}
98 2D point with double precision floating-point coordinates
102 typedef struct CvPoint2D64f
111 \cvarg{x}{x-coordinate}
112 \cvarg{y}{y-coordinate}
117 inline CvPoint2D64f cvPoint2D64f( double x, double y );
119 /* Conversion from CvPoint */
120 inline CvPoint2D64f cvPointTo64f( CvPoint point );
123 2D point, represented as a tuple \texttt{(x, y)}, where x and y are floats.
126 \label{CvPoint3D64f}\cvclass{CvPoint3D64f}
127 3D point with double precision floating-point coordinates
131 typedef struct CvPoint3D64f
141 \cvarg{x}{x-coordinate}
142 \cvarg{y}{y-coordinate}
143 \cvarg{z}{z-coordinate}
148 inline CvPoint3D64f cvPoint3D64f( double x, double y, double z );
151 3D point, represented as a tuple \texttt{(x, y, z)}, where x, y and z are floats.
154 \label{CvSize}\cvclass{CvSize}
155 Pixel-accurate size of a rectangle.
159 typedef struct CvSize
168 \cvarg{width}{Width of the rectangle}
169 \cvarg{height}{Height of the rectangle}
174 inline CvSize cvSize( int width, int height );
177 Size of a rectangle, represented as a tuple \texttt{(width, height)}, where width and height are integers.
180 \label{CvSize2D32f}\cvclass{CvSize2D32f}
181 Sub-pixel accurate size of a rectangle.
185 typedef struct CvSize2D32f
194 \cvarg{width}{Width of the rectangle}
195 \cvarg{height}{Height of the rectangle}
200 inline CvSize2D32f cvSize2D32f( double width, double height );
203 Size of a rectangle, represented as a tuple \texttt{(width, height)}, where width and height are floats.
206 \label{CvRect}\cvclass{CvRect}
207 Offset (usually the top-left corner) and size of a rectangle.
211 typedef struct CvRect
222 \cvarg{x}{x-coordinate of the top-left corner}
223 \cvarg{y}{y-coordinate of the top-left corner (bottom-left for Windows bitmaps)}
224 \cvarg{width}{Width of the rectangle}
225 \cvarg{height}{Height of the rectangle}
230 inline CvRect cvRect( int x, int y, int width, int height );
233 Rectangle, represented as a tuple \texttt{(x, y, width, height)}, where all are integers.
236 \label{CvScalar}\cvclass{CvScalar}
237 A container for 1-,2-,3- or 4-tuples of doubles.
241 typedef struct CvScalar
250 initializes val[0] with val0, val[1] with val1, etc.
252 inline CvScalar cvScalar( double val0, double val1=0,
253 double val2=0, double val3=0 );
255 initializes all of val[0]...val[3] with val0123
257 inline CvScalar cvScalarAll( double val0123 );
260 initializes val[0] with val0, and all of val[1]...val[3] with zeros
262 inline CvScalar cvRealScalar( double val0 );
266 CvScalar is always represented as a 4-tuple.
270 >>> cv.Scalar(1, 2, 3, 4)
276 >>> cv.RGB(17, 110, 255)
277 (255.0, 110.0, 17.0, 0.0)
281 \label{CvTermCriteria}\cvclass{CvTermCriteria}
282 Termination criteria for iterative algorithms.
286 #define CV_TERMCRIT_ITER 1
287 #define CV_TERMCRIT_NUMBER CV_TERMCRIT_ITER
288 #define CV_TERMCRIT_EPS 2
290 typedef struct CvTermCriteria
300 \cvarg{type}{A combination of CV\_TERMCRIT\_ITER and CV\_TERMCRIT\_EPS}
301 \cvarg{max\_iter}{Maximum number of iterations}
302 \cvarg{epsilon}{Required accuracy}
307 inline CvTermCriteria cvTermCriteria( int type, int max_iter, double epsilon );
309 /* Check and transform a CvTermCriteria so that
310 type=CV_TERMCRIT_ITER+CV_TERMCRIT_EPS
311 and both max_iter and epsilon are valid */
312 CvTermCriteria cvCheckTermCriteria( CvTermCriteria criteria,
314 int default_max_iters );
317 Represented by a tuple \texttt{(type, max\_iter, epsilon)}.
320 \cvarg{type}{\texttt{CV\_TERMCRIT\_ITER}, \texttt{CV\_TERMCRIT\_EPS} or \texttt{CV\_TERMCRIT\_ITER | CV\_TERMCRIT\_EPS}}
321 \cvarg{max\_iter}{Maximum number of iterations}
322 \cvarg{epsilon}{Required accuracy}
326 (cv.CV_TERMCRIT_ITER, 10, 0) # terminate after 10 iterations
327 (cv.CV_TERMCRIT_EPS, 0, 0.01) # terminate when epsilon reaches 0.01
328 (cv.CV_TERMCRIT_ITER | cv.CV_TERMCRIT_EPS, 10, 0.01) # terminate as soon as either condition is met
332 \label{CvMat}\cvclass{CvMat}
335 A multi-channel matrix.
375 \cvarg{type}{A CvMat signature (CV\_MAT\_MAGIC\_VAL) containing the type of elements and flags}
376 \cvarg{step}{Full row length in bytes}
377 \cvarg{refcount}{Underlying data reference counter}
378 \cvarg{data}{Pointers to the actual matrix data}
379 \cvarg{rows}{Number of rows}
380 \cvarg{cols}{Number of columns}
383 Matrices are stored row by row. All of the rows are aligned by 4 bytes.
385 A multi-channel 2D matrix. Created by
388 \cross{CreateMatHeader},
392 \cvarg{type}{A CvMat signature containing the type of elements and flags, int}
393 \cvarg{step}{Full row length in bytes, int}
394 \cvarg{rows}{Number of rows, int}
395 \cvarg{cols}{Number of columns, int}
396 \cvarg{tostring() -> str}{Returns the contents of the CvMat as a single string.}
403 \label{CvMatND}\cvclass{CvMatND}
404 Multi-dimensional dense multi-channel array.
408 typedef struct CvMatND
435 \cvarg{type}{A CvMatND signature (CV\_MATND\_MAGIC\_VAL), combining the type of elements and flags}
436 \cvarg{dims}{The number of array dimensions}
437 \cvarg{refcount}{Underlying data reference counter}
438 \cvarg{data}{Pointers to the actual matrix data}
439 \cvarg{dim}{For each dimension, the pair (number of elements, distance between elements in bytes)}
445 \cvarg{type}{A CvMatND signature combining the type of elements and flags, int}
446 \cvarg{tostring() -> str}{Returns the contents of the CvMatND as a single string.}
451 \label{CvSparseMat}\cvclass{CvSparseMat}
452 Multi-dimensional sparse multi-channel array.
455 typedef struct CvSparseMat
466 int size[CV_MAX_DIM];
472 \cvarg{type}{A CvSparseMat signature (CV\_SPARSE\_MAT\_MAGIC\_VAL), combining the type of elements and flags.}
473 \cvarg{dims}{Number of dimensions}
474 \cvarg{refcount}{Underlying reference counter. Not used.}
475 \cvarg{heap}{A pool of hash table nodes}
476 \cvarg{hashtable}{The hash table. Each entry is a list of nodes.}
477 \cvarg{hashsize}{Size of the hash table}
478 \cvarg{total}{Total number of sparse array nodes}
479 \cvarg{valoffset}{The value offset of the array nodes, in bytes}
480 \cvarg{idxoffset}{The index offset of the array nodes, in bytes}
481 \cvarg{size}{Array of dimension sizes}
486 \label{IplImage}\cvclass{IplImage}
491 typedef struct _IplImage
506 struct _IplImage *maskROI;
508 struct _IplTileInfo *tileInfo;
514 char *imageDataOrigin;
520 \cvarg{nSize}{\texttt{sizeof(IplImage)}}
521 \cvarg{ID}{Version, always equals 0}
522 \cvarg{nChannels}{Number of channels. Most OpenCV functions support 1-4 channels.}
523 \cvarg{alphaChannel}{Ignored by OpenCV}
524 \cvarg{depth}{Pixel depth in bits. The supported depths are:
526 \cvarg{IPL\_DEPTH\_8U}{Unsigned 8-bit integer}
527 \cvarg{IPL\_DEPTH\_8S}{Signed 8-bit integer}
528 \cvarg{IPL\_DEPTH\_16U}{Unsigned 16-bit integer}
529 \cvarg{IPL\_DEPTH\_16S}{Signed 16-bit integer}
530 \cvarg{IPL\_DEPTH\_32S}{Signed 32-bit integer}
531 \cvarg{IPL\_DEPTH\_32F}{Single-precision floating point}
532 \cvarg{IPL\_DEPTH\_64F}{Double-precision floating point}
534 \cvarg{colorModel}{Ignored by OpenCV. The OpenCV function \cross{CvtColor} requires the source and destination color spaces as parameters.}
535 \cvarg{channelSeq}{Ignored by OpenCV}
536 \cvarg{dataOrder}{0 = \texttt{IPL\_DATA\_ORDER\_PIXEL} - interleaved color channels, 1 - separate color channels. \cross{CreateImage} only creates images with interleaved channels. For example, the usual layout of a color image is: $ b_{00} g_{00} r_{00} b_{10} g_{10} r_{10} ...$}
537 \cvarg{origin}{0 - top-left origin, 1 - bottom-left origin (Windows bitmap style)}
538 \cvarg{align}{Alignment of image rows (4 or 8). OpenCV ignores this and uses widthStep instead.}
539 \cvarg{width}{Image width in pixels}
540 \cvarg{height}{Image height in pixels}
541 \cvarg{roi}{Region Of Interest (ROI). If not NULL, only this image region will be processed.}
542 \cvarg{maskROI}{Must be NULL in OpenCV}
543 \cvarg{imageId}{Must be NULL in OpenCV}
544 \cvarg{tileInfo}{Must be NULL in OpenCV}
545 \cvarg{imageSize}{Image data size in bytes. For interleaved data, this equals $\texttt{image->height} \cdot \texttt{image->widthStep}$ }
546 \cvarg{imageData}{A pointer to the aligned image data}
547 \cvarg{widthStep}{The size of an aligned image row, in bytes}
548 \cvarg{BorderMode}{Border completion mode, ignored by OpenCV}
549 \cvarg{BorderConst}{Border completion mode, ignored by OpenCV}
550 \cvarg{imageDataOrigin}{A pointer to the origin of the image data (not necessarily aligned). This is used for image deallocation.}
553 The \cross{IplImage} structure was inherited from the Intel Image Processing Library, in which the format is native. OpenCV only supports a subset of possible \cross{IplImage} formats, as outlined in the parameter list above.
555 In addition to the above restrictions, OpenCV handles ROIs differently. OpenCV functions require that the image size or ROI size of all source and destination images match exactly. On the other hand, the Intel Image Processing Library processes the area of intersection between the source and destination images (or ROIs), allowing them to vary independently.
560 The \cross{IplImage} object was inherited from the Intel Image Processing
561 Library, in which the format is native. OpenCV only supports a subset
562 of possible \cross{IplImage} formats.
565 \cvarg{nChannels}{Number of channels, int.}
566 \cvarg{width}{Image width in pixels}
567 \cvarg{height}{Image height in pixels}
568 \cvarg{depth}{Pixel depth in bits. The supported depths are:
570 \cvarg{IPL\_DEPTH\_8U}{Unsigned 8-bit integer}
571 \cvarg{IPL\_DEPTH\_8S}{Signed 8-bit integer}
572 \cvarg{IPL\_DEPTH\_16U}{Unsigned 16-bit integer}
573 \cvarg{IPL\_DEPTH\_16S}{Signed 16-bit integer}
574 \cvarg{IPL\_DEPTH\_32S}{Signed 32-bit integer}
575 \cvarg{IPL\_DEPTH\_32F}{Single-precision floating point}
576 \cvarg{IPL\_DEPTH\_64F}{Double-precision floating point}
578 \cvarg{origin}{0 - top-left origin, 1 - bottom-left origin (Windows bitmap style)}
579 \cvarg{tostring() -> str}{Returns the contents of the CvMatND as a single string.}
583 \label{CvArr}\cvclass{CvArr}
591 The metatype \texttt{CvArr} is used \textit{only} as a function parameter to specify that the function accepts arrays of multiple types, such as IplImage*, CvMat* or even CvSeq* sometimes. The particular array type is determined at runtime by analyzing the first 4 bytes of the header.
595 \texttt{CvArr} is used \textit{only} as a function parameter to specify that the parameter can be:
597 \item{an \cross{IplImage}}
598 \item{a \cross{CvMat}}
599 \item{any other type that exports the \href{http://docs.scipy.org/doc/numpy/reference/arrays.interface.html}{array interface}}
605 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
609 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
612 \subsection{DataType}\label{DataType}
613 Template "traits" class for other OpenCV primitive data types
616 template<typename _Tp> class DataType
618 // value_type is always a synonym for _Tp.
619 typedef _Tp value_type;
621 // intermediate type used for operations on _Tp.
622 // it is int for uchar, signed char, unsigned short, signed short and int,
623 // float for float, double for double, ...
624 typedef <...> work_type;
625 // in the case of multi-channel data it is the data type of each channel
626 typedef <...> channel_type;
630 depth = DataDepth<channel_type>::value,
633 // '1u', '4i', '3f', '2d' etc.
635 // CV_8UC3, CV_32FC2 ...
636 type = CV_MAKETYPE(depth, channels)
641 The template class \texttt{DataType} is descriptive class for OpenCV primitive data types and other types that comply with the following definition. A primitive OpenCV data type is one of \texttt{unsigned char, bool ($\sim$unsigned char), signed char, unsigned short, signed short, int, float, double} or a tuple of values of one of these types, where all the values in the tuple have the same type. If you are familiar with OpenCV \cross{CvMat}'s type notation, CV\_8U ... CV\_32FC3, CV\_64FC2 etc., then a primitive type can be defined as a type for which you can give a unique identifier in a form \verb*"CV\_<bit-depth>{U|S|F}C<number_of_channels>". A universal OpenCV structure able to store a single instance of such primitive data type is \cross{Vec}. Multiple instances of such a type can be stored to a \texttt{std::vector}, \texttt{Mat}, \texttt{Mat\_}, \texttt{MatND}, \texttt{MatND\_}, \texttt{SparseMat}, \texttt{SparseMat\_} or any other container that is able to store \cross{Vec} instances.
643 The class \texttt{DataType} is basically used to provide some description of such primitive data types without adding any fields or methods to the corresponding classes (and it is actually impossible to add anything to primitive C/C++ data types). This technique is known in C++ as class traits. It's not \texttt{DataType} itself that is used, but its specialized versions, such as:
646 template<> class DataType<uchar>
648 typedef uchar value_type;
649 typedef int work_type;
650 typedef uchar channel_type;
651 enum { channel_type = CV_8U, channels = 1, fmt='u', type = CV_8U };
654 template<typename _Tp> DataType<std::complex<_Tp> >
656 typedef std::complex<_Tp> value_type;
657 typedef std::complex<_Tp> work_type;
658 typedef _Tp channel_type;
659 // DataDepth is another helper trait class
660 enum { depth = DataDepth<_Tp>::value, channels=2,
661 fmt=(channels-1)*256+DataDepth<_Tp>::fmt,
662 type=CV_MAKETYPE(depth, channels) };
667 The main purpose of the classes is to convert compile-time type information to OpenCV-compatible data type identifier, for example:
670 // allocates 30x40 floating-point matrix
671 Mat A(30, 40, DataType<float>::type);
673 Mat B = Mat_<std::complex<double> >(3, 3);
674 // the statement below will print 6, 2 /* i.e. depth == CV_64F, channels == 2 */
675 cout << B.depth() << ", " << B.channels() << endl;
678 that is, such traits are used to tell OpenCV which data type you are working with, even if such a type is not native to OpenCV (the matrix \texttt{B} intialization above compiles because OpenCV defines the proper specialized template class \texttt{DataType<complex<\_Tp> >}). Also, this mechanism is useful (and used in OpenCV this way) for generic algorithms implementations.
681 Template class for 2D points
684 template<typename _Tp> class Point_
687 typedef _Tp value_type;
690 Point_(_Tp _x, _Tp _y);
691 Point_(const Point_& pt);
692 Point_(const CvPoint& pt);
693 Point_(const CvPoint2D32f& pt);
694 Point_(const Size_<_Tp>& sz);
695 Point_(const Vec<_Tp, 2>& v);
696 Point_& operator = (const Point_& pt);
697 template<typename _Tp2> operator Point_<_Tp2>() const;
698 operator CvPoint() const;
699 operator CvPoint2D32f() const;
700 operator Vec<_Tp, 2>() const;
702 // computes dot-product (this->x*pt.x + this->y*pt.y)
703 _Tp dot(const Point_& pt) const;
704 // computes dot-product using double-precision arithmetics
705 double ddot(const Point_& pt) const;
706 // returns true if the point is inside the rectangle "r".
707 bool inside(const Rect_<_Tp>& r) const;
713 The class represents a 2D point, specified by its coordinates $x$ and $y$.
714 Instance of the class is interchangeable with C structures \texttt{CvPoint} and \texttt{CvPoint2D32f}. There is also cast operator to convert point coordinates to the specified type. The conversion from floating-point coordinates to integer coordinates is done by rounding; in general case the conversion uses \hyperref[saturatecast]{saturate\_cast} operation on each of the coordinates. Besides the class members listed in the declaration above, the following operations on points are implemented:
724 double value = norm(pt); // L2 norm
729 For user convenience, the following type aliases are defined:
731 typedef Point_<int> Point2i;
732 typedef Point2i Point;
733 typedef Point_<float> Point2f;
734 typedef Point_<double> Point2d;
737 Here is a short example:
739 Point2f a(0.3f, 0.f), b(0.f, 0.4f);
740 Point pt = (a + b)*10.f;
741 cout << pt.x << ", " << pt.y << endl;
744 \subsection{Point3\_}
746 Template class for 3D points
750 template<typename _Tp> class Point3_
753 typedef _Tp value_type;
756 Point3_(_Tp _x, _Tp _y, _Tp _z);
757 Point3_(const Point3_& pt);
758 explicit Point3_(const Point_<_Tp>& pt);
759 Point3_(const CvPoint3D32f& pt);
760 Point3_(const Vec<_Tp, 3>& v);
761 Point3_& operator = (const Point3_& pt);
762 template<typename _Tp2> operator Point3_<_Tp2>() const;
763 operator CvPoint3D32f() const;
764 operator Vec<_Tp, 3>() const;
766 _Tp dot(const Point3_& pt) const;
767 double ddot(const Point3_& pt) const;
773 The class represents a 3D point, specified by its coordinates $x$, $y$ and $z$.
774 Instance of the class is interchangeable with C structure \texttt{CvPoint2D32f}. Similarly to \texttt{Point\_}, the 3D points' coordinates can be converted to another type, and the vector arithmetic and comparison operations are also supported.
776 The following type aliases are available:
779 typedef Point3_<int> Point3i;
780 typedef Point3_<float> Point3f;
781 typedef Point3_<double> Point3d;
786 Template class for specfying image or rectangle size.
789 template<typename _Tp> class Size_
792 typedef _Tp value_type;
795 Size_(_Tp _width, _Tp _height);
796 Size_(const Size_& sz);
797 Size_(const CvSize& sz);
798 Size_(const CvSize2D32f& sz);
799 Size_(const Point_<_Tp>& pt);
800 Size_& operator = (const Size_& sz);
803 operator Size_<int>() const;
804 operator Size_<float>() const;
805 operator Size_<double>() const;
806 operator CvSize() const;
807 operator CvSize2D32f() const;
813 The class \texttt{Size\_} is similar to \texttt{Point\_}, except that the two members are called \texttt{width} and \texttt{height} instead of \texttt{x} and \texttt{y}. The structure can be converted to and from the old OpenCV structures \cross{CvSize} and \cross{CvSize2D32f}. The same set of arithmetic and comparison operations as for \texttt{Point\_} is available.
815 OpenCV defines the following type aliases:
818 typedef Size_<int> Size2i;
820 typedef Size_<float> Size2f;
825 Template class for 2D rectangles
828 template<typename _Tp> class Rect_
831 typedef _Tp value_type;
834 Rect_(_Tp _x, _Tp _y, _Tp _width, _Tp _height);
835 Rect_(const Rect_& r);
836 Rect_(const CvRect& r);
837 // (x, y) <- org, (width, height) <- sz
838 Rect_(const Point_<_Tp>& org, const Size_<_Tp>& sz);
839 // (x, y) <- min(pt1, pt2), (width, height) <- max(pt1, pt2) - (x, y)
840 Rect_(const Point_<_Tp>& pt1, const Point_<_Tp>& pt2);
841 Rect_& operator = ( const Rect_& r );
842 // returns Point_<_Tp>(x, y)
843 Point_<_Tp> tl() const;
844 // returns Point_<_Tp>(x+width, y+height)
845 Point_<_Tp> br() const;
847 // returns Size_<_Tp>(width, height)
848 Size_<_Tp> size() const;
849 // returns width*height
852 operator Rect_<int>() const;
853 operator Rect_<float>() const;
854 operator Rect_<double>() const;
855 operator CvRect() const;
857 // x <= pt.x && pt.x < x + width &&
858 // y <= pt.y && pt.y < y + height ? true : false
859 bool contains(const Point_<_Tp>& pt) const;
861 _Tp x, y, width, height;
865 The rectangle is described by the coordinates of the top-left corner (which is the default interpretation of \texttt{Rect\_::x} and \texttt{Rect\_::y} in OpenCV; though, in your algorithms you may count \texttt{x} and \texttt{y} from the bottom-left corner), the rectangle width and height.
867 Another assumption OpenCV usually makes is that the top and left boundary of the rectangle are inclusive, while the right and bottom boundaries are not, for example, the method \texttt{Rect\_::contains} returns true if
869 x \leq pt.x < x+width,\\
870 y \leq pt.y < y+height
872 And virtually every loop over an image \cross{ROI} in OpenCV (where ROI is specified by \texttt{Rect\_<int>}) is implemented as:
874 for(int y = roi.y; y < roi.y + rect.height; y++)
875 for(int x = roi.x; x < roi.x + rect.width; x++)
881 In addition to the class members, the following operations on rectangles are implemented:
883 \item $\texttt{rect} = \texttt{rect} \pm \texttt{point}$ (shifting rectangle by a certain offset)
884 \item $\texttt{rect} = \texttt{rect} \pm \texttt{size}$ (expanding or shrinking rectangle by a certain amount)
885 \item \texttt{rect += point, rect -= point, rect += size, rect -= size} (augmenting operations)
886 \item \texttt{rect = rect1 \& rect2} (rectangle intersection)
887 \item \texttt{rect = rect1 | rect2} (minimum area rectangle containing \texttt{rect2} and \texttt{rect3})
888 \item \texttt{rect \&= rect1, rect |= rect1} (and the corresponding augmenting operations)
889 \item \texttt{rect == rect1, rect != rect1} (rectangle comparison)
892 Example. Here is how the partial ordering on rectangles can be established (rect1 $\subseteq$ rect2):
894 template<typename _Tp> inline bool
895 operator <= (const Rect_<_Tp>& r1, const Rect_<_Tp>& r2)
897 return (r1 & r2) == r1;
901 For user convenience, the following type alias is available:
903 typedef Rect_<int> Rect;
906 \subsection{RotatedRect}\label{RotatedRect}
907 Possibly rotated rectangle
915 RotatedRect(const Point2f& _center, const Size2f& _size, float _angle);
916 RotatedRect(const CvBox2D& box);
918 // returns minimal up-right rectangle that contains the rotated rectangle
919 Rect boundingRect() const;
920 // backward conversion to CvBox2D
921 operator CvBox2D() const;
923 // mass center of the rectangle
927 // rotation angle in degrees
932 The class \texttt{RotatedRect} replaces the old \cross{CvBox2D} and fully compatible with it.
934 \subsection{TermCriteria}\label{TermCriteria}
936 Termination criteria for iterative algorithms
942 enum { COUNT=1, MAX_ITER=COUNT, EPS=2 };
946 // type can be MAX_ITER, EPS or MAX_ITER+EPS.
947 // type = MAX_ITER means that only the number of iterations does matter;
948 // type = EPS means that only the required precision (epsilon) does matter
949 // (though, most algorithms put some limit on the number of iterations anyway)
950 // type = MAX_ITER + EPS means that algorithm stops when
951 // either the specified number of iterations is made,
952 // or when the specified accuracy is achieved - whatever happens first.
953 TermCriteria(int _type, int _maxCount, double _epsilon);
954 TermCriteria(const CvTermCriteria& criteria);
955 operator CvTermCriteria() const;
963 The class \texttt{TermCriteria} replaces the old \cross{CvTermCriteria} and fully compatible with it.
966 \subsection{Vec}\label{Vec}
967 Template class for short numerical vectors
970 template<typename _Tp, int cn> class Vec
973 typedef _Tp value_type;
974 enum { depth = DataDepth<_Tp>::value, channels = cn,
975 type = CV_MAKETYPE(depth, channels) };
977 // default constructor: all elements are set to 0
979 // constructors taking up to 10 first elements as parameters
982 Vec(_Tp v0, _Tp v1, _Tp v2);
984 Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4,
985 _Tp v5, _Tp v6, _Tp v7, _Tp v8, _Tp v9);
986 Vec(const Vec<_Tp, cn>& v);
987 // constructs vector with all the components set to alpha.
988 static Vec all(_Tp alpha);
990 // two variants of dot-product
991 _Tp dot(const Vec& v) const;
992 double ddot(const Vec& v) const;
994 // cross-product; valid only when cn == 3.
995 Vec cross(const Vec& v) const;
997 // element type conversion
998 template<typename T2> operator Vec<T2, cn>() const;
1000 // conversion to/from CvScalar (valid only when cn==4)
1001 operator CvScalar() const;
1004 _Tp operator [](int i) const;
1005 _Tp& operator[](int i);
1011 The class is the most universal representation of short numerical vectors or tuples. It is possible to convert \texttt{Vec<T,2>} to/from \texttt{Point\_}, \texttt{Vec<T,3>} to/from \texttt{Point3\_}, and \texttt{Vec<T,4>} to \cross{CvScalar}~. The elements of \texttt{Vec} are accessed using \texttt{operator[]}. All the expected vector operations are implemented too:
1014 \item \texttt{v1 = $v2 \pm v3$, v1 = v2 * $\alpha$, v1 = $\alpha$ * v2} (plus the corresponding augmenting operations; note that these operations apply \hyperref[saturatecast]{saturate\_cast.3C.3E} to the each computed vector component)
1015 \item \texttt{v1 == v2, v1 != v2}
1016 \item \texttt{double n = norm(v1); // $L_2$-norm}
1019 For user convenience, the following type aliases are introduced:
1021 typedef Vec<uchar, 2> Vec2b;
1022 typedef Vec<uchar, 3> Vec3b;
1023 typedef Vec<uchar, 4> Vec4b;
1025 typedef Vec<short, 2> Vec2s;
1026 typedef Vec<short, 3> Vec3s;
1027 typedef Vec<short, 4> Vec4s;
1029 typedef Vec<int, 2> Vec2i;
1030 typedef Vec<int, 3> Vec3i;
1031 typedef Vec<int, 4> Vec4i;
1033 typedef Vec<float, 2> Vec2f;
1034 typedef Vec<float, 3> Vec3f;
1035 typedef Vec<float, 4> Vec4f;
1036 typedef Vec<float, 6> Vec6f;
1038 typedef Vec<double, 2> Vec2d;
1039 typedef Vec<double, 3> Vec3d;
1040 typedef Vec<double, 4> Vec4d;
1041 typedef Vec<double, 6> Vec6d;
1044 The class \texttt{Vec} can be used for declaring various numerical objects, e.g. \texttt{Vec<double,9>} can be used to store a 3x3 double-precision matrix. It is also very useful for declaring and processing multi-channel arrays, see \texttt{Mat\_} description.
1046 \subsection{Scalar\_}
1050 template<typename _Tp> class Scalar_ : public Vec<_Tp, 4>
1054 Scalar_(_Tp v0, _Tp v1, _Tp v2=0, _Tp v3=0);
1055 Scalar_(const CvScalar& s);
1057 static Scalar_<_Tp> all(_Tp v0);
1058 operator CvScalar() const;
1060 template<typename T2> operator Scalar_<T2>() const;
1062 Scalar_<_Tp> mul(const Scalar_<_Tp>& t, double scale=1 ) const;
1063 template<typename T2> void convertTo(T2* buf, int channels, int unroll_to=0) const;
1066 typedef Scalar_<double> Scalar;
1069 The template class \texttt{Scalar\_} and it's double-precision instantiation \texttt{Scalar} represent 4-element vector. Being derived from \texttt{Vec<\_Tp, 4>}, they can be used as typical 4-element vectors, but in addition they can be converted to/from \texttt{CvScalar}. The type \texttt{Scalar} is widely used in OpenCV for passing pixel values and it is a drop-in replacement for \cross{CvScalar} that was used for the same purpose in the earlier versions of OpenCV.
1071 \subsection{Range}\label{Range}
1072 Specifies a continuous subsequence (a.k.a. slice) of a sequence.
1079 Range(int _start, int _end);
1080 Range(const CvSlice& slice);
1084 operator CvSlice() const;
1090 The class is used to specify a row or column span in a matrix (\cross{Mat}), and for many other purposes. \texttt{Range(a,b)} is basically the same as \texttt{a:b} in Matlab or \texttt{a..b} in Python. As in Python, \texttt{start} is inclusive left boundary of the range, and \texttt{end} is exclusive right boundary of the range. Such a half-opened interval is usually denoted as $[start,end)$.
1092 The static method \texttt{Range::all()} returns some special variable that means "the whole sequence" or "the whole range", just like "\texttt{:}" in Matlab or "\texttt{...}" in Python. All the methods and functions in OpenCV that take \texttt{Range} support this special \texttt{Range::all()} value, but of course, in the case of your own custom processing you will probably have to check and handle it explicitly:
1094 void my_function(..., const Range& r, ....)
1096 if(r == Range::all()) {
1097 // process all the data
1100 // process [r.start, r.end)
1105 \subsection{Ptr}\label{Ptr}
1107 A template class for smart reference-counting pointers
1110 template<typename _Tp> class Ptr
1113 // default constructor
1115 // constructor that wraps the object pointer
1117 // destructor: calls release()
1119 // copy constructor; increments ptr's reference counter
1120 Ptr(const Ptr& ptr);
1121 // assignment operator; decrements own reference counter
1122 // (with release()) and increments ptr's reference counter
1123 Ptr& operator = (const Ptr& ptr);
1124 // increments reference counter
1126 // decrements reference counter; when it becomes 0,
1127 // delete_obj() is called
1129 // user-specified custom object deletion operation.
1130 // by default, "delete obj;" is called
1132 // returns true if obj == 0;
1135 // provide access to the object fields and methods
1136 _Tp* operator -> ();
1137 const _Tp* operator -> () const;
1139 // return the underlying object pointer;
1140 // thanks to the methods, the Ptr<_Tp> can be
1141 // used instead of _Tp*
1143 operator const _Tp*() const;
1145 // the incapsulated object pointer
1147 // the associated reference counter
1152 The class \texttt{Ptr<\_Tp>} is a template class that wraps pointers of the corresponding type. It is similar to \texttt{shared\_ptr} that is a part of Boost library (\url{http://www.boost.org/doc/libs/1_40_0/libs/smart_ptr/shared_ptr.htm}) and also a part of the
1153 \href{http://en.wikipedia.org/wiki/C++0x}{C++0x} standard.
1155 By using this class you can get the following capabilities:
1158 \item default constructor, copy constructor and assignment operator for an arbitrary C++ class or a C structure. For some objects, like files, windows, mutexes, sockets etc, copy constructor or assignment operator are difficult to define. For some other objects, like complex classifiers in OpenCV, copy constructors are absent and not easy to implement. Finally, some of complex OpenCV and your own data structures may have been written in C. However, copy constructors and default constructors can simplify programming a lot; besides, they are often required (e.g. by STL containers). By wrapping a pointer to such a complex object \texttt{TObj} to \texttt{Ptr<TObj>} you will automatically get all of the necessary constructors and the assignment operator.
1159 \item all the above-mentioned operations running very fast, regardless of the data size, i.e. as "O(1)" operations. Indeed, while some structures, like \texttt{std::vector} provide a copy constructor and an assignment operator, the operations may take considerable time if the data structures are big. But if the structures are put into \texttt{Ptr<>}, the overhead becomes small and independent of the data size.
1160 \item automatic destruction, even for C structures. See the example below with \texttt{FILE*}.
1161 \item heterogeneous collections of objects. The standard STL and most other C++ and OpenCV containers can only store objects of the same type and the same size. The classical solution to store objects of different types in the same container is to store pointers to the base class \texttt{base\_class\_t*} instead, but when you loose the automatic memory management. Again, by using \texttt{Ptr<base\_class\_t>()} instead of the raw pointers, you can solve the problem.
1164 The class \texttt{Ptr} treats the wrapped object as a black box, the reference counter is allocated and managed separately. The only thing the pointer class needs to know about the object is how to deallocate it. This knowledge is incapsulated in \texttt{Ptr::delete\_obj()} method, which is called when the reference counter becomes 0. If the object is a C++ class instance, no additional coding is needed, because the default implementation of this method calls \texttt{delete obj;}.
1165 However, if the object is deallocated in a different way, then the specialized method should be created. For example, if you want to wrap \texttt{FILE}, the \texttt{delete\_obj} may be implemented as following:
1168 template<> inline void Ptr<FILE>::delete_obj()
1170 fclose(obj); // no need to clear the pointer afterwards,
1171 // it is done externally.
1176 Ptr<FILE> f(fopen("myfile.txt", "r"));
1181 // the file will be closed automatically by the Ptr<FILE> destructor.
1184 \textbf{Note}: The reference increment/decrement operations are implemented as atomic operations, and therefore it is normally safe to use the classes in multi-threaded applications. The same is true for \cross{Mat} and other C++ OpenCV classes that operate on the reference counters.
1186 \subsection{Mat}\label{Mat}
1188 OpenCV C++ matrix class.
1196 // constructs matrix of the specified size and type
1197 // (_type is CV_8UC1, CV_64FC3, CV_32SC(12) etc.)
1198 Mat(int _rows, int _cols, int _type);
1199 // constucts matrix and fills it with the specified value _s.
1200 Mat(int _rows, int _cols, int _type, const Scalar& _s);
1201 Mat(Size _size, int _type);
1204 // constructor for matrix headers pointing to user-allocated data
1205 Mat(int _rows, int _cols, int _type, void* _data, size_t _step=AUTO_STEP);
1206 Mat(Size _size, int _type, void* _data, size_t _step=AUTO_STEP);
1207 // creates a matrix header for a part of the bigger matrix
1208 Mat(const Mat& m, const Range& rowRange, const Range& colRange);
1209 Mat(const Mat& m, const Rect& roi);
1210 // converts old-style CvMat to the new matrix; the data is not copied by default
1211 Mat(const CvMat* m, bool copyData=false);
1212 // converts old-style IplImage to the new matrix; the data is not copied by default
1213 Mat(const IplImage* img, bool copyData=false);
1214 // builds matrix from std::vector with or without copying the data
1215 template<typename _Tp> Mat(const vector<_Tp>& vec, bool copyData=false);
1216 // helper constructor to compile matrix expressions
1217 Mat(const MatExpr_Base& expr);
1218 // destructor - calls release()
1220 // assignment operators
1221 Mat& operator = (const Mat& m);
1222 Mat& operator = (const MatExpr_Base& expr);
1225 // returns a new matrix header for the specified row
1226 Mat row(int y) const;
1227 // returns a new matrix header for the specified column
1228 Mat col(int x) const;
1229 // ... for the specified row span
1230 Mat rowRange(int startrow, int endrow) const;
1231 Mat rowRange(const Range& r) const;
1232 // ... for the specified column span
1233 Mat colRange(int startcol, int endcol) const;
1234 Mat colRange(const Range& r) const;
1235 // ... for the specified diagonal
1236 // (d=0 - the main diagonal,
1237 // >0 - a diagonal from the lower half,
1238 // <0 - a diagonal from the upper half)
1239 Mat diag(int d=0) const;
1240 // constructs a square diagonal matrix which main diagonal is vector "d"
1241 static Mat diag(const Mat& d);
1243 // returns deep copy of the matrix, i.e. the data is copied
1245 // copies the matrix content to "m".
1246 // It calls m.create(this->size(), this->type()).
1247 void copyTo( Mat& m ) const;
1248 // copies those matrix elements to "m" that are marked with non-zero mask elements.
1249 void copyTo( Mat& m, const Mat& mask ) const;
1250 // converts matrix to another datatype with optional scalng. See cvConvertScale.
1251 void convertTo( Mat& m, int rtype, double alpha=1, double beta=0 ) const;
1254 // sets every matrix element to s
1255 Mat& operator = (const Scalar& s);
1256 // sets some of the matrix elements to s, according to the mask
1257 Mat& setTo(const Scalar& s, const Mat& mask=Mat());
1258 // creates alternative matrix header for the same data, with different
1259 // number of channels and/or different number of rows. see cvReshape.
1260 Mat reshape(int _cn, int _rows=0) const;
1262 // matrix transposition by means of matrix expressions
1263 MatExpr_<...> t() const;
1264 // matrix inversion by means of matrix expressions
1265 MatExpr_<...> inv(int method=DECOMP_LU) const;
1266 // per-element matrix multiplication by means of matrix expressions
1267 MatExpr_<...> mul(const Mat& m, double scale=1) const;
1268 MatExpr_<...> mul(const MatExpr_<...>& m, double scale=1) const;
1270 // computes cross-product of 2 3D vectors
1271 Mat cross(const Mat& m) const;
1272 // computes dot-product
1273 double dot(const Mat& m) const;
1275 // Matlab-style matrix initialization. see the description
1276 static MatExpr_Initializer zeros(int rows, int cols, int type);
1277 static MatExpr_Initializer zeros(Size size, int type);
1278 static MatExpr_Initializer ones(int rows, int cols, int type);
1279 static MatExpr_Initializer ones(Size size, int type);
1280 static MatExpr_Initializer eye(int rows, int cols, int type);
1281 static MatExpr_Initializer eye(Size size, int type);
1283 // allocates new matrix data unless the matrix already has specified size and type.
1284 // previous data is unreferenced if needed.
1285 void create(int _rows, int _cols, int _type);
1286 void create(Size _size, int _type);
1287 // increases the reference counter; use with care to avoid memleaks
1289 // decreases reference counter;
1290 // deallocate the data when reference counter reaches 0.
1293 // locates matrix header within a parent matrix. See below
1294 void locateROI( Size& wholeSize, Point& ofs ) const;
1295 // moves/resizes the current matrix ROI inside the parent matrix.
1296 Mat& adjustROI( int dtop, int dbottom, int dleft, int dright );
1297 // extracts a rectangular sub-matrix
1298 // (this is a generalized form of row, rowRange etc.)
1299 Mat operator()( Range rowRange, Range colRange ) const;
1300 Mat operator()( const Rect& roi ) const;
1302 // converts header to CvMat; no data is copied
1303 operator CvMat() const;
1304 // converts header to IplImage; no data is copied
1305 operator IplImage() const;
1307 // returns true iff the matrix data is continuous
1308 // (i.e. when there are no gaps between successive rows).
1309 // similar to CV_IS_MAT_CONT(cvmat->type)
1310 bool isContinuous() const;
1311 // returns element size in bytes,
1312 // similar to CV_ELEM_SIZE(cvmat->type)
1313 size_t elemSize() const;
1314 // returns the size of element channel in bytes.
1315 size_t elemSize1() const;
1316 // returns element type, similar to CV_MAT_TYPE(cvmat->type)
1318 // returns element type, similar to CV_MAT_DEPTH(cvmat->type)
1320 // returns element type, similar to CV_MAT_CN(cvmat->type)
1321 int channels() const;
1322 // returns step/elemSize1()
1323 size_t step1() const;
1324 // returns matrix size:
1325 // width == number of columns, height == number of rows
1327 // returns true if matrix data is NULL
1330 // returns pointer to y-th row
1331 uchar* ptr(int y=0);
1332 const uchar* ptr(int y=0) const;
1334 // template version of the above method
1335 template<typename _Tp> _Tp* ptr(int y=0);
1336 template<typename _Tp> const _Tp* ptr(int y=0) const;
1338 // template methods for read-write or read-only element access.
1339 // note that _Tp must match the actual matrix type -
1340 // the functions do not do any on-fly type conversion
1341 template<typename _Tp> _Tp& at(int y, int x);
1342 template<typename _Tp> _Tp& at(Point pt);
1343 template<typename _Tp> const _Tp& at(int y, int x) const;
1344 template<typename _Tp> const _Tp& at(Point pt) const;
1346 // template methods for iteration over matrix elements.
1347 // the iterators take care of skipping gaps in the end of rows (if any)
1348 template<typename _Tp> MatIterator_<_Tp> begin();
1349 template<typename _Tp> MatIterator_<_Tp> end();
1350 template<typename _Tp> MatConstIterator_<_Tp> begin() const;
1351 template<typename _Tp> MatConstIterator_<_Tp> end() const;
1353 enum { MAGIC_VAL=0x42FF0000, AUTO_STEP=0, CONTINUOUS_FLAG=CV_MAT_CONT_FLAG };
1355 // includes several bit-fields:
1356 // * the magic signature
1357 // * continuity flag
1359 // * number of channels
1361 // the number of rows and columns
1363 // a distance between successive rows in bytes; includes the gap if any
1365 // pointer to the data
1368 // pointer to the reference counter;
1369 // when matrix points to user-allocated data, the pointer is NULL
1372 // helper fields used in locateROI and adjustROI
1378 The class \texttt{Mat} represents a 2D numerical array that can act as a matrix (and further it's referred to as a matrix), image, optical flow map etc. It is very similar to \cross{CvMat} type from earlier versions of OpenCV, and similarly to \texttt{CvMat}, the matrix can be multi-channel, but it also fully supports \cross{ROI} mechanism, just like \cross{IplImage}.
1380 There are many different ways to create \texttt{Mat} object. Here are the some popular ones:
1382 \item using \texttt{create(nrows, ncols, type)} method or
1383 the similar constructor \texttt{Mat(nrows, ncols, type[, fill\_value])} constructor.
1384 A new matrix of the specified size and specifed type will be allocated.
1385 \texttt{type} has the same meaning as in \cvCppCross{cvCreateMat} method,
1386 e.g. \texttt{CV\_8UC1} means 8-bit single-channel matrix,
1387 \texttt{CV\_32FC2} means 2-channel (i.e. complex) floating-point matrix etc:
1390 // make 7x7 complex matrix filled with 1+3j.
1391 cv::Mat M(7,7,CV_32FC2,Scalar(1,3));
1392 // and now turn M to 100x60 15-channel 8-bit matrix.
1393 // The old content will be deallocated
1394 M.create(100,60,CV_8UC(15));
1397 As noted in the introduction of this chapter, \texttt{create()}
1398 will only allocate a new matrix when the current matrix dimensionality
1399 or type are different from the specified.
1401 \item by using a copy constructor or assignment operator, where on the right side it can
1402 be a matrix or expression, see below. Again, as noted in the introduction,
1403 matrix assignment is O(1) operation because it only copies the header
1404 and increases the reference counter. \texttt{Mat::clone()} method can be used to get a full
1405 (a.k.a. deep) copy of the matrix when you need it.
1407 \item by constructing a header for a part of another matrix. It can be a single row, single column,
1408 several rows, several columns, rectangular region in the matrix (called a minor in algebra) or
1409 a diagonal. Such operations are also O(1), because the new header will reference the same data.
1410 You can actually modify a part of the matrix using this feature, e.g.
1413 // add 5-th row, multiplied by 3 to the 3rd row
1414 M.row(3) = M.row(3) + M.row(5)*3;
1416 // now copy 7-th column to the 1-st column
1417 // M.col(1) = M.col(7); // this will not work
1419 M.col(7).copyTo(M1);
1421 // create new 320x240 image
1422 cv::Mat img(Size(320,240),CV_8UC3);
1424 cv::Mat roi(img, Rect(10,10,100,100));
1425 // fill the ROI with (0,255,0) (which is green in RGB space);
1426 // the original 320x240 image will be modified
1427 roi = Scalar(0,255,0);
1430 Thanks to the additional \texttt{datastart} and \texttt{dataend} members, it is possible to
1431 compute the relative sub-matrix position in the main \emph{"container"} matrix using \texttt{locateROI()}:
1434 Mat A = Mat::eye(10, 10, CV_32S);
1435 // extracts A columns, 1 (inclusive) to 3 (exclusive).
1436 Mat B = A(Range::all(), Range(1, 3));
1437 // extracts B rows, 5 (inclusive) to 9 (exclusive).
1438 // that is, C ~ A(Range(5, 9), Range(1, 3))
1439 Mat C = B(Range(5, 9), Range::all());
1440 Size size; Point ofs;
1441 C.locateROI(size, ofs);
1442 // size will be (width=10,height=10) and the ofs will be (x=1, y=5)
1445 As in the case of whole matrices, if you need a deep copy, use \texttt{clone()} method
1446 of the extracted sub-matrices.
1448 \item by making a header for user-allocated-data. It can be useful for
1450 \item processing "foreign" data using OpenCV (e.g. when you implement
1451 a DirectShow filter or a processing module for gstreamer etc.), e.g.
1454 void process_video_frame(const unsigned char* pixels,
1455 int width, int height, int step)
1457 cv::Mat img(height, width, CV_8UC3, pixels, step);
1458 cv::GaussianBlur(img, img, cv::Size(7,7), 1.5, 1.5);
1462 \item for quick initialization of small matrices and/or super-fast element access
1464 double m[3][3] = {{a, b, c}, {d, e, f}, {g, h, i}};
1465 cv::Mat M = cv::Mat(3, 3, CV_64F, m).inv();
1469 partial yet very common cases of this "user-allocated data" case are conversions
1470 from \cross{CvMat} and \cross{IplImage} to \texttt{Mat}. For this purpose there are special constructors
1471 taking pointers to \texttt{CvMat} or \texttt{IplImage} and the optional
1472 flag indicating whether to copy the data or not.
1474 Backward conversion from \texttt{Mat} to \texttt{CvMat} or \texttt{IplImage} is provided via cast operators
1475 \texttt{Mat::operator CvMat() const} an \texttt{Mat::operator IplImage()}.
1476 The operators do \emph{not} copy the data.
1479 IplImage* img = cvLoadImage("greatwave.jpg", 1);
1480 Mat mtx(img); // convert IplImage* -> cv::Mat
1481 CvMat oldmat = mtx; // convert cv::Mat -> CvMat
1482 CV_Assert(oldmat.cols == img->width && oldmat.rows == img->height &&
1483 oldmat.data.ptr == (uchar*)img->imageData && oldmat.step == img->widthStep);
1486 \item by using MATLAB-style matrix initializers, \texttt{zeros(), ones(), eye()}, e.g.:
1489 // create a double-precision identity martix and add it to M.
1490 M += Mat::eye(M.rows, M.cols, CV_64F);
1493 \item by using comma-separated initializer:
1495 // create 3x3 double-precision identity matrix
1496 Mat M = (Mat_<double>(3,3) << 1, 0, 0, 0, 1, 0, 0, 0, 1);
1499 here we first call constructor of \texttt{Mat\_} class (that we describe further) with the proper matrix, and then we just put \texttt{<<} operator followed by comma-separated values that can be constants, variables, expressions etc. Also, note the extra parentheses that are needed to avoid compiler errors.
1503 Once matrix is created, it will be automatically managed by using reference-counting mechanism (unless the matrix header is built on top of user-allocated data, in which case you should handle the data by yourself).
1504 The matrix data will be deallocated when no one points to it; if you want to release the data pointed by a matrix header before the matrix destructor is called, use \texttt{Mat::release()}.
1506 The next important thing to learn about the matrix class is element access. Here is how the matrix is stored. The elements are stored in row-major order (row by row). The \texttt{Mat::data} member points to the first element of the first row, \texttt{Mat::rows} contains the number of matrix rows and \texttt{Mat::cols} -- the number of matrix columns. There is yet another member, called \texttt{Mat::step} that is used to actually compute address of a matrix element. The \texttt{Mat::step} is needed because the matrix can be a part of another matrix or because there can some padding space in the end of each row for a proper alignment.
1507 %\includegraphics[width=1.0\textwidth]{pics/roi.png}
1509 Given these parameters, address of the matrix element $M_{ij}$ is computed as following:
1512 \texttt{addr($M_{ij}$)=M.data + M.step*i + j*M.elemSize()}
1515 if you know the matrix element type, e.g. it is \texttt{float}, then you can use \texttt{at<>()} method:
1518 \texttt{addr($M_{ij}$)=\&M.at<float>(i,j)}
1520 (where \& is used to convert the reference returned by \texttt{at} to a pointer).
1521 if you need to process a whole row of matrix, the most efficient way is to get the pointer to the row first, and then just use plain C operator \texttt{[]}:
1524 // compute sum of positive matrix elements
1525 // (assuming that M is double-precision matrix)
1527 for(int i = 0; i < M.rows; i++)
1529 const double* Mi = M.ptr<double>(i);
1530 for(int j = 0; j < M.cols; j++)
1531 sum += std::max(Mi[j], 0.);
1535 Some operations, like the above one, do not actually depend on the matrix shape, they just process elements of a matrix one by one (or elements from multiple matrices that are sitting in the same place, e.g. matrix addition). Such operations are called element-wise and it makes sense to check whether all the input/output matrices are continuous, i.e. have no gaps in the end of each row, and if yes, process them as a single long row:
1538 // compute sum of positive matrix elements, optimized variant
1540 int cols = M.cols, rows = M.rows;
1541 if(M.isContinuous())
1546 for(int i = 0; i < rows; i++)
1548 const double* Mi = M.ptr<double>(i);
1549 for(int j = 0; j < cols; j++)
1550 sum += std::max(Mi[j], 0.);
1553 in the case of continuous matrix the outer loop body will be executed just once, so the overhead will be smaller, which will be especially noticeable in the case of small matrices.
1555 Finally, there are STL-style iterators that are smart enough to skip gaps between successive rows:
1557 // compute sum of positive matrix elements, iterator-based variant
1559 MatConstIterator_<double> it = M.begin<double>(), it_end = M.end<double>();
1560 for(; it != it_end; ++it)
1561 sum += std::max(*it, 0.);
1564 The matrix iterators are random-access iterators, so they can be passed to any STL algorithm, including \texttt{std::sort()}.
1566 \subsection{Matrix Expressions}
1568 This is a list of implemented matrix operations that can be combined in arbitrary complex expressions
1569 (here \emph{A}, \emph{B} stand for matrices (\texttt{Mat}), \emph{s} for a scalar (\texttt{Scalar}),
1570 \emph{$\alpha$} for a real-valued scalar (\texttt{double})):
1573 \item addition, subtraction, negation: $\texttt{A}\pm \texttt{B},\;\texttt{A}\pm \texttt{s},\;\texttt{s}\pm \texttt{A},\;-\texttt{A}$
1574 \item scaling: \texttt{A*$\alpha$, A/$\alpha$}
1575 \item per-element multiplication and division: \texttt{A.mul(B), A/B, $\alpha$/A}
1576 \item matrix multiplication: \texttt{A*B}
1577 \item transposition: \texttt{A.t() $\sim A^t$}
1578 \item matrix inversion and pseudo-inversion, solving linear systems and least-squares problems:
1579 \texttt{A.inv([method]) $\sim A^{-1}$}, \texttt{A.inv([method])*B $\sim X:\,AX=B$}
1580 \item comparison: $\texttt{A}\gtreqqless \texttt{B},\;\texttt{A} \ne \texttt{B},\;\texttt{A}\gtreqqless \alpha,\; \texttt{A} \ne \alpha$.
1581 The result of comparison is 8-bit single channel mask, which elements are set to 255
1582 (if the particular element or pair of elements satisfy the condition) and 0 otherwise.
1583 \item bitwise logical operations: \verb"A & B, A & s, A | B, A | s, A ^ B, A ^ s, ~A"
1584 \item element-wise minimum and maximum: \texttt{min(A, B), min(A, $\alpha$), max(A, B), max(A, $\alpha$)}
1585 \item element-wise absolute value: \texttt{abs(A)}
1586 \item cross-product, dot-product: \texttt{A.cross(B), A.dot(B)}
1587 \item any function of matrix or matrices and scalars that returns a matrix or a scalar, such as
1588 \cvCppCross{norm}, \cvCppCross{mean}, \cvCppCross{sum}, \cvCppCross{countNonZero}, \cvCppCross{trace},
1589 \cvCppCross{determinant}, \cvCppCross{repeat} etc.
1590 \item matrix initializers (\texttt{eye(), zeros(), ones()}), matrix comma-separated initializers,
1591 matrix constructors and operators that extract sub-matrices (see \cross{Mat} description).
1592 \item \verb"Mat_<destination_type>()" constructors to cast the result to the proper type.
1594 Note, however, that comma-separated initializers and probably some other operations may require additional explicit \texttt{Mat()} or \verb"Mat_<T>()" constuctor calls to resolve possible ambiguity.
1596 \subsection{Mat\_}\label{MatT}
1597 Template matrix class derived from \cross{Mat}
1600 template<typename _Tp> class Mat_ : public Mat
1603 typedef _Tp value_type;
1604 typedef typename DataType<_Tp>::channel_type channel_type;
1605 typedef MatIterator_<_Tp> iterator;
1606 typedef MatConstIterator_<_Tp> const_iterator;
1609 // equivalent to Mat(_rows, _cols, DataType<_Tp>::type)
1610 Mat_(int _rows, int _cols);
1611 // other forms of the above constructor
1612 Mat_(int _rows, int _cols, const _Tp& value);
1613 explicit Mat_(Size _size);
1614 Mat_(Size _size, const _Tp& value);
1615 // copy/conversion contructor. If m is of different type, it's converted
1618 Mat_(const Mat_& m);
1619 // construct a matrix on top of user-allocated data.
1620 // step is in bytes(!!!), regardless of the type
1621 Mat_(int _rows, int _cols, _Tp* _data, size_t _step=AUTO_STEP);
1623 Mat_(const Mat_& m, const Range& rowRange, const Range& colRange);
1624 Mat_(const Mat_& m, const Rect& roi);
1625 // to support complex matrix expressions
1626 Mat_(const MatExpr_Base& expr);
1627 // makes a matrix out of Vec or std::vector. The matrix will have a single column
1628 template<int n> explicit Mat_(const Vec<_Tp, n>& vec);
1629 Mat_(const vector<_Tp>& vec, bool copyData=false);
1631 Mat_& operator = (const Mat& m);
1632 Mat_& operator = (const Mat_& m);
1633 // set all the elements to s.
1634 Mat_& operator = (const _Tp& s);
1636 // iterators; they are smart enough to skip gaps in the end of rows
1639 const_iterator begin() const;
1640 const_iterator end() const;
1642 // equivalent to Mat::create(_rows, _cols, DataType<_Tp>::type)
1643 void create(int _rows, int _cols);
1644 void create(Size _size);
1646 Mat_ cross(const Mat_& m) const;
1647 // to support complex matrix expressions
1648 Mat_& operator = (const MatExpr_Base& expr);
1649 // data type conversion
1650 template<typename T2> operator Mat_<T2>() const;
1651 // overridden forms of Mat::row() etc.
1652 Mat_ row(int y) const;
1653 Mat_ col(int x) const;
1654 Mat_ diag(int d=0) const;
1657 // transposition, inversion, per-element multiplication
1658 MatExpr_<...> t() const;
1659 MatExpr_<...> inv(int method=DECOMP_LU) const;
1661 MatExpr_<...> mul(const Mat_& m, double scale=1) const;
1662 MatExpr_<...> mul(const MatExpr_<...>& m, double scale=1) const;
1664 // overridden forms of Mat::elemSize() etc.
1665 size_t elemSize() const;
1666 size_t elemSize1() const;
1669 int channels() const;
1670 size_t step1() const;
1671 // returns step()/sizeof(_Tp)
1672 size_t stepT() const;
1674 // overridden forms of Mat::zeros() etc. Data type is omitted, of course
1675 static MatExpr_Initializer zeros(int rows, int cols);
1676 static MatExpr_Initializer zeros(Size size);
1677 static MatExpr_Initializer ones(int rows, int cols);
1678 static MatExpr_Initializer ones(Size size);
1679 static MatExpr_Initializer eye(int rows, int cols);
1680 static MatExpr_Initializer eye(Size size);
1682 // some more overriden methods
1683 Mat_ reshape(int _rows) const;
1684 Mat_& adjustROI( int dtop, int dbottom, int dleft, int dright );
1685 Mat_ operator()( const Range& rowRange, const Range& colRange ) const;
1686 Mat_ operator()( const Rect& roi ) const;
1688 // more convenient forms of row and element access operators
1689 _Tp* operator [](int y);
1690 const _Tp* operator [](int y) const;
1692 _Tp& operator ()(int row, int col);
1693 const _Tp& operator ()(int row, int col) const;
1694 _Tp& operator ()(Point pt);
1695 const _Tp& operator ()(Point pt) const;
1697 // to support matrix expressions
1698 operator MatExpr_<Mat_, Mat_>() const;
1700 // conversion to vector.
1701 operator vector<_Tp>() const;
1705 The class \texttt{Mat\_<\_Tp>} is a "thin" template wrapper on top of \texttt{Mat} class. It does not have any extra data fields, nor it or \texttt{Mat} have any virtual methods and thus references or pointers to these two classes can be freely converted one to another. But do it with care, e.g.:
1708 // create 100x100 8-bit matrix
1709 Mat M(100,100,CV_8U);
1710 // this will compile fine. no any data conversion will be done.
1711 Mat_<float>& M1 = (Mat_<float>&)M;
1712 // the program will likely crash at the statement below
1716 While \texttt{Mat} is sufficient in most cases, \texttt{Mat\_} can be more convenient if you use a lot of element access operations and if you know matrix type at compile time. Note that \texttt{Mat::at<\_Tp>(int y, int x)} and \texttt{Mat\_<\_Tp>::operator ()(int y, int x)} do absolutely the same and run at the same speed, but the latter is certainly shorter:
1719 Mat_<double> M(20,20);
1720 for(int i = 0; i < M.rows; i++)
1721 for(int j = 0; j < M.cols; j++)
1722 M(i,j) = 1./(i+j+1);
1725 cout << E.at<double>(0,0)/E.at<double>(M.rows-1,0);
1728 \emph{How to use \texttt{Mat\_} for multi-channel images/matrices?}
1730 This is simple - just pass \texttt{Vec} as \texttt{Mat\_} parameter:
1732 // allocate 320x240 color image and fill it with green (in RGB space)
1733 Mat_<Vec3b> img(240, 320, Vec3b(0,255,0));
1734 // now draw a diagonal white line
1735 for(int i = 0; i < 100; i++)
1736 img(i,i)=Vec3b(255,255,255);
1737 // and now scramble the 2nd (red) channel of each pixel
1738 for(int i = 0; i < img.rows; i++)
1739 for(int j = 0; j < img.cols; j++)
1740 img(i,j)[2] ^= (uchar)(i ^ j);
1743 \subsection{MatND}\label{MatND}
1744 n-dimensional dense array
1750 // default constructor
1752 // constructs array with specific size and data type
1753 MatND(int _ndims, const int* _sizes, int _type);
1754 // constructs array and fills it with the specified value
1755 MatND(int _ndims, const int* _sizes, int _type, const Scalar& _s);
1756 // copy constructor. only the header is copied.
1757 MatND(const MatND& m);
1758 // sub-array selection. only the header is copied
1759 MatND(const MatND& m, const Range* ranges);
1760 // converts old-style nd array to MatND; optionally, copies the data
1761 MatND(const CvMatND* m, bool copyData=false);
1763 MatND& operator = (const MatND& m);
1765 // creates a complete copy of the matrix (all the data is copied)
1766 MatND clone() const;
1767 // sub-array selection; only the header is copied
1768 MatND operator()(const Range* ranges) const;
1770 // copies the data to another matrix.
1771 // Calls m.create(this->size(), this->type()) prior to
1773 void copyTo( MatND& m ) const;
1774 // copies only the selected elements to another matrix.
1775 void copyTo( MatND& m, const MatND& mask ) const;
1776 // converts data to the specified data type.
1777 // calls m.create(this->size(), rtype) prior to the conversion
1778 void convertTo( MatND& m, int rtype, double alpha=1, double beta=0 ) const;
1780 // assigns "s" to each array element.
1781 MatND& operator = (const Scalar& s);
1782 // assigns "s" to the selected elements of array
1783 // (or to all the elements if mask==MatND())
1784 MatND& setTo(const Scalar& s, const MatND& mask=MatND());
1785 // modifies geometry of array without copying the data
1786 MatND reshape(int _newcn, int _newndims=0, const int* _newsz=0) const;
1788 // allocates a new buffer for the data unless the current one already
1789 // has the specified size and type.
1790 void create(int _ndims, const int* _sizes, int _type);
1791 // manually increment reference counter (use with care !!!)
1793 // decrements the reference counter. Dealloctes the data when
1794 // the reference counter reaches zero.
1797 // converts the matrix to 2D Mat or to the old-style CvMatND.
1798 // In either case the data is not copied.
1799 operator Mat() const;
1800 operator CvMatND() const;
1801 // returns true if the array data is stored continuously
1802 bool isContinuous() const;
1803 // returns size of each element in bytes
1804 size_t elemSize() const;
1805 // returns size of each element channel in bytes
1806 size_t elemSize1() const;
1807 // returns OpenCV data type id (CV_8UC1, ... CV_64FC4,...)
1809 // returns depth (CV_8U ... CV_64F)
1811 // returns the number of channels
1812 int channels() const;
1813 // step1() ~ step()/elemSize1()
1814 size_t step1(int i) const;
1816 // return pointer to the element (versions for 1D, 2D, 3D and generic nD cases)
1818 const uchar* ptr(int i0) const;
1819 uchar* ptr(int i0, int i1);
1820 const uchar* ptr(int i0, int i1) const;
1821 uchar* ptr(int i0, int i1, int i2);
1822 const uchar* ptr(int i0, int i1, int i2) const;
1823 uchar* ptr(const int* idx);
1824 const uchar* ptr(const int* idx) const;
1826 // convenient template methods for element access.
1827 // note that _Tp must match the actual matrix type -
1828 // the functions do not do any on-fly type conversion
1829 template<typename _Tp> _Tp& at(int i0);
1830 template<typename _Tp> const _Tp& at(int i0) const;
1831 template<typename _Tp> _Tp& at(int i0, int i1);
1832 template<typename _Tp> const _Tp& at(int i0, int i1) const;
1833 template<typename _Tp> _Tp& at(int i0, int i1, int i2);
1834 template<typename _Tp> const _Tp& at(int i0, int i1, int i2) const;
1835 template<typename _Tp> _Tp& at(const int* idx);
1836 template<typename _Tp> const _Tp& at(const int* idx) const;
1838 enum { MAGIC_VAL=0x42FE0000, AUTO_STEP=-1,
1839 CONTINUOUS_FLAG=CV_MAT_CONT_FLAG, MAX_DIM=CV_MAX_DIM };
1841 // combines data type, continuity flag, signature (magic value)
1843 // the array dimensionality
1846 // data reference counter
1848 // pointer to the data
1850 // and its actual beginning and end
1854 // step and size for each dimension, MAX_DIM at max
1856 size_t step[MAX_DIM];
1860 The class \texttt{MatND} describes n-dimensional dense numerical single-channel or multi-channel array. This is a convenient representation for multi-dimensional histograms (when they are not very sparse, otherwise \texttt{SparseMat} will do better), voxel volumes, stacked motion fields etc. The data layout of matrix $M$ is defined by the array of \texttt{M.step[]}, so that the address of element $(i_0,...,i_{M.dims-1})$, where $0\leq i_k<M.size[k]$ is computed as:
1862 addr(M_{i_0,...,i_{M.dims-1}}) = M.data + M.step[0]*i_0 + M.step[1]*i_1 + ... + M.step[M.dims-1]*i_{M.dims-1}
1864 which is more general form of the respective formula for \cross{Mat}, wherein $\texttt{size[0]}\sim\texttt{rows}$,
1865 $\texttt{size[1]}\sim\texttt{cols}$, \texttt{step[0]} was simply called \texttt{step}, and \texttt{step[1]} was not stored at all but computed as \texttt{Mat::elemSize()}.
1867 In other aspects \texttt{MatND} is also very similar to \texttt{Mat}, with the following limitations and differences:
1869 \item much less operations are implemented for \texttt{MatND}
1870 \item currently, algebraic expressions with \texttt{MatND}'s are not supported
1871 \item the \texttt{MatND} iterator is completely different from \texttt{Mat} and \texttt{Mat\_} iterators. The latter are per-element iterators, while the former is per-slice iterator, see below.
1874 Here is how you can use \texttt{MatND} to compute NxNxN histogram of color 8bpp image (i.e. each channel value ranges from 0..255 and we quantize it to 0..N-1):
1877 void computeColorHist(const Mat& image, MatND& hist, int N)
1879 const int histSize[] = {N, N, N};
1881 // make sure that the histogram has proper size and type
1882 hist.create(3, histSize, CV_32F);
1887 // the loop below assumes that the image
1888 // is 8-bit 3-channel, so let's check it.
1889 CV_Assert(image.type() == CV_8UC3);
1890 MatConstIterator_<Vec3b> it = image.begin<Vec3b>(),
1891 it_end = image.end<Vec3b>();
1892 for( ; it != it_end; ++it )
1894 const Vec3b& pix = *it;
1896 // we could have incremented the cells by 1.f/(image.rows*image.cols)
1897 // instead of 1.f to make the histogram normalized.
1898 hist.at<float>(pix[0]*N/256, pix[1]*N/256, pix[2]*N/256) += 1.f;
1903 And here is how you can iterate through \texttt{MatND} elements:
1906 void normalizeColorHist(MatND& hist)
1909 // intialize iterator (the style is different from STL).
1910 // after initialization the iterator will contain
1911 // the number of slices or planes
1912 // the iterator will go through
1913 MatNDIterator it(hist);
1915 // iterate through the matrix. on each iteration
1916 // it.planes[*] (of type Mat) will be set to the current plane.
1917 for(int p = 0; p < it.nplanes; p++, ++it)
1918 s += sum(it.planes[0])[0];
1919 it = MatNDIterator(hist);
1921 for(int p = 0; p < it.nplanes; p++, ++it)
1924 // this is a shorter implementation of the above
1925 // using built-in operations on MatND
1926 double s = sum(hist)[0];
1927 hist.convertTo(hist, hist.type(), 1./s, 0);
1929 // and this is even shorter one
1930 // (assuming that the histogram elements are non-negative)
1931 normalize(hist, hist, 1, 0, NORM_L1);
1936 You can iterate though several matrices simultaneously as long as they have the same geometry (dimensionality and all the dimension sizes are the same), which is useful for binary and n-ary operations on such matrices. Just pass those matrices to \texttt{MatNDIterator}. Then, during the iteration \texttt{it.planes[0]}, \texttt{it.planes[1]}, ... will be the slices of the corresponding matrices.
1938 \subsection{MatND\_}
1939 Template class for n-dimensional dense array derived from \cross{MatND}.
1942 template<typename _Tp> class MatND_ : public MatND
1945 typedef _Tp value_type;
1946 typedef typename DataType<_Tp>::channel_type channel_type;
1948 // constructors, the same as in MatND, only the type is omitted
1950 MatND_(int dims, const int* _sizes);
1951 MatND_(int dims, const int* _sizes, const _Tp& _s);
1952 MatND_(const MatND& m);
1953 MatND_(const MatND_& m);
1954 MatND_(const MatND_& m, const Range* ranges);
1955 MatND_(const CvMatND* m, bool copyData=false);
1956 MatND_& operator = (const MatND& m);
1957 MatND_& operator = (const MatND_& m);
1958 // different initialization function
1959 // where we take _Tp instead of Scalar
1960 MatND_& operator = (const _Tp& s);
1962 // no special destructor is needed; use the one from MatND
1964 void create(int dims, const int* _sizes);
1965 template<typename T2> operator MatND_<T2>() const;
1966 MatND_ clone() const;
1967 MatND_ operator()(const Range* ranges) const;
1969 size_t elemSize() const;
1970 size_t elemSize1() const;
1973 int channels() const;
1974 // step[i]/elemSize()
1975 size_t stepT(int i) const;
1976 size_t step1(int i) const;
1978 // shorter alternatives for MatND::at<_Tp>.
1979 _Tp& operator ()(const int* idx);
1980 const _Tp& operator ()(const int* idx) const;
1981 _Tp& operator ()(int idx0);
1982 const _Tp& operator ()(int idx0) const;
1983 _Tp& operator ()(int idx0, int idx1);
1984 const _Tp& operator ()(int idx0, int idx1) const;
1985 _Tp& operator ()(int idx0, int idx1, int idx2);
1986 const _Tp& operator ()(int idx0, int idx1, int idx2) const;
1987 _Tp& operator ()(int idx0, int idx1, int idx2);
1988 const _Tp& operator ()(int idx0, int idx1, int idx2) const;
1992 \texttt{MatND\_} relates to \texttt{MatND} almost like \texttt{Mat\_} to \texttt{Mat} - it provides a bit more convenient element access operations and adds no extra members of virtual methods to the base class, thus references/pointers to \texttt{MatND\_} and \texttt{MatND} can be easily converted one to another, e.g.
1995 // alternative variant of the above histogram accumulation loop
1997 CV_Assert(hist.type() == CV_32FC1);
1998 MatND_<float>& _hist = (MatND_<float>&)hist;
1999 for( ; it != it_end; ++it )
2001 const Vec3b& pix = *it;
2002 _hist(pix[0]*N/256, pix[1]*N/256, pix[2]*N/256) += 1.f;
2007 \subsection{SparseMat}\label{SparseMat}
2008 Sparse n-dimensional array.
2014 typedef SparseMatIterator iterator;
2015 typedef SparseMatConstIterator const_iterator;
2017 // internal structure - sparse matrix header
2023 // sparse matrix node - element of a hash table
2028 int idx[CV_MAX_DIM];
2031 ////////// constructors and destructor //////////
2032 // default constructor
2034 // creates matrix of the specified size and type
2035 SparseMat(int dims, const int* _sizes, int _type);
2037 SparseMat(const SparseMat& m);
2038 // converts dense 2d matrix to the sparse form,
2039 // if try1d is true and matrix is a single-column matrix (Nx1),
2040 // then the sparse matrix will be 1-dimensional.
2041 SparseMat(const Mat& m, bool try1d=false);
2042 // converts dense n-d matrix to the sparse form
2043 SparseMat(const MatND& m);
2044 // converts old-style sparse matrix to the new-style.
2045 // all the data is copied, so that "m" can be safely
2046 // deleted after the conversion
2047 SparseMat(const CvSparseMat* m);
2051 ///////// assignment operations ///////////
2053 // this is O(1) operation; no data is copied
2054 SparseMat& operator = (const SparseMat& m);
2055 // (equivalent to the corresponding constructor with try1d=false)
2056 SparseMat& operator = (const Mat& m);
2057 SparseMat& operator = (const MatND& m);
2059 // creates full copy of the matrix
2060 SparseMat clone() const;
2062 // copy all the data to the destination matrix.
2063 // the destination will be reallocated if needed.
2064 void copyTo( SparseMat& m ) const;
2065 // converts 1D or 2D sparse matrix to dense 2D matrix.
2066 // If the sparse matrix is 1D, then the result will
2067 // be a single-column matrix.
2068 void copyTo( Mat& m ) const;
2069 // converts arbitrary sparse matrix to dense matrix.
2070 // watch out the memory!
2071 void copyTo( MatND& m ) const;
2072 // multiplies all the matrix elements by the specified scalar
2073 void convertTo( SparseMat& m, int rtype, double alpha=1 ) const;
2074 // converts sparse matrix to dense matrix with optional type conversion and scaling.
2075 // When rtype=-1, the destination element type will be the same
2076 // as the sparse matrix element type.
2077 // Otherwise rtype will specify the depth and
2078 // the number of channels will remain the same is in the sparse matrix
2079 void convertTo( Mat& m, int rtype, double alpha=1, double beta=0 ) const;
2080 void convertTo( MatND& m, int rtype, double alpha=1, double beta=0 ) const;
2083 void assignTo( SparseMat& m, int type=-1 ) const;
2085 // reallocates sparse matrix. If it was already of the proper size and type,
2086 // it is simply cleared with clear(), otherwise,
2087 // the old matrix is released (using release()) and the new one is allocated.
2088 void create(int dims, const int* _sizes, int _type);
2089 // sets all the matrix elements to 0, which means clearing the hash table.
2091 // manually increases reference counter to the header.
2093 // decreses the header reference counter, when it reaches 0,
2094 // the header and all the underlying data are deallocated.
2097 // converts sparse matrix to the old-style representation.
2098 // all the elements are copied.
2099 operator CvSparseMat*() const;
2100 // size of each element in bytes
2101 // (the matrix nodes will be bigger because of
2102 // element indices and other SparseMat::Node elements).
2103 size_t elemSize() const;
2104 // elemSize()/channels()
2105 size_t elemSize1() const;
2107 // the same is in Mat and MatND
2110 int channels() const;
2112 // returns the array of sizes and 0 if the matrix is not allocated
2113 const int* size() const;
2114 // returns i-th size (or 0)
2115 int size(int i) const;
2116 // returns the matrix dimensionality
2118 // returns the number of non-zero elements
2119 size_t nzcount() const;
2121 // compute element hash value from the element indices:
2123 size_t hash(int i0) const;
2125 size_t hash(int i0, int i1) const;
2127 size_t hash(int i0, int i1, int i2) const;
2129 size_t hash(const int* idx) const;
2131 // low-level element-acccess functions,
2132 // special variants for 1D, 2D, 3D cases and the generic one for n-D case.
2134 // return pointer to the matrix element.
2135 // if the element is there (it's non-zero), the pointer to it is returned
2136 // if it's not there and createMissing=false, NULL pointer is returned
2137 // if it's not there and createMissing=true, then the new element
2138 // is created and initialized with 0. Pointer to it is returned
2139 // If the optional hashval pointer is not NULL, the element hash value is
2140 // not computed, but *hashval is taken instead.
2141 uchar* ptr(int i0, bool createMissing, size_t* hashval=0);
2142 uchar* ptr(int i0, int i1, bool createMissing, size_t* hashval=0);
2143 uchar* ptr(int i0, int i1, int i2, bool createMissing, size_t* hashval=0);
2144 uchar* ptr(const int* idx, bool createMissing, size_t* hashval=0);
2146 // higher-level element access functions:
2147 // ref<_Tp>(i0,...[,hashval]) - equivalent to *(_Tp*)ptr(i0,...true[,hashval]).
2148 // always return valid reference to the element.
2149 // If it's did not exist, it is created.
2150 // find<_Tp>(i0,...[,hashval]) - equivalent to (_const Tp*)ptr(i0,...false[,hashval]).
2151 // return pointer to the element or NULL pointer if the element is not there.
2152 // value<_Tp>(i0,...[,hashval]) - equivalent to
2153 // { const _Tp* p = find<_Tp>(i0,...[,hashval]); return p ? *p : _Tp(); }
2154 // that is, 0 is returned when the element is not there.
2155 // note that _Tp must match the actual matrix type -
2156 // the functions do not do any on-fly type conversion
2159 template<typename _Tp> _Tp& ref(int i0, size_t* hashval=0);
2160 template<typename _Tp> _Tp value(int i0, size_t* hashval=0) const;
2161 template<typename _Tp> const _Tp* find(int i0, size_t* hashval=0) const;
2164 template<typename _Tp> _Tp& ref(int i0, int i1, size_t* hashval=0);
2165 template<typename _Tp> _Tp value(int i0, int i1, size_t* hashval=0) const;
2166 template<typename _Tp> const _Tp* find(int i0, int i1, size_t* hashval=0) const;
2169 template<typename _Tp> _Tp& ref(int i0, int i1, int i2, size_t* hashval=0);
2170 template<typename _Tp> _Tp value(int i0, int i1, int i2, size_t* hashval=0) const;
2171 template<typename _Tp> const _Tp* find(int i0, int i1, int i2, size_t* hashval=0) const;
2174 template<typename _Tp> _Tp& ref(const int* idx, size_t* hashval=0);
2175 template<typename _Tp> _Tp value(const int* idx, size_t* hashval=0) const;
2176 template<typename _Tp> const _Tp* find(const int* idx, size_t* hashval=0) const;
2178 // erase the specified matrix element.
2179 // When there is no such element, the methods do nothing
2180 void erase(int i0, int i1, size_t* hashval=0);
2181 void erase(int i0, int i1, int i2, size_t* hashval=0);
2182 void erase(const int* idx, size_t* hashval=0);
2184 // return the matrix iterators,
2185 // pointing to the first sparse matrix element,
2186 SparseMatIterator begin();
2187 SparseMatConstIterator begin() const;
2188 // ... or to the point after the last sparse matrix element
2189 SparseMatIterator end();
2190 SparseMatConstIterator end() const;
2192 // and the template forms of the above methods.
2193 // _Tp must match the actual matrix type.
2194 template<typename _Tp> SparseMatIterator_<_Tp> begin();
2195 template<typename _Tp> SparseMatConstIterator_<_Tp> begin() const;
2196 template<typename _Tp> SparseMatIterator_<_Tp> end();
2197 template<typename _Tp> SparseMatConstIterator_<_Tp> end() const;
2199 // return value stored in the sparse martix node
2200 template<typename _Tp> _Tp& value(Node* n);
2201 template<typename _Tp> const _Tp& value(const Node* n) const;
2203 ////////////// some internal-use methods ///////////////
2206 // pointer to the sparse matrix header
2211 The class \texttt{SparseMat} represents multi-dimensional sparse numerical arrays. Such a sparse array can store elements of any type that \cross{Mat} and \cross{MatND} can store. "Sparse" means that only non-zero elements are stored (though, as a result of operations on a sparse matrix, some of its stored elements can actually become 0. It's up to the user to detect such elements and delete them using \texttt{SparseMat::erase}). The non-zero elements are stored in a hash table that grows when it's filled enough, so that the search time is O(1) in average (regardless of whether element is there or not). Elements can be accessed using the following methods:
2214 \item query operations (\texttt{SparseMat::ptr} and the higher-level \texttt{SparseMat::ref}, \texttt{SparseMat::value} and \texttt{SparseMat::find}), e.g.:
2217 int size[] = {10, 10, 10, 10, 10};
2218 SparseMat sparse_mat(dims, size, CV_32F);
2219 for(int i = 0; i < 1000; i++)
2222 for(int k = 0; k < dims; k++)
2223 idx[k] = rand()%sparse_mat.size(k);
2224 sparse_mat.ref<float>(idx) += 1.f;
2227 \item sparse matrix iterators. Like \cross{Mat} iterators and unlike \cross{MatND} iterators, the sparse matrix iterators are STL-style, that is, the iteration loop is familiar to C++ users:
2229 // prints elements of a sparse floating-point matrix
2230 // and the sum of elements.
2231 SparseMatConstIterator_<float>
2232 it = sparse_mat.begin<float>(),
2233 it_end = sparse_mat.end<float>();
2235 int dims = sparse_mat.dims();
2236 for(; it != it_end; ++it)
2238 // print element indices and the element value
2239 const Node* n = it.node();
2241 for(int i = 0; i < dims; i++)
2242 printf("%3d%c", n->idx[i], i < dims-1 ? ',' : ')');
2243 printf(": %f\n", *it);
2246 printf("Element sum is %g\n", s);
2248 If you run this loop, you will notice that elements are enumerated in no any logical order (lexicographical etc.), they come in the same order as they stored in the hash table, i.e. semi-randomly. You may collect pointers to the nodes and sort them to get the proper ordering. Note, however, that pointers to the nodes may become invalid when you add more elements to the matrix; this is because of possible buffer reallocation.
2249 \item a combination of the above 2 methods when you need to process 2 or more sparse matrices simultaneously, e.g. this is how you can compute unnormalized cross-correlation of the 2 floating-point sparse matrices:
2251 double cross_corr(const SparseMat& a, const SparseMat& b)
2253 const SparseMat *_a = &a, *_b = &b;
2254 // if b contains less elements than a,
2255 // it's faster to iterate through b
2256 if(_a->nzcount() > _b->nzcount())
2258 SparseMatConstIterator_<float> it = _a->begin<float>(),
2259 it_end = _a->end<float>();
2261 for(; it != it_end; ++it)
2263 // take the next element from the first matrix
2265 const Node* anode = it.node();
2266 // and try to find element with the same index in the second matrix.
2267 // since the hash value depends only on the element index,
2268 // we reuse hashvalue stored in the node
2269 float bvalue = _b->value<float>(anode->idx,&anode->hashval);
2270 ccorr += avalue*bvalue;
2277 \subsection{SparseMat\_}
2278 Template sparse n-dimensional array class derived from \cross{SparseMat}
2281 template<typename _Tp> class SparseMat_ : public SparseMat
2284 typedef SparseMatIterator_<_Tp> iterator;
2285 typedef SparseMatConstIterator_<_Tp> const_iterator;
2288 // the created matrix will have data type = DataType<_Tp>::type
2290 SparseMat_(int dims, const int* _sizes);
2291 SparseMat_(const SparseMat& m);
2292 SparseMat_(const SparseMat_& m);
2293 SparseMat_(const Mat& m);
2294 SparseMat_(const MatND& m);
2295 SparseMat_(const CvSparseMat* m);
2296 // assignment operators; data type conversion is done when necessary
2297 SparseMat_& operator = (const SparseMat& m);
2298 SparseMat_& operator = (const SparseMat_& m);
2299 SparseMat_& operator = (const Mat& m);
2300 SparseMat_& operator = (const MatND& m);
2302 // equivalent to the correspoding parent class methods
2303 SparseMat_ clone() const;
2304 void create(int dims, const int* _sizes);
2305 operator CvSparseMat*() const;
2307 // overriden methods that do extra checks for the data type
2310 int channels() const;
2312 // more convenient element access operations.
2313 // ref() is retained (but <_Tp> specification is not need anymore);
2314 // operator () is equivalent to SparseMat::value<_Tp>
2315 _Tp& ref(int i0, size_t* hashval=0);
2316 _Tp operator()(int i0, size_t* hashval=0) const;
2317 _Tp& ref(int i0, int i1, size_t* hashval=0);
2318 _Tp operator()(int i0, int i1, size_t* hashval=0) const;
2319 _Tp& ref(int i0, int i1, int i2, size_t* hashval=0);
2320 _Tp operator()(int i0, int i1, int i2, size_t* hashval=0) const;
2321 _Tp& ref(const int* idx, size_t* hashval=0);
2322 _Tp operator()(const int* idx, size_t* hashval=0) const;
2325 SparseMatIterator_<_Tp> begin();
2326 SparseMatConstIterator_<_Tp> begin() const;
2327 SparseMatIterator_<_Tp> end();
2328 SparseMatConstIterator_<_Tp> end() const;
2332 \texttt{SparseMat\_} is a thin wrapper on top of \cross{SparseMat}, made in the same way as \texttt{Mat\_} and \texttt{MatND\_}.
2333 It simplifies notation of some operations, and that's it.
2335 int sz[] = {10, 20, 30};
2336 SparseMat_<double> M(3, sz);
2338 M.ref(1, 2, 3) = M(4, 5, 6) + M(7, 8, 9);