1 \section{Basic Structures}
3 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
7 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
10 \subsection{CvPoint}\label{CvPoint}
11 2D point with integer coordinates (usually zero-based).
14 typedef struct CvPoint
23 \cvarg{x}{x-coordinate}
24 \cvarg{y}{y-coordinate}
29 inline CvPoint cvPoint( int x, int y );
31 /* Conversion from CvPoint2D32f */
32 inline CvPoint cvPointFrom32f( CvPoint2D32f point );
36 \subsection{CvPoint2D32f}\label{CvPoint2D32f}
37 2D point with floating-point coordinates
40 typedef struct CvPoint2D32f
49 \cvarg{x}{x-coordinate}
50 \cvarg{y}{y-coordinate}
55 inline CvPoint2D32f cvPoint2D32f( double x, double y );
57 /* Conversion from CvPoint */
58 inline CvPoint2D32f cvPointTo32f( CvPoint point );
62 \subsection{CvPoint3D32f}\label{CvPoint3D32f}
63 3D point with floating-point coordinates
66 typedef struct CvPoint3D32f
76 \cvarg{x}{x-coordinate}
77 \cvarg{y}{y-coordinate}
78 \cvarg{z}{z-coordinate}
83 inline CvPoint3D32f cvPoint3D32f( double x, double y, double z );
86 \subsection{CvPoint2D64f}\label{CvPoint2D64f}
87 2D point with double precision floating-point coordinates
90 typedef struct CvPoint2D64f
99 \cvarg{x}{x-coordinate}
100 \cvarg{y}{y-coordinate}
105 inline CvPoint2D64f cvPoint2D64f( double x, double y );
107 /* Conversion from CvPoint */
108 inline CvPoint2D64f cvPointTo64f( CvPoint point );
111 \subsection{CvPoint3D64f}\label{CvPoint3D64f}
112 3D point with double precision floating-point coordinates
115 typedef struct CvPoint3D64f
125 \cvarg{x}{x-coordinate}
126 \cvarg{y}{y-coordinate}
127 \cvarg{z}{z-coordinate}
132 inline CvPoint3D64f cvPoint3D64f( double x, double y, double z );
135 \subsection{CvSize}\label{CvSize}
136 Pixel-accurate size of a rectangle.
139 typedef struct CvSize
148 \cvarg{width}{Width of the rectangle}
149 \cvarg{height}{Height of the rectangle}
154 inline CvSize cvSize( int width, int height );
157 \subsection{CvSize2D32f}\label{CvSize2D32f}
158 Sub-pixel accurate size of a rectangle.
161 typedef struct CvSize2D32f
170 \cvarg{width}{Width of the rectangle}
171 \cvarg{height}{Height of the rectangle}
176 inline CvSize2D32f cvSize2D32f( double width, double height );
179 \subsection{CvRect}\label{CvRect}
180 Offset (usually the top-left corner) and size of a rectangle.
183 typedef struct CvRect
194 \cvarg{x}{x-coordinate of the top-left corner}
195 \cvarg{y}{y-coordinate of the top-left corner (bottom-left for Windows bitmaps)}
196 \cvarg{width}{Width of the rectangle}
197 \cvarg{height}{Height of the rectangle}
202 inline CvRect cvRect( int x, int y, int width, int height );
205 \subsection{CvScalar}\label{CvScalar}
206 A container for 1-,2-,3- or 4-tuples of doubles.
209 typedef struct CvScalar
218 initializes val[0] with val0, val[1] with val1, etc.
220 inline CvScalar cvScalar( double val0, double val1=0,
221 double val2=0, double val3=0 );
223 initializes all of val[0]...val[3] with val0123
225 inline CvScalar cvScalarAll( double val0123 );
228 initializes val[0] with val0, and all of val[1]...val[3] with zeros
230 inline CvScalar cvRealScalar( double val0 );
233 \subsection{CvTermCriteria}\label{CvTermCriteria}
234 Termination criteria for iterative algorithms.
237 #define CV_TERMCRIT_ITER 1
238 #define CV_TERMCRIT_NUMBER CV_TERMCRIT_ITER
239 #define CV_TERMCRIT_EPS 2
241 typedef struct CvTermCriteria
251 \cvarg{type}{A combination of CV\_TERMCRIT\_ITER and CV\_TERMCRIT\_EPS}
252 \cvarg{max\_iter}{Maximum number of iterations}
253 \cvarg{epsilon}{Required accuracy}
258 inline CvTermCriteria cvTermCriteria( int type, int max_iter, double epsilon );
260 /* Check and transform a CvTermCriteria so that
261 type=CV_TERMCRIT_ITER+CV_TERMCRIT_EPS
262 and both max_iter and epsilon are valid */
263 CvTermCriteria cvCheckTermCriteria( CvTermCriteria criteria,
265 int default_max_iters );
268 \subsection{CvMat}\label{CvMat}
269 A multi-channel matrix.
309 \cvarg{type}{A CvMat signature (CV\_MAT\_MAGIC\_VAL) containing the type of elements and flags}
310 \cvarg{step}{Full row length in bytes}
311 \cvarg{refcount}{Underlying data reference counter}
312 \cvarg{data}{Pointers to the actual matrix data}
313 \cvarg{rows}{Number of rows}
314 \cvarg{cols}{Number of columns}
317 Matrices are stored row by row. All of the rows are aligned by 4 bytes.
320 \subsection{CvMatND}\label{CvMatND}
321 Multi-dimensional dense multi-channel array.
324 typedef struct CvMatND
351 \cvarg{type}{A CvMatND signature (CV\_MATND\_MAGIC\_VAL), combining the type of elements and flags}
352 \cvarg{dims}{The number of array dimensions}
353 \cvarg{refcount}{Underlying data reference counter}
354 \cvarg{data}{Pointers to the actual matrix data}
355 \cvarg{dim}{For each dimension, the pair (number of elements, distance between elements in bytes)}
358 \subsection{CvSparseMat}\label{CvSparseMat}
359 Multi-dimensional sparse multi-channel array.
362 typedef struct CvSparseMat
373 int size[CV_MAX_DIM];
379 \cvarg{type}{A CvSparseMat signature (CV\_SPARSE\_MAT\_MAGIC\_VAL), combining the type of elements and flags.}
380 \cvarg{dims}{Number of dimensions}
381 \cvarg{refcount}{Underlying reference counter. Not used.}
382 \cvarg{heap}{A pool of hash table nodes}
383 \cvarg{hashtable}{The hash table. Each entry is a list of nodes.}
384 \cvarg{hashsize}{Size of the hash table}
385 \cvarg{total}{Total number of sparse array nodes}
386 \cvarg{valoffset}{The value offset of the array nodes, in bytes}
387 \cvarg{idxoffset}{The index offset of the array nodes, in bytes}
388 \cvarg{size}{Array of dimension sizes}
391 \subsection{IplImage}\label{IplImage}
395 typedef struct _IplImage
410 struct _IplImage *maskROI;
412 struct _IplTileInfo *tileInfo;
418 char *imageDataOrigin;
424 \cvarg{nSize}{\texttt{sizeof(IplImage)}}
425 \cvarg{ID}{Version, always equals 0}
426 \cvarg{nChannels}{Number of channels. Most OpenCV functions support 1-4 channels.}
427 \cvarg{alphaChannel}{Ignored by OpenCV}
428 \cvarg{depth}{Pixel depth in bits. The supported depths are:
430 \cvarg{IPL\_DEPTH\_8U}{Unsigned 8-bit integer}
431 \cvarg{IPL\_DEPTH\_8S}{Signed 8-bit integer}
432 \cvarg{IPL\_DEPTH\_16U}{Unsigned 16-bit integer}
433 \cvarg{IPL\_DEPTH\_16S}{Signed 16-bit integer}
434 \cvarg{IPL\_DEPTH\_32S}{Signed 32-bit integer}
435 \cvarg{IPL\_DEPTH\_32F}{Single-precision floating point}
436 \cvarg{IPL\_DEPTH\_64F}{Double-precision floating point}
438 \cvarg{colorModel}{Ignored by OpenCV. The OpenCV function \cross{CvtColor} requires the source and destination color spaces as parameters.}
439 \cvarg{channelSeq}{Ignored by OpenCV}
440 \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} ...$}
441 \cvarg{origin}{0 - top-left origin, 1 - bottom-left origin (Windows bitmap style)}
442 \cvarg{align}{Alignment of image rows (4 or 8). OpenCV ignores this and uses widthStep instead.}
443 \cvarg{width}{Image width in pixels}
444 \cvarg{height}{Image height in pixels}
445 \cvarg{roi}{Region Of Interest (ROI). If not NULL, only this image region will be processed.}
446 \cvarg{maskROI}{Must be NULL in OpenCV}
447 \cvarg{imageId}{Must be NULL in OpenCV}
448 \cvarg{tileInfo}{Must be NULL in OpenCV}
449 \cvarg{imageSize}{Image data size in bytes. For interleaved data, this equals $\texttt{image->height} \cdot \texttt{image->widthStep}$ }
450 \cvarg{imageData}{A pointer to the aligned image data}
451 \cvarg{widthStep}{The size of an aligned image row, in bytes}
452 \cvarg{BorderMode}{Border completion mode, ignored by OpenCV}
453 \cvarg{BorderConst}{Border completion mode, ignored by OpenCV}
454 \cvarg{imageDataOrigin}{A pointer to the origin of the image data (not necessarily aligned). This is used for image deallocation.}
457 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.
459 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.
461 \subsection{CvArr}\label{CvArr}
468 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.
471 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
475 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
478 \subsection{DataType}\label{DataType}
479 Template "traits" class for other OpenCV primitive data types
482 template<typename _Tp> class DataType
484 // value_type is always a synonym for _Tp.
485 typedef _Tp value_type;
487 // intermediate type used for operations on _Tp.
488 // it is int for uchar, signed char, unsigned short, signed short and int,
489 // float for float, double for double, ...
490 typedef <...> work_type;
491 // in the case of multi-channel data it is the data type of each channel
492 typedef <...> channel_type;
496 depth = DataDepth<channel_type>::value,
499 // '1u', '4i', '3f', '2d' etc.
501 // CV_8UC3, CV_32FC2 ...
502 type = CV_MAKETYPE(depth, channels)
507 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.
509 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:
512 template<> class DataType<uchar>
514 typedef uchar value_type;
515 typedef int work_type;
516 typedef uchar channel_type;
517 enum { channel_type = CV_8U, channels = 1, fmt='u', type = CV_8U };
520 template<typename _Tp> DataType<std::complex<_Tp> >
522 typedef std::complex<_Tp> value_type;
523 typedef std::complex<_Tp> work_type;
524 typedef _Tp channel_type;
525 // DataDepth is another helper trait class
526 enum { depth = DataDepth<_Tp>::value, channels=2,
527 fmt=(channels-1)*256+DataDepth<_Tp>::fmt,
528 type=CV_MAKETYPE(depth, channels) };
533 The main purpose of the classes is to convert compile-time type information to OpenCV-compatible data type identifier, for example:
536 // allocates 30x40 floating-point matrix
537 Mat A(30, 40, DataType<float>::type);
539 Mat B = Mat_<std::complex<double> >(3, 3);
540 // the statement below will print 6, 2 /* i.e. depth == CV_64F, channels == 2 */
541 cout << B.depth() << ", " << B.channels() << endl;
544 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.
547 Template class for 2D points
550 template<typename _Tp> class Point_
553 typedef _Tp value_type;
556 Point_(_Tp _x, _Tp _y);
557 Point_(const Point_& pt);
558 Point_(const CvPoint& pt);
559 Point_(const CvPoint2D32f& pt);
560 Point_(const Size_<_Tp>& sz);
561 Point_(const Vec<_Tp, 2>& v);
562 Point_& operator = (const Point_& pt);
563 template<typename _Tp2> operator Point_<_Tp2>() const;
564 operator CvPoint() const;
565 operator CvPoint2D32f() const;
566 operator Vec<_Tp, 2>() const;
568 // computes dot-product (this->x*pt.x + this->y*pt.y)
569 _Tp dot(const Point_& pt) const;
570 // computes dot-product using double-precision arithmetics
571 double ddot(const Point_& pt) const;
572 // returns true if the point is inside the rectangle "r".
573 bool inside(const Rect_<_Tp>& r) const;
579 The class represents a 2D point, specified by its coordinates $x$ and $y$.
580 Instance of the class is interchangeable with С 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:
583 \item $\texttt{pt1} = \texttt{pt2} \pm \texttt{pt3}$
584 \item \texttt{pt1 = pt2 * $\alpha$, pt1 = $\alpha$ * pt2}
585 \item \texttt{pt1 += pt2, pt1 -= pt2, pt1 *= $\alpha$}
586 \item \texttt{double value = norm(pt); // $L_2$-norm}
587 \item \texttt{pt1 == pt2, pt1 != pt2}
590 For user convenience, the following type aliases are defined:
592 typedef Point_<int> Point2i;
593 typedef Point2i Point;
594 typedef Point_<float> Point2f;
595 typedef Point_<double> Point2d;
598 Here is a short example:
600 Point2f a(0.3f, 0.f), b(0.f, 0.4f);
601 Point pt = (a + b)*10.f;
602 cout << pt.x << ", " << pt.y << endl;
605 \subsection{Point3\_}
607 Template class for 3D points
611 template<typename _Tp> class Point3_
614 typedef _Tp value_type;
617 Point3_(_Tp _x, _Tp _y, _Tp _z);
618 Point3_(const Point3_& pt);
619 explicit Point3_(const Point_<_Tp>& pt);
620 Point3_(const CvPoint3D32f& pt);
621 Point3_(const Vec<_Tp, 3>& v);
622 Point3_& operator = (const Point3_& pt);
623 template<typename _Tp2> operator Point3_<_Tp2>() const;
624 operator CvPoint3D32f() const;
625 operator Vec<_Tp, 3>() const;
627 _Tp dot(const Point3_& pt) const;
628 double ddot(const Point3_& pt) const;
634 The class represents a 3D point, specified by its coordinates $x$, $y$ and $z$.
635 Instance of the class is interchangeable with С 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.
637 The following type aliases are available:
640 typedef Point3_<int> Point3i;
641 typedef Point3_<float> Point3f;
642 typedef Point3_<double> Point3d;
647 Template class for specfying image or rectangle size.
650 template<typename _Tp> class Size_
653 typedef _Tp value_type;
656 Size_(_Tp _width, _Tp _height);
657 Size_(const Size_& sz);
658 Size_(const CvSize& sz);
659 Size_(const CvSize2D32f& sz);
660 Size_(const Point_<_Tp>& pt);
661 Size_& operator = (const Size_& sz);
664 operator Size_<int>() const;
665 operator Size_<float>() const;
666 operator Size_<double>() const;
667 operator CvSize() const;
668 operator CvSize2D32f() const;
674 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.
676 OpenCV defines the following type aliases:
679 typedef Size_<int> Size2i;
681 typedef Size_<float> Size2f;
686 Template class for 2D rectangles
689 template<typename _Tp> class Rect_
692 typedef _Tp value_type;
695 Rect_(_Tp _x, _Tp _y, _Tp _width, _Tp _height);
696 Rect_(const Rect_& r);
697 Rect_(const CvRect& r);
698 // (x, y) <- org, (width, height) <- sz
699 Rect_(const Point_<_Tp>& org, const Size_<_Tp>& sz);
700 // (x, y) <- min(pt1, pt2), (width, height) <- max(pt1, pt2) - (x, y)
701 Rect_(const Point_<_Tp>& pt1, const Point_<_Tp>& pt2);
702 Rect_& operator = ( const Rect_& r );
703 // returns Point_<_Tp>(x, y)
704 Point_<_Tp> tl() const;
705 // returns Point_<_Tp>(x+width, y+height)
706 Point_<_Tp> br() const;
708 // returns Size_<_Tp>(width, height)
709 Size_<_Tp> size() const;
710 // returns width*height
713 operator Rect_<int>() const;
714 operator Rect_<float>() const;
715 operator Rect_<double>() const;
716 operator CvRect() const;
718 // x <= pt.x && pt.x < x + width &&
719 // y <= pt.y && pt.y < y + height ? true : false
720 bool contains(const Point_<_Tp>& pt) const;
722 _Tp x, y, width, height;
726 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.
728 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
730 x \leq pt.x < x+width,\\
731 y \leq pt.y < y+height
733 And virtually every loop over an image \cross{ROI} in OpenCV (where ROI is specified by \texttt{Rect\_<int>}) is implemented as:
735 for(int y = roi.y; y < roi.y + rect.height; y++)
736 for(int x = roi.x; x < roi.x + rect.width; x++)
742 In addition to the class members, the following operations on rectangles are implemented:
744 \item $\texttt{rect} = \texttt{rect} \pm \texttt{point}$ (shifting rectangle by a certain offset)
745 \item $\texttt{rect} = \texttt{rect} \pm \texttt{size}$ (expanding or shrinking rectangle by a certain amount)
746 \item \texttt{rect += point, rect -= point, rect += size, rect -= size} (augmenting operations)
747 \item \texttt{rect = rect1 \& rect2} (rectangle intersection)
748 \item \texttt{rect = rect1 | rect2} (minimum area rectangle containing \texttt{rect2} and \texttt{rect3})
749 \item \texttt{rect \&= rect1, rect |= rect1} (and the corresponding augmenting operations)
750 \item \texttt{rect == rect1, rect != rect1} (rectangle comparison)
753 Example. Here is how the partial ordering on rectangles can be established (rect1 $\subseteq$ rect2):
755 template<typename _Tp> inline bool
756 operator <= (const Rect_<_Tp>& r1, const Rect_<_Tp>& r2)
758 return (r1 & r2) == r1;
762 For user convenience, the following type alias is available:
764 typedef Rect_<int> Rect;
767 \subsection{RotatedRect}\label{RotatedRect}
768 Possibly rotated rectangle
776 RotatedRect(const Point2f& _center, const Size2f& _size, float _angle);
777 RotatedRect(const CvBox2D& box);
779 // returns minimal up-right rectangle that contains the rotated rectangle
780 Rect boundingRect() const;
781 // backward conversion to CvBox2D
782 operator CvBox2D() const;
784 // mass center of the rectangle
788 // rotation angle in degrees
793 The class \texttt{RotatedRect} replaces the old \cross{CvBox2D} and fully compatible with it.
795 \subsection{TermCriteria}\label{TermCriteria}
797 Termination criteria for iterative algorithms
803 enum { COUNT=1, MAX_ITER=COUNT, EPS=2 };
807 // type can be MAX_ITER, EPS or MAX_ITER+EPS.
808 // type = MAX_ITER means that only the number of iterations does matter;
809 // type = EPS means that only the required precision (epsilon) does matter
810 // (though, most algorithms put some limit on the number of iterations anyway)
811 // type = MAX_ITER + EPS means that algorithm stops when
812 // either the specified number of iterations is made,
813 // or when the specified accuracy is achieved - whatever happens first.
814 TermCriteria(int _type, int _maxCount, double _epsilon);
815 TermCriteria(const CvTermCriteria& criteria);
816 operator CvTermCriteria() const;
824 The class \texttt{TermCriteria} replaces the old \cross{CvTermCriteria} and fully compatible with it.
827 \subsection{Vec}\label{Vec}
828 Template class for short numerical vectors
831 template<typename _Tp, int cn> class Vec
834 typedef _Tp value_type;
835 enum { depth = DataDepth<_Tp>::value, channels = cn,
836 type = CV_MAKETYPE(depth, channels) };
838 // default constructor: all elements are set to 0
840 // constructors taking up to 10 first elements as parameters
843 Vec(_Tp v0, _Tp v1, _Tp v2);
845 Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4,
846 _Tp v5, _Tp v6, _Tp v7, _Tp v8, _Tp v9);
847 Vec(const Vec<_Tp, cn>& v);
848 // constructs vector with all the components set to alpha.
849 static Vec all(_Tp alpha);
851 // two variants of dot-product
852 _Tp dot(const Vec& v) const;
853 double ddot(const Vec& v) const;
855 // cross-product; valid only when cn == 3.
856 Vec cross(const Vec& v) const;
858 // element type conversion
859 template<typename T2> operator Vec<T2, cn>() const;
861 // conversion to/from CvScalar (valid only when cn==4)
862 operator CvScalar() const;
865 _Tp operator [](int i) const;
866 _Tp& operator[](int i);
872 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:
875 \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)
876 \item \texttt{v1 == v2, v1 != v2}
877 \item \texttt{double n = norm(v1); // $L_2$-norm}
880 For user convenience, the following type aliases are introduced:
882 typedef Vec<uchar, 2> Vec2b;
883 typedef Vec<uchar, 3> Vec3b;
884 typedef Vec<uchar, 4> Vec4b;
886 typedef Vec<short, 2> Vec2s;
887 typedef Vec<short, 3> Vec3s;
888 typedef Vec<short, 4> Vec4s;
890 typedef Vec<int, 2> Vec2i;
891 typedef Vec<int, 3> Vec3i;
892 typedef Vec<int, 4> Vec4i;
894 typedef Vec<float, 2> Vec2f;
895 typedef Vec<float, 3> Vec3f;
896 typedef Vec<float, 4> Vec4f;
897 typedef Vec<float, 6> Vec6f;
899 typedef Vec<double, 2> Vec2d;
900 typedef Vec<double, 3> Vec3d;
901 typedef Vec<double, 4> Vec4d;
902 typedef Vec<double, 6> Vec6d;
905 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.
907 \subsection{Scalar\_}
911 template<typename _Tp> class Scalar_ : public Vec<_Tp, 4>
915 Scalar_(_Tp v0, _Tp v1, _Tp v2=0, _Tp v3=0);
916 Scalar_(const CvScalar& s);
918 static Scalar_<_Tp> all(_Tp v0);
919 operator CvScalar() const;
921 template<typename T2> operator Scalar_<T2>() const;
923 Scalar_<_Tp> mul(const Scalar_<_Tp>& t, double scale=1 ) const;
924 template<typename T2> void convertTo(T2* buf, int channels, int unroll_to=0) const;
927 typedef Scalar_<double> Scalar;
930 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.
932 \subsection{Range}\label{Range}
933 Specifies a continuous subsequence (a.k.a. slice) of a sequence.
940 Range(int _start, int _end);
941 Range(const CvSlice& slice);
945 operator CvSlice() const;
951 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 $[start,end)$.
953 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:
955 void my_function(..., const Range& r, ....)
957 if(r == Range::all()) {
958 // process all the data
961 // process [r.start, r.end)
966 \subsection{Ptr}\label{Ptr}
968 A template class for smart reference-counting pointers
971 template<typename _Tp> class Ptr
974 // default constructor
976 // constructor that wraps the object pointer
978 // destructor: calls release()
980 // copy constructor; increments ptr's reference counter
982 // assignment operator; decrements own reference counter
983 // (with release()) and increments ptr's reference counter
984 Ptr& operator = (const Ptr& ptr);
985 // increments reference counter
987 // decrements reference counter; when it becomes 0,
988 // delete_obj() is called
990 // user-specified custom object deletion operation.
991 // by default, "delete obj;" is called
993 // returns true if obj == 0;
996 // provide access to the object fields and methods
998 const _Tp* operator -> () const;
1000 // return the underlying object pointer;
1001 // thanks to the methods, the Ptr<_Tp> can be
1002 // used instead of _Tp*
1004 operator const _Tp*() const;
1006 // the incapsulated object pointer
1008 // the associated reference counter
1013 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
1014 \href{http://en.wikipedia.org/wiki/C%2B%2B0x}{C++0x} standard.
1016 By using this class you can get the following capabilities:
1019 \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.
1020 \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.
1021 \item automatic destruction, even for C structures. See the example below with \texttt{FILE*}.
1022 \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.
1025 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;}.
1026 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:
1029 template<> inline void Ptr<FILE>::delete_obj()
1031 fclose(obj); // no need to clear the pointer afterwards,
1032 // it is done externally.
1037 Ptr<FILE> f(fopen("myfile.txt", "r"));
1042 // the file will be closed automatically by the Ptr<FILE> destructor.
1045 \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.
1047 \subsection{Mat}\label{Mat}
1049 OpenCV C++ matrix class.
1057 // constructs matrix of the specified size and type
1058 // (_type is CV_8UC1, CV_64FC3, CV_32SC(12) etc.)
1059 Mat(int _rows, int _cols, int _type);
1060 // constucts matrix and fills it with the specified value _s.
1061 Mat(int _rows, int _cols, int _type, const Scalar& _s);
1062 Mat(Size _size, int _type);
1065 // constructor for matrix headers pointing to user-allocated data
1066 Mat(int _rows, int _cols, int _type, void* _data, size_t _step=AUTO_STEP);
1067 Mat(Size _size, int _type, void* _data, size_t _step=AUTO_STEP);
1068 // creates a matrix header for a part of the bigger matrix
1069 Mat(const Mat& m, const Range& rowRange, const Range& colRange);
1070 Mat(const Mat& m, const Rect& roi);
1071 // converts old-style CvMat to the new matrix; the data is not copied by default
1072 Mat(const CvMat* m, bool copyData=false);
1073 // converts old-style IplImage to the new matrix; the data is not copied by default
1074 Mat(const IplImage* img, bool copyData=false);
1075 // builds matrix from std::vector with or without copying the data
1076 template<typename _Tp> Mat(const vector<_Tp>& vec, bool copyData=false);
1077 // helper constructor to compile matrix expressions
1078 Mat(const MatExpr_Base& expr);
1079 // destructor - calls release()
1081 // assignment operators
1082 Mat& operator = (const Mat& m);
1083 Mat& operator = (const MatExpr_Base& expr);
1086 // returns a new matrix header for the specified row
1087 Mat row(int y) const;
1088 // returns a new matrix header for the specified column
1089 Mat col(int x) const;
1090 // ... for the specified row span
1091 Mat rowRange(int startrow, int endrow) const;
1092 Mat rowRange(const Range& r) const;
1093 // ... for the specified column span
1094 Mat colRange(int startcol, int endcol) const;
1095 Mat colRange(const Range& r) const;
1096 // ... for the specified diagonal
1097 // (d=0 - the main diagonal,
1098 // >0 - a diagonal from the lower half,
1099 // <0 - a diagonal from the upper half)
1100 Mat diag(int d=0) const;
1101 // constructs a square diagonal matrix which main diagonal is vector "d"
1102 static Mat diag(const Mat& d);
1104 // returns deep copy of the matrix, i.e. the data is copied
1106 // copies the matrix content to "m".
1107 // It calls m.create(this->size(), this->type()).
1108 void copyTo( Mat& m ) const;
1109 // copies those matrix elements to "m" that are marked with non-zero mask elements.
1110 void copyTo( Mat& m, const Mat& mask ) const;
1111 // converts matrix to another datatype with optional scalng. See cvConvertScale.
1112 void convertTo( Mat& m, int rtype, double alpha=1, double beta=0 ) const;
1115 // sets every matrix element to s
1116 Mat& operator = (const Scalar& s);
1117 // sets some of the matrix elements to s, according to the mask
1118 Mat& setTo(const Scalar& s, const Mat& mask=Mat());
1119 // creates alternative matrix header for the same data, with different
1120 // number of channels and/or different number of rows. see cvReshape.
1121 Mat reshape(int _cn, int _rows=0) const;
1123 // matrix transposition by means of matrix expressions
1124 MatExpr_<...> t() const;
1125 // matrix inversion by means of matrix expressions
1126 MatExpr_<...> inv(int method=DECOMP_LU) const;
1127 // per-element matrix multiplication by means of matrix expressions
1128 MatExpr_<...> mul(const Mat& m, double scale=1) const;
1129 MatExpr_<...> mul(const MatExpr_<...>& m, double scale=1) const;
1131 // computes cross-product of 2 3D vectors
1132 Mat cross(const Mat& m) const;
1133 // computes dot-product
1134 double dot(const Mat& m) const;
1136 // Matlab-style matrix initialization. see the description
1137 static MatExpr_Initializer zeros(int rows, int cols, int type);
1138 static MatExpr_Initializer zeros(Size size, int type);
1139 static MatExpr_Initializer ones(int rows, int cols, int type);
1140 static MatExpr_Initializer ones(Size size, int type);
1141 static MatExpr_Initializer eye(int rows, int cols, int type);
1142 static MatExpr_Initializer eye(Size size, int type);
1144 // allocates new matrix data unless the matrix already has specified size and type.
1145 // previous data is unreferenced if needed.
1146 void create(int _rows, int _cols, int _type);
1147 void create(Size _size, int _type);
1148 // increases the reference counter; use with care to avoid memleaks
1150 // decreases reference counter;
1151 // deallocate the data when reference counter reaches 0.
1154 // locates matrix header within a parent matrix. See below
1155 void locateROI( Size& wholeSize, Point& ofs ) const;
1156 // moves/resizes the current matrix ROI inside the parent matrix.
1157 Mat& adjustROI( int dtop, int dbottom, int dleft, int dright );
1158 // extracts a rectangular sub-matrix
1159 // (this is a generalized form of row, rowRange etc.)
1160 Mat operator()( Range rowRange, Range colRange ) const;
1161 Mat operator()( const Rect& roi ) const;
1163 // converts header to CvMat; no data is copied
1164 operator CvMat() const;
1165 // converts header to IplImage; no data is copied
1166 operator IplImage() const;
1168 // returns true iff the matrix data is continuous
1169 // (i.e. when there are no gaps between successive rows).
1170 // similar to CV_IS_MAT_CONT(cvmat->type)
1171 bool isContinuous() const;
1172 // returns element size in bytes,
1173 // similar to CV_ELEM_SIZE(cvmat->type)
1174 size_t elemSize() const;
1175 // returns the size of element channel in bytes.
1176 size_t elemSize1() const;
1177 // returns element type, similar to CV_MAT_TYPE(cvmat->type)
1179 // returns element type, similar to CV_MAT_DEPTH(cvmat->type)
1181 // returns element type, similar to CV_MAT_CN(cvmat->type)
1182 int channels() const;
1183 // returns step/elemSize1()
1184 size_t step1() const;
1185 // returns matrix size:
1186 // width == number of columns, height == number of rows
1188 // returns true if matrix data is NULL
1191 // returns pointer to y-th row
1192 uchar* ptr(int y=0);
1193 const uchar* ptr(int y=0) const;
1195 // template version of the above method
1196 template<typename _Tp> _Tp* ptr(int y=0);
1197 template<typename _Tp> const _Tp* ptr(int y=0) const;
1199 // template methods for read-write or read-only element access.
1200 // note that _Tp must match the actual matrix type -
1201 // the functions do not do any on-fly type conversion
1202 template<typename _Tp> _Tp& at(int y, int x);
1203 template<typename _Tp> _Tp& at(Point pt);
1204 template<typename _Tp> const _Tp& at(int y, int x) const;
1205 template<typename _Tp> const _Tp& at(Point pt) const;
1207 // template methods for iteration over matrix elements.
1208 // the iterators take care of skipping gaps in the end of rows (if any)
1209 template<typename _Tp> MatIterator_<_Tp> begin();
1210 template<typename _Tp> MatIterator_<_Tp> end();
1211 template<typename _Tp> MatConstIterator_<_Tp> begin() const;
1212 template<typename _Tp> MatConstIterator_<_Tp> end() const;
1214 enum { MAGIC_VAL=0x42FF0000, AUTO_STEP=0, CONTINUOUS_FLAG=CV_MAT_CONT_FLAG };
1216 // includes several bit-fields:
1217 // * the magic signature
1218 // * continuity flag
1220 // * number of channels
1222 // the number of rows and columns
1224 // a distance between successive rows in bytes; includes the gap if any
1226 // pointer to the data
1229 // pointer to the reference counter;
1230 // when matrix points to user-allocated data, the pointer is NULL
1233 // helper fields used in locateROI and adjustROI
1239 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}.
1241 There are many different ways to create \texttt{Mat} object. Here are the some popular ones:
1243 \item using \texttt{create(nrows, ncols, type)} method or
1244 the similar constructor \texttt{Mat(nrows, ncols, type[, fill\_value])} constructor.
1245 A new matrix of the specified size and specifed type will be allocated.
1246 \texttt{type} has the same meaning as in \cvCppCross{cvCreateMat} method,
1247 e.g. \texttt{CV\_8UC1} means 8-bit single-channel matrix,
1248 \texttt{CV\_32FC2} means 2-channel (i.e. complex) floating-point matrix etc:
1251 // make 7x7 complex matrix filled with 1+3j.
1252 cv::Mat M(7,7,CV_32FC2,Scalar(1,3));
1253 // and now turn M to 100x60 15-channel 8-bit matrix.
1254 // The old content will be deallocated
1255 M.create(100,60,CV_8UC(15));
1258 As noted in the introduction of this chapter, \texttt{create()}
1259 will only allocate a new matrix when the current matrix dimensionality
1260 or type are different from the specified.
1262 \item by using a copy constructor or assignment operator, where on the right side it can
1263 be a matrix or expression, see below. Again, as noted in the introduction,
1264 matrix assignment is O(1) operation because it only copies the header
1265 and increases the reference counter. \texttt{Mat::clone()} method can be used to get a full
1266 (a.k.a. deep) copy of the matrix when you need it.
1268 \item by constructing a header for a part of another matrix. It can be a single row, single column,
1269 several rows, several columns, rectangular region in the matrix (called a minor in algebra) or
1270 a diagonal. Such operations are also O(1), because the new header will reference the same data.
1271 You can actually modify a part of the matrix using this feature, e.g.
1274 // add 5-th row, multiplied by 3 to the 3rd row
1275 M.row(3) = M.row(3) + M.row(5)*3;
1277 // now copy 7-th column to the 1-st column
1278 // M.col(1) = M.col(7); // this will not work
1280 M.col(7).copyTo(M1);
1282 // create new 320x240 image
1283 cv::Mat img(Size(320,240),CV_8UC3);
1285 cv::Mat roi(img, Rect(10,10,100,100));
1286 // fill the ROI with (0,255,0) (which is green in RGB space);
1287 // the original 320x240 image will be modified
1288 roi = Scalar(0,255,0);
1291 Thanks to the additional \texttt{datastart} and \texttt{dataend} members, it is possible to
1292 compute the relative sub-matrix position in the main \emph{"container"} matrix using \texttt{locateROI()}:
1295 Mat A = Mat::eye(10, 10, CV_32S);
1296 // extracts A columns, 1 (inclusive) to 3 (exclusive).
1297 Mat B = A(Range::all(), Range(1, 3));
1298 // extracts B rows, 5 (inclusive) to 9 (exclusive).
1299 // that is, C ~ A(Range(5, 9), Range(1, 3))
1300 Mat C = B(Range(5, 9), Range::all());
1301 Size size; Point ofs;
1302 C.locateROI(size, ofs);
1303 // size will be (width=10,height=10) and the ofs will be (x=1, y=5)
1306 As in the case of whole matrices, if you need a deep copy, use \texttt{clone()} method
1307 of the extracted sub-matrices.
1309 \item by making a header for user-allocated-data. It can be useful for
1311 \item processing "foreign" data using OpenCV (e.g. when you implement
1312 a DirectShow filter or a processing module for gstreamer etc.), e.g.
1315 void process_video_frame(const unsigned char* pixels,
1316 int width, int height, int step)
1318 cv::Mat img(height, width, CV_8UC3, pixels, step);
1319 cv::GaussianBlur(img, img, cv::Size(7,7), 1.5, 1.5);
1323 \item for quick initialization of small matrices and/or super-fast element access
1325 double m[3][3] = {{a, b, c}, {d, e, f}, {g, h, i}};
1326 cv::Mat M = cv::Mat(3, 3, CV_64F, m).inv();
1330 partial yet very common cases of this "user-allocated data" case are conversions
1331 from \cross{CvMat} and \cross{IplImage} to \texttt{Mat}. For this purpose there are special constructors
1332 taking pointers to \texttt{CvMat} or \texttt{IplImage} and the optional
1333 flag indicating whether to copy the data or not.
1335 Backward conversion from \texttt{Mat} to \texttt{CvMat} or \texttt{IplImage} is provided via cast operators
1336 \texttt{Mat::operator CvMat() const} an \texttt{Mat::operator IplImage()}.
1337 The operators do \emph{not} copy the data.
1340 IplImage* img = cvLoadImage("greatwave.jpg", 1);
1341 Mat mtx(img); // convert IplImage* -> cv::Mat
1342 CvMat oldmat = mtx; // convert cv::Mat -> CvMat
1343 CV_Assert(oldmat.cols == img->width && oldmat.rows == img->height &&
1344 oldmat.data.ptr == (uchar*)img->imageData && oldmat.step == img->widthStep);
1347 \item by using MATLAB-style matrix initializers, \texttt{zeros(), ones(), eye()}, e.g.:
1350 // create a double-precision identity martix and add it to M.
1351 M += Mat::eye(M.rows, M.cols, CV_64F);
1354 \item by using comma-separated initializer:
1356 // create 3x3 double-precision identity matrix
1357 Mat M = (Mat_<double>(3,3) << 1, 0, 0, 0, 1, 0, 0, 0, 1);
1360 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.
1364 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).
1365 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()}.
1367 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.
1368 %\includegraphics[width=1.0\textwidth]{pics/roi.png}
1370 Given these parameters, address of the matrix element $M_{ij}$ is computed as following:
1373 \texttt{addr($M_{ij}$)=M.data + M.step*i + j*M.elemSize()}
1376 if you know the matrix element type, e.g. it is \texttt{float}, then you can use \texttt{at<>()} method:
1379 \texttt{addr($M_{ij}$)=\&M.at<float>(i,j)}
1381 (where \& is used to convert the reference returned by \texttt{at} to a pointer).
1382 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{[]}:
1385 // compute sum of positive matrix elements
1386 // (assuming that M is double-precision matrix)
1388 for(int i = 0; i < M.rows; i++)
1390 const double* Mi = M.ptr<double>(i);
1391 for(int j = 0; j < M.cols; j++)
1392 sum += std::max(Mi[j], 0.);
1396 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:
1399 // compute sum of positive matrix elements, optimized variant
1401 int cols = M.cols, rows = M.rows;
1402 if(M.isContinuous())
1407 for(int i = 0; i < rows; i++)
1409 const double* Mi = M.ptr<double>(i);
1410 for(int j = 0; j < cols; j++)
1411 sum += std::max(Mi[j], 0.);
1414 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.
1416 Finally, there are STL-style iterators that are smart enough to skip gaps between successive rows:
1418 // compute sum of positive matrix elements, iterator-based variant
1420 MatConstIterator_<double> it = M.begin<double>(), it_end = M.end<double>();
1421 for(; it != it_end; ++it)
1422 sum += std::max(*it, 0.);
1425 The matrix iterators are random-access iterators, so they can be passed to any STL algorithm, including \texttt{std::sort()}.
1427 \subsection{Matrix Expressions}\label{Matrix Expressions}
1429 This is a list of implemented matrix operations that can be combined in arbitrary complex expressions
1430 (here \emph{A}, \emph{B} stand for matrices (\texttt{Mat}), \emph{s} for a scalar (\texttt{Scalar}),
1431 \emph{$\alpha$} for a real-valued scalar (\texttt{double})):
1434 \item addition, subtraction, negation: $\texttt{A}\pm \texttt{B},\;\texttt{A}\pm \texttt{s},\;\texttt{s}\pm \texttt{A},\;-\texttt{A}$
1435 \item scaling: \texttt{A*$\alpha$, A/$\alpha$}
1436 \item per-element multiplication and division: \texttt{A.mul(B), A/B, $\alpha$/A}
1437 \item matrix multiplication: \texttt{A*B}
1438 \item transposition: \texttt{A.t() $\sim A^t$}
1439 \item matrix inversion and pseudo-inversion, solving linear systems and least-squares problems:
1440 \texttt{A.inv([method]) $\sim A^{-1}$}, \texttt{A.inv([method])*B $\sim X:\,AX=B$}
1441 \item comparison: $\texttt{A}\gtreqqless \texttt{B},\;\texttt{A} \ne \texttt{B},\;\texttt{A}\gtreqqless \alpha,\; \texttt{A} \ne \alpha$.
1442 The result of comparison is 8-bit single channel mask, which elements are set to 255
1443 (if the particular element or pair of elements satisfy the condition) and 0 otherwise.
1444 \item bitwise logical operations: \verb"A & B, A & s, A | B, A | s, A ^ B, A ^ s, ~A"
1445 \item element-wise minimum and maximum: \texttt{min(A, B), min(A, $\alpha$), max(A, B), max(A, $\alpha$)}
1446 \item element-wise absolute value: \texttt{abs(A)}
1447 \item cross-product, dot-product: \texttt{A.cross(B), A.dot(B)}
1448 \item any function of matrix or matrices and scalars that returns a matrix or a scalar, such as
1449 \cvCppCross{norm}, \cvCppCross{mean}, \cvCppCross{sum}, \cvCppCross{countNonZero}, \cvCppCross{trace},
1450 \cvCppCross{determinant}, \cvCppCross{repeat} etc.
1451 \item matrix initializers (\texttt{eye(), zeros(), ones()}), matrix comma-separated initializers,
1452 matrix constructors and operators that extract sub-matrices (see \cross{Mat} description).
1453 \item \verb"Mat_<destination_type>()" constructors to cast the result to the proper type.
1455 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.
1457 \subsection{Mat\_}\label{MatT}
1458 Template matrix class derived from \cross{Mat}
1461 template<typename _Tp> class Mat_ : public Mat
1464 typedef _Tp value_type;
1465 typedef typename DataType<_Tp>::channel_type channel_type;
1466 typedef MatIterator_<_Tp> iterator;
1467 typedef MatConstIterator_<_Tp> const_iterator;
1470 // equivalent to Mat(_rows, _cols, DataType<_Tp>::type)
1471 Mat_(int _rows, int _cols);
1472 // other forms of the above constructor
1473 Mat_(int _rows, int _cols, const _Tp& value);
1474 explicit Mat_(Size _size);
1475 Mat_(Size _size, const _Tp& value);
1476 // copy/conversion contructor. If m is of different type, it's converted
1479 Mat_(const Mat_& m);
1480 // construct a matrix on top of user-allocated data.
1481 // step is in bytes(!!!), regardless of the type
1482 Mat_(int _rows, int _cols, _Tp* _data, size_t _step=AUTO_STEP);
1484 Mat_(const Mat_& m, const Range& rowRange, const Range& colRange);
1485 Mat_(const Mat_& m, const Rect& roi);
1486 // to support complex matrix expressions
1487 Mat_(const MatExpr_Base& expr);
1488 // makes a matrix out of Vec or std::vector. The matrix will have a single column
1489 template<int n> explicit Mat_(const Vec<_Tp, n>& vec);
1490 Mat_(const vector<_Tp>& vec, bool copyData=false);
1492 Mat_& operator = (const Mat& m);
1493 Mat_& operator = (const Mat_& m);
1494 // set all the elements to s.
1495 Mat_& operator = (const _Tp& s);
1497 // iterators; they are smart enough to skip gaps in the end of rows
1500 const_iterator begin() const;
1501 const_iterator end() const;
1503 // equivalent to Mat::create(_rows, _cols, DataType<_Tp>::type)
1504 void create(int _rows, int _cols);
1505 void create(Size _size);
1507 Mat_ cross(const Mat_& m) const;
1508 // to support complex matrix expressions
1509 Mat_& operator = (const MatExpr_Base& expr);
1510 // data type conversion
1511 template<typename T2> operator Mat_<T2>() const;
1512 // overridden forms of Mat::row() etc.
1513 Mat_ row(int y) const;
1514 Mat_ col(int x) const;
1515 Mat_ diag(int d=0) const;
1518 // transposition, inversion, per-element multiplication
1519 MatExpr_<...> t() const;
1520 MatExpr_<...> inv(int method=DECOMP_LU) const;
1522 MatExpr_<...> mul(const Mat_& m, double scale=1) const;
1523 MatExpr_<...> mul(const MatExpr_<...>& m, double scale=1) const;
1525 // overridden forms of Mat::elemSize() etc.
1526 size_t elemSize() const;
1527 size_t elemSize1() const;
1530 int channels() const;
1531 size_t step1() const;
1532 // returns step()/sizeof(_Tp)
1533 size_t stepT() const;
1535 // overridden forms of Mat::zeros() etc. Data type is omitted, of course
1536 static MatExpr_Initializer zeros(int rows, int cols);
1537 static MatExpr_Initializer zeros(Size size);
1538 static MatExpr_Initializer ones(int rows, int cols);
1539 static MatExpr_Initializer ones(Size size);
1540 static MatExpr_Initializer eye(int rows, int cols);
1541 static MatExpr_Initializer eye(Size size);
1543 // some more overriden methods
1544 Mat_ reshape(int _rows) const;
1545 Mat_& adjustROI( int dtop, int dbottom, int dleft, int dright );
1546 Mat_ operator()( const Range& rowRange, const Range& colRange ) const;
1547 Mat_ operator()( const Rect& roi ) const;
1549 // more convenient forms of row and element access operators
1550 _Tp* operator [](int y);
1551 const _Tp* operator [](int y) const;
1553 _Tp& operator ()(int row, int col);
1554 const _Tp& operator ()(int row, int col) const;
1555 _Tp& operator ()(Point pt);
1556 const _Tp& operator ()(Point pt) const;
1558 // to support matrix expressions
1559 operator MatExpr_<Mat_, Mat_>() const;
1561 // conversion to vector.
1562 operator vector<_Tp>() const;
1566 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.:
1569 // create 100x100 8-bit matrix
1570 Mat M(100,100,CV_8U);
1571 // this will compile fine. no any data conversion will be done.
1572 Mat_<float>& M1 = (Mat_<float>&)M;
1573 // the program will likely crash at the statement below
1577 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:
1580 Mat_<double> M(20,20);
1581 for(int i = 0; i < M.rows; i++)
1582 for(int j = 0; j < M.cols; j++)
1583 M(i,j) = 1./(i+j+1);
1586 cout << E.at<double>(0,0)/E.at<double>(M.rows-1,0);
1589 \emph{How to use \texttt{Mat\_} for multi-channel images/matrices?}
1591 This is simple - just pass \texttt{Vec} as \texttt{Mat\_} parameter:
1593 // allocate 320x240 color image and fill it with green (in RGB space)
1594 Mat_<Vec3b> img(240, 320, Vec3b(0,255,0));
1595 // now draw a diagonal white line
1596 for(int i = 0; i < 100; i++)
1597 img(i,i)=Vec3b(255,255,255);
1598 // and now scramble the 2nd (red) channel of each pixel
1599 for(int i = 0; i < img.rows; i++)
1600 for(int j = 0; j < img.cols; j++)
1601 img(i,j)[2] ^= (uchar)(i ^ j);
1604 \subsection{MatND}\label{MatND}
1605 n-dimensional dense array
1611 // default constructor
1613 // constructs array with specific size and data type
1614 MatND(int _ndims, const int* _sizes, int _type);
1615 // constructs array and fills it with the specified value
1616 MatND(int _ndims, const int* _sizes, int _type, const Scalar& _s);
1617 // copy constructor. only the header is copied.
1618 MatND(const MatND& m);
1619 // sub-array selection. only the header is copied
1620 MatND(const MatND& m, const Range* ranges);
1621 // converts old-style nd array to MatND; optionally, copies the data
1622 MatND(const CvMatND* m, bool copyData=false);
1624 MatND& operator = (const MatND& m);
1626 // creates a complete copy of the matrix (all the data is copied)
1627 MatND clone() const;
1628 // sub-array selection; only the header is copied
1629 MatND operator()(const Range* ranges) const;
1631 // copies the data to another matrix.
1632 // Calls m.create(this->size(), this->type()) prior to
1634 void copyTo( MatND& m ) const;
1635 // copies only the selected elements to another matrix.
1636 void copyTo( MatND& m, const MatND& mask ) const;
1637 // converts data to the specified data type.
1638 // calls m.create(this->size(), rtype) prior to the conversion
1639 void convertTo( MatND& m, int rtype, double alpha=1, double beta=0 ) const;
1641 // assigns "s" to each array element.
1642 MatND& operator = (const Scalar& s);
1643 // assigns "s" to the selected elements of array
1644 // (or to all the elements if mask==MatND())
1645 MatND& setTo(const Scalar& s, const MatND& mask=MatND());
1646 // modifies geometry of array without copying the data
1647 MatND reshape(int _newcn, int _newndims=0, const int* _newsz=0) const;
1649 // allocates a new buffer for the data unless the current one already
1650 // has the specified size and type.
1651 void create(int _ndims, const int* _sizes, int _type);
1652 // manually increment reference counter (use with care !!!)
1654 // decrements the reference counter. Dealloctes the data when
1655 // the reference counter reaches zero.
1658 // converts the matrix to 2D Mat or to the old-style CvMatND.
1659 // In either case the data is not copied.
1660 operator Mat() const;
1661 operator CvMatND() const;
1662 // returns true if the array data is stored continuously
1663 bool isContinuous() const;
1664 // returns size of each element in bytes
1665 size_t elemSize() const;
1666 // returns size of each element channel in bytes
1667 size_t elemSize1() const;
1668 // returns OpenCV data type id (CV_8UC1, ... CV_64FC4,...)
1670 // returns depth (CV_8U ... CV_64F)
1672 // returns the number of channels
1673 int channels() const;
1674 // step1() ~ step()/elemSize1()
1675 size_t step1(int i) const;
1677 // return pointer to the element (versions for 1D, 2D, 3D and generic nD cases)
1679 const uchar* ptr(int i0) const;
1680 uchar* ptr(int i0, int i1);
1681 const uchar* ptr(int i0, int i1) const;
1682 uchar* ptr(int i0, int i1, int i2);
1683 const uchar* ptr(int i0, int i1, int i2) const;
1684 uchar* ptr(const int* idx);
1685 const uchar* ptr(const int* idx) const;
1687 // convenient template methods for element access.
1688 // note that _Tp must match the actual matrix type -
1689 // the functions do not do any on-fly type conversion
1690 template<typename _Tp> _Tp& at(int i0);
1691 template<typename _Tp> const _Tp& at(int i0) const;
1692 template<typename _Tp> _Tp& at(int i0, int i1);
1693 template<typename _Tp> const _Tp& at(int i0, int i1) const;
1694 template<typename _Tp> _Tp& at(int i0, int i1, int i2);
1695 template<typename _Tp> const _Tp& at(int i0, int i1, int i2) const;
1696 template<typename _Tp> _Tp& at(const int* idx);
1697 template<typename _Tp> const _Tp& at(const int* idx) const;
1699 enum { MAGIC_VAL=0x42FE0000, AUTO_STEP=-1,
1700 CONTINUOUS_FLAG=CV_MAT_CONT_FLAG, MAX_DIM=CV_MAX_DIM };
1702 // combines data type, continuity flag, signature (magic value)
1704 // the array dimensionality
1707 // data reference counter
1709 // pointer to the data
1711 // and its actual beginning and end
1715 // step and size for each dimension, MAX_DIM at max
1717 size_t step[MAX_DIM];
1721 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:
1723 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}
1725 which is more general form of the respective formula for \cross{Mat}, wherein $\texttt{size[0]}\sim\texttt{rows}$,
1726 $\texttt{size[1]}\sim\texttt{cols}$, \texttt{step[0]} was simply called \texttt{step}, and \texttt{step[1]} was not stored at all but computed as \texttt{Mat::elemSize()}.
1728 In other aspects \texttt{MatND} is also very similar to \texttt{Mat}, with the following limitations and differences:
1730 \item much less operations are implemented for \texttt{MatND}
1731 \item currently, algebraic expressions with \texttt{MatND}'s are not supported
1732 \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.
1735 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):
1738 void computeColorHist(const Mat& image, MatND& hist, int N)
1740 const int histSize[] = {N, N, N};
1742 // make sure that the histogram has proper size and type
1743 hist.create(3, histSize, CV_32F);
1748 // the loop below assumes that the image
1749 // is 8-bit 3-channel, so let's check it.
1750 CV_Assert(image.type() == CV_8UC3);
1751 MatConstIterator_<Vec3b> it = image.begin<Vec3b>(),
1752 it_end = image.end<Vec3b>();
1753 for( ; it != it_end; ++it )
1755 const Vec3b& pix = *it;
1757 // we could have incremented the cells by 1.f/(image.rows*image.cols)
1758 // instead of 1.f to make the histogram normalized.
1759 hist.at<float>(pix[0]*N/256, pix[1]*N/256, pix[2]*N/256) += 1.f;
1764 And here is how you can iterate through \texttt{MatND} elements:
1767 void normalizeColorHist(MatND& hist)
1770 // intialize iterator (the style is different from STL).
1771 // after initialization the iterator will contain
1772 // the number of slices or planes
1773 // the iterator will go through
1774 MatNDIterator it(hist);
1776 // iterate through the matrix. on each iteration
1777 // it.planes[*] (of type Mat) will be set to the current plane.
1778 for(int p = 0; p < it.nplanes; p++, ++it)
1779 s += sum(it.planes[0])[0];
1780 it = MatNDIterator(hist);
1782 for(int p = 0; p < it.nplanes; p++, ++it)
1785 // this is a shorter implementation of the above
1786 // using built-in operations on MatND
1787 double s = sum(hist)[0];
1788 hist.convertTo(hist, hist.type(), 1./s, 0);
1790 // and this is even shorter one
1791 // (assuming that the histogram elements are non-negative)
1792 normalize(hist, hist, 1, 0, NORM_L1);
1797 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.
1799 \subsection{MatND\_}
1800 Template class for n-dimensional dense array derived from \cross{MatND}.
1803 template<typename _Tp> class MatND_ : public MatND
1806 typedef _Tp value_type;
1807 typedef typename DataType<_Tp>::channel_type channel_type;
1809 // constructors, the same as in MatND, only the type is omitted
1811 MatND_(int dims, const int* _sizes);
1812 MatND_(int dims, const int* _sizes, const _Tp& _s);
1813 MatND_(const MatND& m);
1814 MatND_(const MatND_& m);
1815 MatND_(const MatND_& m, const Range* ranges);
1816 MatND_(const CvMatND* m, bool copyData=false);
1817 MatND_& operator = (const MatND& m);
1818 MatND_& operator = (const MatND_& m);
1819 // different initialization function
1820 // where we take _Tp instead of Scalar
1821 MatND_& operator = (const _Tp& s);
1823 // no special destructor is needed; use the one from MatND
1825 void create(int dims, const int* _sizes);
1826 template<typename T2> operator MatND_<T2>() const;
1827 MatND_ clone() const;
1828 MatND_ operator()(const Range* ranges) const;
1830 size_t elemSize() const;
1831 size_t elemSize1() const;
1834 int channels() const;
1835 // step[i]/elemSize()
1836 size_t stepT(int i) const;
1837 size_t step1(int i) const;
1839 // shorter alternatives for MatND::at<_Tp>.
1840 _Tp& operator ()(const int* idx);
1841 const _Tp& operator ()(const int* idx) const;
1842 _Tp& operator ()(int idx0);
1843 const _Tp& operator ()(int idx0) const;
1844 _Tp& operator ()(int idx0, int idx1);
1845 const _Tp& operator ()(int idx0, int idx1) const;
1846 _Tp& operator ()(int idx0, int idx1, int idx2);
1847 const _Tp& operator ()(int idx0, int idx1, int idx2) const;
1848 _Tp& operator ()(int idx0, int idx1, int idx2);
1849 const _Tp& operator ()(int idx0, int idx1, int idx2) const;
1853 \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.
1856 // alternative variant of the above histogram accumulation loop
1858 CV_Assert(hist.type() == CV_32FC1);
1859 MatND_<float>& _hist = (MatND_<float>&)hist;
1860 for( ; it != it_end; ++it )
1862 const Vec3b& pix = *it;
1863 _hist(pix[0]*N/256, pix[1]*N/256, pix[2]*N/256) += 1.f;
1868 \subsection{SparseMat}\label{SparseMat}
1869 Sparse n-dimensional array.
1875 typedef SparseMatIterator iterator;
1876 typedef SparseMatConstIterator const_iterator;
1878 // internal structure - sparse matrix header
1884 // sparse matrix node - element of a hash table
1889 int idx[CV_MAX_DIM];
1892 ////////// constructors and destructor //////////
1893 // default constructor
1895 // creates matrix of the specified size and type
1896 SparseMat(int dims, const int* _sizes, int _type);
1898 SparseMat(const SparseMat& m);
1899 // converts dense 2d matrix to the sparse form,
1900 // if try1d is true and matrix is a single-column matrix (Nx1),
1901 // then the sparse matrix will be 1-dimensional.
1902 SparseMat(const Mat& m, bool try1d=false);
1903 // converts dense n-d matrix to the sparse form
1904 SparseMat(const MatND& m);
1905 // converts old-style sparse matrix to the new-style.
1906 // all the data is copied, so that "m" can be safely
1907 // deleted after the conversion
1908 SparseMat(const CvSparseMat* m);
1912 ///////// assignment operations ///////////
1914 // this is O(1) operation; no data is copied
1915 SparseMat& operator = (const SparseMat& m);
1916 // (equivalent to the corresponding constructor with try1d=false)
1917 SparseMat& operator = (const Mat& m);
1918 SparseMat& operator = (const MatND& m);
1920 // creates full copy of the matrix
1921 SparseMat clone() const;
1923 // copy all the data to the destination matrix.
1924 // the destination will be reallocated if needed.
1925 void copyTo( SparseMat& m ) const;
1926 // converts 1D or 2D sparse matrix to dense 2D matrix.
1927 // If the sparse matrix is 1D, then the result will
1928 // be a single-column matrix.
1929 void copyTo( Mat& m ) const;
1930 // converts arbitrary sparse matrix to dense matrix.
1931 // watch out the memory!
1932 void copyTo( MatND& m ) const;
1933 // multiplies all the matrix elements by the specified scalar
1934 void convertTo( SparseMat& m, int rtype, double alpha=1 ) const;
1935 // converts sparse matrix to dense matrix with optional type conversion and scaling.
1936 // When rtype=-1, the destination element type will be the same
1937 // as the sparse matrix element type.
1938 // Otherwise rtype will specify the depth and
1939 // the number of channels will remain the same is in the sparse matrix
1940 void convertTo( Mat& m, int rtype, double alpha=1, double beta=0 ) const;
1941 void convertTo( MatND& m, int rtype, double alpha=1, double beta=0 ) const;
1944 void assignTo( SparseMat& m, int type=-1 ) const;
1946 // reallocates sparse matrix. If it was already of the proper size and type,
1947 // it is simply cleared with clear(), otherwise,
1948 // the old matrix is released (using release()) and the new one is allocated.
1949 void create(int dims, const int* _sizes, int _type);
1950 // sets all the matrix elements to 0, which means clearing the hash table.
1952 // manually increases reference counter to the header.
1954 // decreses the header reference counter, when it reaches 0,
1955 // the header and all the underlying data are deallocated.
1958 // converts sparse matrix to the old-style representation.
1959 // all the elements are copied.
1960 operator CvSparseMat*() const;
1961 // size of each element in bytes
1962 // (the matrix nodes will be bigger because of
1963 // element indices and other SparseMat::Node elements).
1964 size_t elemSize() const;
1965 // elemSize()/channels()
1966 size_t elemSize1() const;
1968 // the same is in Mat and MatND
1971 int channels() const;
1973 // returns the array of sizes and 0 if the matrix is not allocated
1974 const int* size() const;
1975 // returns i-th size (or 0)
1976 int size(int i) const;
1977 // returns the matrix dimensionality
1979 // returns the number of non-zero elements
1980 size_t nzcount() const;
1982 // compute element hash value from the element indices:
1984 size_t hash(int i0) const;
1986 size_t hash(int i0, int i1) const;
1988 size_t hash(int i0, int i1, int i2) const;
1990 size_t hash(const int* idx) const;
1992 // low-level element-acccess functions,
1993 // special variants for 1D, 2D, 3D cases and the generic one for n-D case.
1995 // return pointer to the matrix element.
1996 // if the element is there (it's non-zero), the pointer to it is returned
1997 // if it's not there and createMissing=false, NULL pointer is returned
1998 // if it's not there and createMissing=true, then the new element
1999 // is created and initialized with 0. Pointer to it is returned
2000 // If the optional hashval pointer is not NULL, the element hash value is
2001 // not computed, but *hashval is taken instead.
2002 uchar* ptr(int i0, bool createMissing, size_t* hashval=0);
2003 uchar* ptr(int i0, int i1, bool createMissing, size_t* hashval=0);
2004 uchar* ptr(int i0, int i1, int i2, bool createMissing, size_t* hashval=0);
2005 uchar* ptr(const int* idx, bool createMissing, size_t* hashval=0);
2007 // higher-level element access functions:
2008 // ref<_Tp>(i0,...[,hashval]) - equivalent to *(_Tp*)ptr(i0,...true[,hashval]).
2009 // always return valid reference to the element.
2010 // If it's did not exist, it is created.
2011 // find<_Tp>(i0,...[,hashval]) - equivalent to (_const Tp*)ptr(i0,...false[,hashval]).
2012 // return pointer to the element or NULL pointer if the element is not there.
2013 // value<_Tp>(i0,...[,hashval]) - equivalent to
2014 // { const _Tp* p = find<_Tp>(i0,...[,hashval]); return p ? *p : _Tp(); }
2015 // that is, 0 is returned when the element is not there.
2016 // note that _Tp must match the actual matrix type -
2017 // the functions do not do any on-fly type conversion
2020 template<typename _Tp> _Tp& ref(int i0, size_t* hashval=0);
2021 template<typename _Tp> _Tp value(int i0, size_t* hashval=0) const;
2022 template<typename _Tp> const _Tp* find(int i0, size_t* hashval=0) const;
2025 template<typename _Tp> _Tp& ref(int i0, int i1, size_t* hashval=0);
2026 template<typename _Tp> _Tp value(int i0, int i1, size_t* hashval=0) const;
2027 template<typename _Tp> const _Tp* find(int i0, int i1, size_t* hashval=0) const;
2030 template<typename _Tp> _Tp& ref(int i0, int i1, int i2, size_t* hashval=0);
2031 template<typename _Tp> _Tp value(int i0, int i1, int i2, size_t* hashval=0) const;
2032 template<typename _Tp> const _Tp* find(int i0, int i1, int i2, size_t* hashval=0) const;
2035 template<typename _Tp> _Tp& ref(const int* idx, size_t* hashval=0);
2036 template<typename _Tp> _Tp value(const int* idx, size_t* hashval=0) const;
2037 template<typename _Tp> const _Tp* find(const int* idx, size_t* hashval=0) const;
2039 // erase the specified matrix element.
2040 // When there is no such element, the methods do nothing
2041 void erase(int i0, int i1, size_t* hashval=0);
2042 void erase(int i0, int i1, int i2, size_t* hashval=0);
2043 void erase(const int* idx, size_t* hashval=0);
2045 // return the matrix iterators,
2046 // pointing to the first sparse matrix element,
2047 SparseMatIterator begin();
2048 SparseMatConstIterator begin() const;
2049 // ... or to the point after the last sparse matrix element
2050 SparseMatIterator end();
2051 SparseMatConstIterator end() const;
2053 // and the template forms of the above methods.
2054 // _Tp must match the actual matrix type.
2055 template<typename _Tp> SparseMatIterator_<_Tp> begin();
2056 template<typename _Tp> SparseMatConstIterator_<_Tp> begin() const;
2057 template<typename _Tp> SparseMatIterator_<_Tp> end();
2058 template<typename _Tp> SparseMatConstIterator_<_Tp> end() const;
2060 // return value stored in the sparse martix node
2061 template<typename _Tp> _Tp& value(Node* n);
2062 template<typename _Tp> const _Tp& value(const Node* n) const;
2064 ////////////// some internal-use methods ///////////////
2067 // pointer to the sparse matrix header
2072 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:
2075 \item query operations (\texttt{SparseMat::ptr} and the higher-level \texttt{SparseMat::ref}, \texttt{SparseMat::value} and \texttt{SparseMat::find}), e.g.:
2078 int size[] = {10, 10, 10, 10, 10};
2079 SparseMat sparse_mat(dims, size, CV_32F);
2080 for(int i = 0; i < 1000; i++)
2083 for(int k = 0; k < dims; k++)
2084 idx[k] = rand()%sparse_mat.size(k);
2085 sparse_mat.ref<float>(idx) += 1.f;
2088 \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:
2090 // prints elements of a sparse floating-point matrix
2091 // and the sum of elements.
2092 SparseMatConstIterator_<float>
2093 it = sparse_mat.begin<float>(),
2094 it_end = sparse_mat.end<float>();
2096 int dims = sparse_mat.dims();
2097 for(; it != it_end; ++it)
2099 // print element indices and the element value
2100 const Node* n = it.node();
2102 for(int i = 0; i < dims; i++)
2103 printf("%3d%c", n->idx[i], i < dims-1 ? ',' : ')');
2104 printf(": %f\n", *it);
2107 printf("Element sum is %g\n", s);
2109 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.
2110 \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:
2112 double cross_corr(const SparseMat& a, const SparseMat& b)
2114 const SparseMat *_a = &a, *_b = &b;
2115 // if b contains less elements than a,
2116 // it's faster to iterate through b
2117 if(_a->nzcount() > _b->nzcount())
2119 SparseMatConstIterator_<float> it = _a->begin<float>(),
2120 it_end = _a->end<float>();
2122 for(; it != it_end; ++it)
2124 // take the next element from the first matrix
2126 const Node* anode = it.node();
2127 // and try to find element with the same index in the second matrix.
2128 // since the hash value depends only on the element index,
2129 // we reuse hashvalue stored in the node
2130 float bvalue = _b->value<float>(anode->idx,&anode->hashval);
2131 ccorr += avalue*bvalue;
2138 \subsection{SparseMat\_}
2139 Template sparse n-dimensional array class derived from \cross{SparseMat}
2142 template<typename _Tp> class SparseMat_ : public SparseMat
2145 typedef SparseMatIterator_<_Tp> iterator;
2146 typedef SparseMatConstIterator_<_Tp> const_iterator;
2149 // the created matrix will have data type = DataType<_Tp>::type
2151 SparseMat_(int dims, const int* _sizes);
2152 SparseMat_(const SparseMat& m);
2153 SparseMat_(const SparseMat_& m);
2154 SparseMat_(const Mat& m);
2155 SparseMat_(const MatND& m);
2156 SparseMat_(const CvSparseMat* m);
2157 // assignment operators; data type conversion is done when necessary
2158 SparseMat_& operator = (const SparseMat& m);
2159 SparseMat_& operator = (const SparseMat_& m);
2160 SparseMat_& operator = (const Mat& m);
2161 SparseMat_& operator = (const MatND& m);
2163 // equivalent to the correspoding parent class methods
2164 SparseMat_ clone() const;
2165 void create(int dims, const int* _sizes);
2166 operator CvSparseMat*() const;
2168 // overriden methods that do extra checks for the data type
2171 int channels() const;
2173 // more convenient element access operations.
2174 // ref() is retained (but <_Tp> specification is not need anymore);
2175 // operator () is equivalent to SparseMat::value<_Tp>
2176 _Tp& ref(int i0, size_t* hashval=0);
2177 _Tp operator()(int i0, size_t* hashval=0) const;
2178 _Tp& ref(int i0, int i1, size_t* hashval=0);
2179 _Tp operator()(int i0, int i1, size_t* hashval=0) const;
2180 _Tp& ref(int i0, int i1, int i2, size_t* hashval=0);
2181 _Tp operator()(int i0, int i1, int i2, size_t* hashval=0) const;
2182 _Tp& ref(const int* idx, size_t* hashval=0);
2183 _Tp operator()(const int* idx, size_t* hashval=0) const;
2186 SparseMatIterator_<_Tp> begin();
2187 SparseMatConstIterator_<_Tp> begin() const;
2188 SparseMatIterator_<_Tp> end();
2189 SparseMatConstIterator_<_Tp> end() const;
2193 \texttt{SparseMat\_} is a thin wrapper on top of \cross{SparseMat}, made in the same way as \texttt{Mat\_} and \texttt{MatND\_}.
2194 It simplifies notation of some operations, and that's it.
2196 int sz[] = {10, 20, 30};
2197 SparseMat_<double> M(3, sz);
2199 M.ref(1, 2, 3) = M(4, 5, 6) + M(7, 8, 9);