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45 #ifndef __OPENCV_CORE_HPP__
46 #define __OPENCV_CORE_HPP__
49 # error core.hpp header must be compiled as C++
52 #include "opencv2/core/cvdef.h"
53 #include "opencv2/core/version.hpp"
54 #include "opencv2/core/base.hpp"
55 #include "opencv2/core/cvstd.hpp"
56 #include "opencv2/core/traits.hpp"
57 #include "opencv2/core/matx.hpp"
58 #include "opencv2/core/types.hpp"
59 #include "opencv2/core/mat.hpp"
60 #include "opencv2/core/persistence.hpp"
63 @defgroup core Core functionality
65 @defgroup core_basic Basic structures
66 @defgroup core_c C structures and operations
68 @defgroup core_c_glue Connections with C++
70 @defgroup core_array Operations on arrays
71 @defgroup core_xml XML/YAML Persistence
72 @defgroup core_cluster Clustering
73 @defgroup core_utils Utility and system functions and macros
75 @defgroup core_utils_neon NEON utilities
77 @defgroup core_opengl OpenGL interoperability
78 @defgroup core_ipp Intel IPP Asynchronous C/C++ Converters
79 @defgroup core_optim Optimization Algorithms
80 @defgroup core_directx DirectX interoperability
81 @defgroup core_eigen Eigen support
82 @defgroup core_opencl OpenCL support
88 //! @addtogroup core_utils
91 /*! @brief Class passed to an error.
93 This class encapsulates all or almost all necessary
94 information about the error happened in the program. The exception is
95 usually constructed and thrown implicitly via CV_Error and CV_Error_ macros.
98 class CV_EXPORTS Exception : public std::exception
106 Full constructor. Normally the constuctor is not called explicitly.
107 Instead, the macros CV_Error(), CV_Error_() and CV_Assert() are used.
109 Exception(int _code, const String& _err, const String& _func, const String& _file, int _line);
110 virtual ~Exception() throw();
113 \return the error description and the context as a text string.
115 virtual const char *what() const throw();
116 void formatMessage();
118 String msg; ///< the formatted error message
120 int code; ///< error code @see CVStatus
121 String err; ///< error description
122 String func; ///< function name. Available only when the compiler supports getting it
123 String file; ///< source file name where the error has occured
124 int line; ///< line number in the source file where the error has occured
127 /*! @brief Signals an error and raises the exception.
129 By default the function prints information about the error to stderr,
130 then it either stops if cv::setBreakOnError() had been called before or raises the exception.
131 It is possible to alternate error processing by using cv::redirectError().
132 @param exc the exception raisen.
133 @deprecated drop this version
135 CV_EXPORTS void error( const Exception& exc );
137 enum SortFlags { SORT_EVERY_ROW = 0, //!< each matrix row is sorted independently
138 SORT_EVERY_COLUMN = 1, //!< each matrix column is sorted
139 //!< independently; this flag and the previous one are
140 //!< mutually exclusive.
141 SORT_ASCENDING = 0, //!< each matrix row is sorted in the ascending
143 SORT_DESCENDING = 16 //!< each matrix row is sorted in the
144 //!< descending order; this flag and the previous one are also
145 //!< mutually exclusive.
153 //! Covariation flags
155 /** The output covariance matrix is calculated as:
156 \f[\texttt{scale} \cdot [ \texttt{vects} [0]- \texttt{mean} , \texttt{vects} [1]- \texttt{mean} ,...]^T \cdot [ \texttt{vects} [0]- \texttt{mean} , \texttt{vects} [1]- \texttt{mean} ,...],\f]
157 The covariance matrix will be nsamples x nsamples. Such an unusual covariance matrix is used
158 for fast PCA of a set of very large vectors (see, for example, the EigenFaces technique for
159 face recognition). Eigenvalues of this "scrambled" matrix match the eigenvalues of the true
160 covariance matrix. The "true" eigenvectors can be easily calculated from the eigenvectors of
161 the "scrambled" covariance matrix. */
163 /**The output covariance matrix is calculated as:
164 \f[\texttt{scale} \cdot [ \texttt{vects} [0]- \texttt{mean} , \texttt{vects} [1]- \texttt{mean} ,...] \cdot [ \texttt{vects} [0]- \texttt{mean} , \texttt{vects} [1]- \texttt{mean} ,...]^T,\f]
165 covar will be a square matrix of the same size as the total number of elements in each input
166 vector. One and only one of COVAR_SCRAMBLED and COVAR_NORMAL must be specified.*/
168 /** If the flag is specified, the function does not calculate mean from
169 the input vectors but, instead, uses the passed mean vector. This is useful if mean has been
170 pre-calculated or known in advance, or if the covariance matrix is calculated by parts. In
171 this case, mean is not a mean vector of the input sub-set of vectors but rather the mean
172 vector of the whole set.*/
174 /** If the flag is specified, the covariance matrix is scaled. In the
175 "normal" mode, scale is 1./nsamples . In the "scrambled" mode, scale is the reciprocal of the
176 total number of elements in each input vector. By default (if the flag is not specified), the
177 covariance matrix is not scaled ( scale=1 ).*/
180 specified, all the input vectors are stored as rows of the samples matrix. mean should be a
181 single-row vector in this case.*/
184 specified, all the input vectors are stored as columns of the samples matrix. mean should be a
185 single-column vector in this case.*/
191 /** Select random initial centers in each attempt.*/
192 KMEANS_RANDOM_CENTERS = 0,
193 /** Use kmeans++ center initialization by Arthur and Vassilvitskii [Arthur2007].*/
194 KMEANS_PP_CENTERS = 2,
195 /** During the first (and possibly the only) attempt, use the
196 user-supplied labels instead of computing them from the initial centers. For the second and
197 further attempts, use the random or semi-random centers. Use one of KMEANS_\*_CENTERS flag
198 to specify the exact method.*/
199 KMEANS_USE_INITIAL_LABELS = 1
205 LINE_4 = 4, //!< 4-connected line
206 LINE_8 = 8, //!< 8-connected line
207 LINE_AA = 16 //!< antialiased line
210 //! Only a subset of Hershey fonts
211 //! <http://sources.isc.org/utils/misc/hershey-font.txt> are supported
213 FONT_HERSHEY_SIMPLEX = 0, //!< normal size sans-serif font
214 FONT_HERSHEY_PLAIN = 1, //!< small size sans-serif font
215 FONT_HERSHEY_DUPLEX = 2, //!< normal size sans-serif font (more complex than FONT_HERSHEY_SIMPLEX)
216 FONT_HERSHEY_COMPLEX = 3, //!< normal size serif font
217 FONT_HERSHEY_TRIPLEX = 4, //!< normal size serif font (more complex than FONT_HERSHEY_COMPLEX)
218 FONT_HERSHEY_COMPLEX_SMALL = 5, //!< smaller version of FONT_HERSHEY_COMPLEX
219 FONT_HERSHEY_SCRIPT_SIMPLEX = 6, //!< hand-writing style font
220 FONT_HERSHEY_SCRIPT_COMPLEX = 7, //!< more complex variant of FONT_HERSHEY_SCRIPT_SIMPLEX
221 FONT_ITALIC = 16 //!< flag for italic font
224 enum ReduceTypes { REDUCE_SUM = 0, //!< the output is the sum of all rows/columns of the matrix.
225 REDUCE_AVG = 1, //!< the output is the mean vector of all rows/columns of the matrix.
226 REDUCE_MAX = 2, //!< the output is the maximum (column/row-wise) of all rows/columns of the matrix.
227 REDUCE_MIN = 3 //!< the output is the minimum (column/row-wise) of all rows/columns of the matrix.
231 /** @brief Swaps two matrices
233 CV_EXPORTS void swap(Mat& a, Mat& b);
235 CV_EXPORTS void swap( UMat& a, UMat& b );
239 //! @addtogroup core_array
242 /** @brief Computes the source location of an extrapolated pixel.
244 The function computes and returns the coordinate of a donor pixel corresponding to the specified
245 extrapolated pixel when using the specified extrapolation border mode. For example, if you use
246 cv::BORDER_WRAP mode in the horizontal direction, cv::BORDER_REFLECT_101 in the vertical direction and
247 want to compute value of the "virtual" pixel Point(-5, 100) in a floating-point image img , it
250 float val = img.at<float>(borderInterpolate(100, img.rows, cv::BORDER_REFLECT_101),
251 borderInterpolate(-5, img.cols, cv::BORDER_WRAP));
253 Normally, the function is not called directly. It is used inside filtering functions and also in
255 @param p 0-based coordinate of the extrapolated pixel along one of the axes, likely \<0 or \>= len
256 @param len Length of the array along the corresponding axis.
257 @param borderType Border type, one of the cv::BorderTypes, except for cv::BORDER_TRANSPARENT and
258 cv::BORDER_ISOLATED . When borderType==cv::BORDER_CONSTANT , the function always returns -1, regardless
263 CV_EXPORTS_W int borderInterpolate(int p, int len, int borderType);
265 /** @brief Forms a border around an image.
267 The function copies the source image into the middle of the destination image. The areas to the
268 left, to the right, above and below the copied source image will be filled with extrapolated
269 pixels. This is not what filtering functions based on it do (they extrapolate pixels on-fly), but
270 what other more complex functions, including your own, may do to simplify image boundary handling.
272 The function supports the mode when src is already in the middle of dst . In this case, the
273 function does not copy src itself but simply constructs the border, for example:
276 // let border be the same in all directions
278 // constructs a larger image to fit both the image and the border
279 Mat gray_buf(rgb.rows + border*2, rgb.cols + border*2, rgb.depth());
280 // select the middle part of it w/o copying data
281 Mat gray(gray_canvas, Rect(border, border, rgb.cols, rgb.rows));
282 // convert image from RGB to grayscale
283 cvtColor(rgb, gray, COLOR_RGB2GRAY);
284 // form a border in-place
285 copyMakeBorder(gray, gray_buf, border, border,
286 border, border, BORDER_REPLICATE);
287 // now do some custom filtering ...
290 @note When the source image is a part (ROI) of a bigger image, the function will try to use the
291 pixels outside of the ROI to form a border. To disable this feature and always do extrapolation, as
292 if src was not a ROI, use borderType | BORDER_ISOLATED.
294 @param src Source image.
295 @param dst Destination image of the same type as src and the size Size(src.cols+left+right,
296 src.rows+top+bottom) .
300 @param right Parameter specifying how many pixels in each direction from the source image rectangle
301 to extrapolate. For example, top=1, bottom=1, left=1, right=1 mean that 1 pixel-wide border needs
303 @param borderType Border type. See borderInterpolate for details.
304 @param value Border value if borderType==BORDER_CONSTANT .
306 @sa borderInterpolate
308 CV_EXPORTS_W void copyMakeBorder(InputArray src, OutputArray dst,
309 int top, int bottom, int left, int right,
310 int borderType, const Scalar& value = Scalar() );
312 /** @brief Calculates the per-element sum of two arrays or an array and a scalar.
314 The function add calculates:
315 - Sum of two arrays when both input arrays have the same size and the same number of channels:
316 \f[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1}(I) + \texttt{src2}(I)) \quad \texttt{if mask}(I) \ne0\f]
317 - Sum of an array and a scalar when src2 is constructed from Scalar or has the same number of
318 elements as `src1.channels()`:
319 \f[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1}(I) + \texttt{src2} ) \quad \texttt{if mask}(I) \ne0\f]
320 - Sum of a scalar and an array when src1 is constructed from Scalar or has the same number of
321 elements as `src2.channels()`:
322 \f[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1} + \texttt{src2}(I) ) \quad \texttt{if mask}(I) \ne0\f]
323 where `I` is a multi-dimensional index of array elements. In case of multi-channel arrays, each
324 channel is processed independently.
326 The first function in the list above can be replaced with matrix expressions:
329 dst += src1; // equivalent to add(dst, src1, dst);
331 The input arrays and the output array can all have the same or different depths. For example, you
332 can add a 16-bit unsigned array to a 8-bit signed array and store the sum as a 32-bit
333 floating-point array. Depth of the output array is determined by the dtype parameter. In the second
334 and third cases above, as well as in the first case, when src1.depth() == src2.depth(), dtype can
335 be set to the default -1. In this case, the output array will have the same depth as the input
336 array, be it src1, src2 or both.
337 @note Saturation is not applied when the output array has the depth CV_32S. You may even get
338 result of an incorrect sign in the case of overflow.
339 @param src1 first input array or a scalar.
340 @param src2 second input array or a scalar.
341 @param dst output array that has the same size and number of channels as the input array(s); the
342 depth is defined by dtype or src1/src2.
343 @param mask optional operation mask - 8-bit single channel array, that specifies elements of the
344 output array to be changed.
345 @param dtype optional depth of the output array (see the discussion below).
346 @sa subtract, addWeighted, scaleAdd, Mat::convertTo
348 CV_EXPORTS_W void add(InputArray src1, InputArray src2, OutputArray dst,
349 InputArray mask = noArray(), int dtype = -1);
351 /** @brief Calculates the per-element difference between two arrays or array and a scalar.
353 The function subtract calculates:
354 - Difference between two arrays, when both input arrays have the same size and the same number of
356 \f[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1}(I) - \texttt{src2}(I)) \quad \texttt{if mask}(I) \ne0\f]
357 - Difference between an array and a scalar, when src2 is constructed from Scalar or has the same
358 number of elements as `src1.channels()`:
359 \f[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1}(I) - \texttt{src2} ) \quad \texttt{if mask}(I) \ne0\f]
360 - Difference between a scalar and an array, when src1 is constructed from Scalar or has the same
361 number of elements as `src2.channels()`:
362 \f[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1} - \texttt{src2}(I) ) \quad \texttt{if mask}(I) \ne0\f]
363 - The reverse difference between a scalar and an array in the case of `SubRS`:
364 \f[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src2} - \texttt{src1}(I) ) \quad \texttt{if mask}(I) \ne0\f]
365 where I is a multi-dimensional index of array elements. In case of multi-channel arrays, each
366 channel is processed independently.
368 The first function in the list above can be replaced with matrix expressions:
371 dst -= src1; // equivalent to subtract(dst, src1, dst);
373 The input arrays and the output array can all have the same or different depths. For example, you
374 can subtract to 8-bit unsigned arrays and store the difference in a 16-bit signed array. Depth of
375 the output array is determined by dtype parameter. In the second and third cases above, as well as
376 in the first case, when src1.depth() == src2.depth(), dtype can be set to the default -1. In this
377 case the output array will have the same depth as the input array, be it src1, src2 or both.
378 @note Saturation is not applied when the output array has the depth CV_32S. You may even get
379 result of an incorrect sign in the case of overflow.
380 @param src1 first input array or a scalar.
381 @param src2 second input array or a scalar.
382 @param dst output array of the same size and the same number of channels as the input array.
383 @param mask optional operation mask; this is an 8-bit single channel array that specifies elements
384 of the output array to be changed.
385 @param dtype optional depth of the output array
386 @sa add, addWeighted, scaleAdd, Mat::convertTo
388 CV_EXPORTS_W void subtract(InputArray src1, InputArray src2, OutputArray dst,
389 InputArray mask = noArray(), int dtype = -1);
392 /** @brief Calculates the per-element scaled product of two arrays.
394 The function multiply calculates the per-element product of two arrays:
396 \f[\texttt{dst} (I)= \texttt{saturate} ( \texttt{scale} \cdot \texttt{src1} (I) \cdot \texttt{src2} (I))\f]
398 There is also a @ref MatrixExpressions -friendly variant of the first function. See Mat::mul .
400 For a not-per-element matrix product, see gemm .
402 @note Saturation is not applied when the output array has the depth
403 CV_32S. You may even get result of an incorrect sign in the case of
405 @param src1 first input array.
406 @param src2 second input array of the same size and the same type as src1.
407 @param dst output array of the same size and type as src1.
408 @param scale optional scale factor.
409 @param dtype optional depth of the output array
410 @sa add, subtract, divide, scaleAdd, addWeighted, accumulate, accumulateProduct, accumulateSquare,
413 CV_EXPORTS_W void multiply(InputArray src1, InputArray src2,
414 OutputArray dst, double scale = 1, int dtype = -1);
416 /** @brief Performs per-element division of two arrays or a scalar by an array.
418 The functions divide divide one array by another:
419 \f[\texttt{dst(I) = saturate(src1(I)*scale/src2(I))}\f]
420 or a scalar by an array when there is no src1 :
421 \f[\texttt{dst(I) = saturate(scale/src2(I))}\f]
423 When src2(I) is zero, dst(I) will also be zero. Different channels of
424 multi-channel arrays are processed independently.
426 @note Saturation is not applied when the output array has the depth CV_32S. You may even get
427 result of an incorrect sign in the case of overflow.
428 @param src1 first input array.
429 @param src2 second input array of the same size and type as src1.
430 @param scale scalar factor.
431 @param dst output array of the same size and type as src2.
432 @param dtype optional depth of the output array; if -1, dst will have depth src2.depth(), but in
433 case of an array-by-array division, you can only pass -1 when src1.depth()==src2.depth().
434 @sa multiply, add, subtract
436 CV_EXPORTS_W void divide(InputArray src1, InputArray src2, OutputArray dst,
437 double scale = 1, int dtype = -1);
440 CV_EXPORTS_W void divide(double scale, InputArray src2,
441 OutputArray dst, int dtype = -1);
443 /** @brief Calculates the sum of a scaled array and another array.
445 The function scaleAdd is one of the classical primitive linear algebra operations, known as DAXPY
446 or SAXPY in [BLAS](http://en.wikipedia.org/wiki/Basic_Linear_Algebra_Subprograms). It calculates
447 the sum of a scaled array and another array:
448 \f[\texttt{dst} (I)= \texttt{scale} \cdot \texttt{src1} (I) + \texttt{src2} (I)\f]
449 The function can also be emulated with a matrix expression, for example:
453 A.row(0) = A.row(1)*2 + A.row(2);
455 @param src1 first input array.
456 @param alpha scale factor for the first array.
457 @param src2 second input array of the same size and type as src1.
458 @param dst output array of the same size and type as src1.
459 @sa add, addWeighted, subtract, Mat::dot, Mat::convertTo
461 CV_EXPORTS_W void scaleAdd(InputArray src1, double alpha, InputArray src2, OutputArray dst);
463 /** @brief Calculates the weighted sum of two arrays.
465 The function addWeighted calculates the weighted sum of two arrays as follows:
466 \f[\texttt{dst} (I)= \texttt{saturate} ( \texttt{src1} (I)* \texttt{alpha} + \texttt{src2} (I)* \texttt{beta} + \texttt{gamma} )\f]
467 where I is a multi-dimensional index of array elements. In case of multi-channel arrays, each
468 channel is processed independently.
469 The function can be replaced with a matrix expression:
471 dst = src1*alpha + src2*beta + gamma;
473 @note Saturation is not applied when the output array has the depth CV_32S. You may even get
474 result of an incorrect sign in the case of overflow.
475 @param src1 first input array.
476 @param alpha weight of the first array elements.
477 @param src2 second input array of the same size and channel number as src1.
478 @param beta weight of the second array elements.
479 @param gamma scalar added to each sum.
480 @param dst output array that has the same size and number of channels as the input arrays.
481 @param dtype optional depth of the output array; when both input arrays have the same depth, dtype
482 can be set to -1, which will be equivalent to src1.depth().
483 @sa add, subtract, scaleAdd, Mat::convertTo
485 CV_EXPORTS_W void addWeighted(InputArray src1, double alpha, InputArray src2,
486 double beta, double gamma, OutputArray dst, int dtype = -1);
488 /** @brief Scales, calculates absolute values, and converts the result to 8-bit.
490 On each element of the input array, the function convertScaleAbs
491 performs three operations sequentially: scaling, taking an absolute
492 value, conversion to an unsigned 8-bit type:
493 \f[\texttt{dst} (I)= \texttt{saturate\_cast<uchar>} (| \texttt{src} (I)* \texttt{alpha} + \texttt{beta} |)\f]
494 In case of multi-channel arrays, the function processes each channel
495 independently. When the output is not 8-bit, the operation can be
496 emulated by calling the Mat::convertTo method (or by using matrix
497 expressions) and then by calculating an absolute value of the result.
500 Mat_<float> A(30,30);
501 randu(A, Scalar(-100), Scalar(100));
502 Mat_<float> B = A*5 + 3;
504 // Mat_<float> B = abs(A*5+3) will also do the job,
505 // but it will allocate a temporary matrix
507 @param src input array.
508 @param dst output array.
509 @param alpha optional scale factor.
510 @param beta optional delta added to the scaled values.
511 @sa Mat::convertTo, cv::abs(const Mat&)
513 CV_EXPORTS_W void convertScaleAbs(InputArray src, OutputArray dst,
514 double alpha = 1, double beta = 0);
516 /** @brief Performs a look-up table transform of an array.
518 The function LUT fills the output array with values from the look-up table. Indices of the entries
519 are taken from the input array. That is, the function processes each element of src as follows:
520 \f[\texttt{dst} (I) \leftarrow \texttt{lut(src(I) + d)}\f]
522 \f[d = \fork{0}{if \(\texttt{src}\) has depth \(\texttt{CV_8U}\)}{128}{if \(\texttt{src}\) has depth \(\texttt{CV_8S}\)}\f]
523 @param src input array of 8-bit elements.
524 @param lut look-up table of 256 elements; in case of multi-channel input array, the table should
525 either have a single channel (in this case the same table is used for all channels) or the same
526 number of channels as in the input array.
527 @param dst output array of the same size and number of channels as src, and the same depth as lut.
528 @sa convertScaleAbs, Mat::convertTo
530 CV_EXPORTS_W void LUT(InputArray src, InputArray lut, OutputArray dst);
532 /** @brief Calculates the sum of array elements.
534 The functions sum calculate and return the sum of array elements,
535 independently for each channel.
536 @param src input array that must have from 1 to 4 channels.
537 @sa countNonZero, mean, meanStdDev, norm, minMaxLoc, reduce
539 CV_EXPORTS_AS(sumElems) Scalar sum(InputArray src);
541 /** @brief Counts non-zero array elements.
543 The function returns the number of non-zero elements in src :
544 \f[\sum _{I: \; \texttt{src} (I) \ne0 } 1\f]
545 @param src single-channel array.
546 @sa mean, meanStdDev, norm, minMaxLoc, calcCovarMatrix
548 CV_EXPORTS_W int countNonZero( InputArray src );
550 /** @brief Returns the list of locations of non-zero pixels
552 Given a binary matrix (likely returned from an operation such
553 as threshold(), compare(), >, ==, etc, return all of
554 the non-zero indices as a cv::Mat or std::vector<cv::Point> (x,y)
557 cv::Mat binaryImage; // input, binary image
558 cv::Mat locations; // output, locations of non-zero pixels
559 cv::findNonZero(binaryImage, locations);
561 // access pixel coordinates
562 Point pnt = locations.at<Point>(i);
566 cv::Mat binaryImage; // input, binary image
567 vector<Point> locations; // output, locations of non-zero pixels
568 cv::findNonZero(binaryImage, locations);
570 // access pixel coordinates
571 Point pnt = locations[i];
573 @param src single-channel array (type CV_8UC1)
574 @param idx the output array, type of cv::Mat or std::vector<Point>, corresponding to non-zero indices in the input
576 CV_EXPORTS_W void findNonZero( InputArray src, OutputArray idx );
578 /** @brief Calculates an average (mean) of array elements.
580 The function mean calculates the mean value M of array elements,
581 independently for each channel, and return it:
582 \f[\begin{array}{l} N = \sum _{I: \; \texttt{mask} (I) \ne 0} 1 \\ M_c = \left ( \sum _{I: \; \texttt{mask} (I) \ne 0}{ \texttt{mtx} (I)_c} \right )/N \end{array}\f]
583 When all the mask elements are 0's, the functions return Scalar::all(0)
584 @param src input array that should have from 1 to 4 channels so that the result can be stored in
586 @param mask optional operation mask.
587 @sa countNonZero, meanStdDev, norm, minMaxLoc
589 CV_EXPORTS_W Scalar mean(InputArray src, InputArray mask = noArray());
591 /** Calculates a mean and standard deviation of array elements.
593 The function meanStdDev calculates the mean and the standard deviation M
594 of array elements independently for each channel and returns it via the
596 \f[\begin{array}{l} N = \sum _{I, \texttt{mask} (I) \ne 0} 1 \\ \texttt{mean} _c = \frac{\sum_{ I: \; \texttt{mask}(I) \ne 0} \texttt{src} (I)_c}{N} \\ \texttt{stddev} _c = \sqrt{\frac{\sum_{ I: \; \texttt{mask}(I) \ne 0} \left ( \texttt{src} (I)_c - \texttt{mean} _c \right )^2}{N}} \end{array}\f]
597 When all the mask elements are 0's, the functions return
598 mean=stddev=Scalar::all(0).
599 @note The calculated standard deviation is only the diagonal of the
600 complete normalized covariance matrix. If the full matrix is needed, you
601 can reshape the multi-channel array M x N to the single-channel array
602 M\*N x mtx.channels() (only possible when the matrix is continuous) and
603 then pass the matrix to calcCovarMatrix .
604 @param src input array that should have from 1 to 4 channels so that the results can be stored in
606 @param mean output parameter: calculated mean value.
607 @param stddev output parameter: calculateded standard deviation.
608 @param mask optional operation mask.
609 @sa countNonZero, mean, norm, minMaxLoc, calcCovarMatrix
611 CV_EXPORTS_W void meanStdDev(InputArray src, OutputArray mean, OutputArray stddev,
612 InputArray mask=noArray());
614 /** @brief Calculates an absolute array norm, an absolute difference norm, or a
615 relative difference norm.
617 The functions norm calculate an absolute norm of src1 (when there is no
620 \f[norm = \forkthree{\|\texttt{src1}\|_{L_{\infty}} = \max _I | \texttt{src1} (I)|}{if \(\texttt{normType} = \texttt{NORM_INF}\) }
621 { \| \texttt{src1} \| _{L_1} = \sum _I | \texttt{src1} (I)|}{if \(\texttt{normType} = \texttt{NORM_L1}\) }
622 { \| \texttt{src1} \| _{L_2} = \sqrt{\sum_I \texttt{src1}(I)^2} }{if \(\texttt{normType} = \texttt{NORM_L2}\) }\f]
624 or an absolute or relative difference norm if src2 is there:
626 \f[norm = \forkthree{\|\texttt{src1}-\texttt{src2}\|_{L_{\infty}} = \max _I | \texttt{src1} (I) - \texttt{src2} (I)|}{if \(\texttt{normType} = \texttt{NORM_INF}\) }
627 { \| \texttt{src1} - \texttt{src2} \| _{L_1} = \sum _I | \texttt{src1} (I) - \texttt{src2} (I)|}{if \(\texttt{normType} = \texttt{NORM_L1}\) }
628 { \| \texttt{src1} - \texttt{src2} \| _{L_2} = \sqrt{\sum_I (\texttt{src1}(I) - \texttt{src2}(I))^2} }{if \(\texttt{normType} = \texttt{NORM_L2}\) }\f]
632 \f[norm = \forkthree{\frac{\|\texttt{src1}-\texttt{src2}\|_{L_{\infty}} }{\|\texttt{src2}\|_{L_{\infty}} }}{if \(\texttt{normType} = \texttt{NORM_RELATIVE_INF}\) }
633 { \frac{\|\texttt{src1}-\texttt{src2}\|_{L_1} }{\|\texttt{src2}\|_{L_1}} }{if \(\texttt{normType} = \texttt{NORM_RELATIVE_L1}\) }
634 { \frac{\|\texttt{src1}-\texttt{src2}\|_{L_2} }{\|\texttt{src2}\|_{L_2}} }{if \(\texttt{normType} = \texttt{NORM_RELATIVE_L2}\) }\f]
636 The functions norm return the calculated norm.
638 When the mask parameter is specified and it is not empty, the norm is
639 calculated only over the region specified by the mask.
641 A multi-channel input arrays are treated as a single-channel, that is,
642 the results for all channels are combined.
644 @param src1 first input array.
645 @param normType type of the norm (see cv::NormTypes).
646 @param mask optional operation mask; it must have the same size as src1 and CV_8UC1 type.
648 CV_EXPORTS_W double norm(InputArray src1, int normType = NORM_L2, InputArray mask = noArray());
651 @param src1 first input array.
652 @param src2 second input array of the same size and the same type as src1.
653 @param normType type of the norm (cv::NormTypes).
654 @param mask optional operation mask; it must have the same size as src1 and CV_8UC1 type.
656 CV_EXPORTS_W double norm(InputArray src1, InputArray src2,
657 int normType = NORM_L2, InputArray mask = noArray());
659 @param src first input array.
660 @param normType type of the norm (see cv::NormTypes).
662 CV_EXPORTS double norm( const SparseMat& src, int normType );
664 /** @brief computes PSNR image/video quality metric
666 see http://en.wikipedia.org/wiki/Peak_signal-to-noise_ratio for details
669 CV_EXPORTS_W double PSNR(InputArray src1, InputArray src2);
671 /** @brief naive nearest neighbor finder
673 see http://en.wikipedia.org/wiki/Nearest_neighbor_search
676 CV_EXPORTS_W void batchDistance(InputArray src1, InputArray src2,
677 OutputArray dist, int dtype, OutputArray nidx,
678 int normType = NORM_L2, int K = 0,
679 InputArray mask = noArray(), int update = 0,
680 bool crosscheck = false);
682 /** @brief Normalizes the norm or value range of an array.
684 The functions normalize scale and shift the input array elements so that
685 \f[\| \texttt{dst} \| _{L_p}= \texttt{alpha}\f]
686 (where p=Inf, 1 or 2) when normType=NORM_INF, NORM_L1, or NORM_L2, respectively; or so that
687 \f[\min _I \texttt{dst} (I)= \texttt{alpha} , \, \, \max _I \texttt{dst} (I)= \texttt{beta}\f]
689 when normType=NORM_MINMAX (for dense arrays only). The optional mask specifies a sub-array to be
690 normalized. This means that the norm or min-n-max are calculated over the sub-array, and then this
691 sub-array is modified to be normalized. If you want to only use the mask to calculate the norm or
692 min-max but modify the whole array, you can use norm and Mat::convertTo.
694 In case of sparse matrices, only the non-zero values are analyzed and transformed. Because of this,
695 the range transformation for sparse matrices is not allowed since it can shift the zero level.
697 Possible usage with some positive example data:
699 vector<double> positiveData = { 2.0, 8.0, 10.0 };
700 vector<double> normalizedData_l1, normalizedData_l2, normalizedData_inf, normalizedData_minmax;
702 // Norm to probability (total count)
703 // sum(numbers) = 20.0
704 // 2.0 0.1 (2.0/20.0)
705 // 8.0 0.4 (8.0/20.0)
706 // 10.0 0.5 (10.0/20.0)
707 normalize(positiveData, normalizedData_l1, 1.0, 0.0, NORM_L1);
709 // Norm to unit vector: ||positiveData|| = 1.0
713 normalize(positiveData, normalizedData_l2, 1.0, 0.0, NORM_L2);
715 // Norm to max element
716 // 2.0 0.2 (2.0/10.0)
717 // 8.0 0.8 (8.0/10.0)
718 // 10.0 1.0 (10.0/10.0)
719 normalize(positiveData, normalizedData_inf, 1.0, 0.0, NORM_INF);
721 // Norm to range [0.0;1.0]
722 // 2.0 0.0 (shift to left border)
723 // 8.0 0.75 (6.0/8.0)
724 // 10.0 1.0 (shift to right border)
725 normalize(positiveData, normalizedData_minmax, 1.0, 0.0, NORM_MINMAX);
728 @param src input array.
729 @param dst output array of the same size as src .
730 @param alpha norm value to normalize to or the lower range boundary in case of the range
732 @param beta upper range boundary in case of the range normalization; it is not used for the norm
734 @param norm_type normalization type (see cv::NormTypes).
735 @param dtype when negative, the output array has the same type as src; otherwise, it has the same
736 number of channels as src and the depth =CV_MAT_DEPTH(dtype).
737 @param mask optional operation mask.
738 @sa norm, Mat::convertTo, SparseMat::convertTo
740 CV_EXPORTS_W void normalize( InputArray src, InputOutputArray dst, double alpha = 1, double beta = 0,
741 int norm_type = NORM_L2, int dtype = -1, InputArray mask = noArray());
744 @param src input array.
745 @param dst output array of the same size as src .
746 @param alpha norm value to normalize to or the lower range boundary in case of the range
748 @param normType normalization type (see cv::NormTypes).
750 CV_EXPORTS void normalize( const SparseMat& src, SparseMat& dst, double alpha, int normType );
752 /** @brief Finds the global minimum and maximum in an array.
754 The functions minMaxLoc find the minimum and maximum element values and their positions. The
755 extremums are searched across the whole array or, if mask is not an empty array, in the specified
758 The functions do not work with multi-channel arrays. If you need to find minimum or maximum
759 elements across all the channels, use Mat::reshape first to reinterpret the array as
760 single-channel. Or you may extract the particular channel using either extractImageCOI , or
761 mixChannels , or split .
762 @param src input single-channel array.
763 @param minVal pointer to the returned minimum value; NULL is used if not required.
764 @param maxVal pointer to the returned maximum value; NULL is used if not required.
765 @param minLoc pointer to the returned minimum location (in 2D case); NULL is used if not required.
766 @param maxLoc pointer to the returned maximum location (in 2D case); NULL is used if not required.
767 @param mask optional mask used to select a sub-array.
768 @sa max, min, compare, inRange, extractImageCOI, mixChannels, split, Mat::reshape
770 CV_EXPORTS_W void minMaxLoc(InputArray src, CV_OUT double* minVal,
771 CV_OUT double* maxVal = 0, CV_OUT Point* minLoc = 0,
772 CV_OUT Point* maxLoc = 0, InputArray mask = noArray());
775 /** @brief Finds the global minimum and maximum in an array
777 The function minMaxIdx finds the minimum and maximum element values and their positions. The
778 extremums are searched across the whole array or, if mask is not an empty array, in the specified
779 array region. The function does not work with multi-channel arrays. If you need to find minimum or
780 maximum elements across all the channels, use Mat::reshape first to reinterpret the array as
781 single-channel. Or you may extract the particular channel using either extractImageCOI , or
782 mixChannels , or split . In case of a sparse matrix, the minimum is found among non-zero elements
784 @note When minIdx is not NULL, it must have at least 2 elements (as well as maxIdx), even if src is
785 a single-row or single-column matrix. In OpenCV (following MATLAB) each array has at least 2
786 dimensions, i.e. single-column matrix is Mx1 matrix (and therefore minIdx/maxIdx will be
787 (i1,0)/(i2,0)) and single-row matrix is 1xN matrix (and therefore minIdx/maxIdx will be
789 @param src input single-channel array.
790 @param minVal pointer to the returned minimum value; NULL is used if not required.
791 @param maxVal pointer to the returned maximum value; NULL is used if not required.
792 @param minIdx pointer to the returned minimum location (in nD case); NULL is used if not required;
793 Otherwise, it must point to an array of src.dims elements, the coordinates of the minimum element
794 in each dimension are stored there sequentially.
795 @param maxIdx pointer to the returned maximum location (in nD case). NULL is used if not required.
796 @param mask specified array region
798 CV_EXPORTS void minMaxIdx(InputArray src, double* minVal, double* maxVal = 0,
799 int* minIdx = 0, int* maxIdx = 0, InputArray mask = noArray());
802 @param a input single-channel array.
803 @param minVal pointer to the returned minimum value; NULL is used if not required.
804 @param maxVal pointer to the returned maximum value; NULL is used if not required.
805 @param minIdx pointer to the returned minimum location (in nD case); NULL is used if not required;
806 Otherwise, it must point to an array of src.dims elements, the coordinates of the minimum element
807 in each dimension are stored there sequentially.
808 @param maxIdx pointer to the returned maximum location (in nD case). NULL is used if not required.
810 CV_EXPORTS void minMaxLoc(const SparseMat& a, double* minVal,
811 double* maxVal, int* minIdx = 0, int* maxIdx = 0);
813 /** @brief Reduces a matrix to a vector.
815 The function reduce reduces the matrix to a vector by treating the matrix rows/columns as a set of
816 1D vectors and performing the specified operation on the vectors until a single row/column is
817 obtained. For example, the function can be used to compute horizontal and vertical projections of a
818 raster image. In case of REDUCE_SUM and REDUCE_AVG , the output may have a larger element
819 bit-depth to preserve accuracy. And multi-channel arrays are also supported in these two reduction
821 @param src input 2D matrix.
822 @param dst output vector. Its size and type is defined by dim and dtype parameters.
823 @param dim dimension index along which the matrix is reduced. 0 means that the matrix is reduced to
824 a single row. 1 means that the matrix is reduced to a single column.
825 @param rtype reduction operation that could be one of cv::ReduceTypes
826 @param dtype when negative, the output vector will have the same type as the input matrix,
827 otherwise, its type will be CV_MAKE_TYPE(CV_MAT_DEPTH(dtype), src.channels()).
830 CV_EXPORTS_W void reduce(InputArray src, OutputArray dst, int dim, int rtype, int dtype = -1);
832 /** @brief Creates one multichannel array out of several single-channel ones.
834 The functions merge merge several arrays to make a single multi-channel array. That is, each
835 element of the output array will be a concatenation of the elements of the input arrays, where
836 elements of i-th input array are treated as mv[i].channels()-element vectors.
838 The function split does the reverse operation. If you need to shuffle channels in some other
839 advanced way, use mixChannels .
840 @param mv input array of matrices to be merged; all the matrices in mv must have the same
841 size and the same depth.
842 @param count number of input matrices when mv is a plain C array; it must be greater than zero.
843 @param dst output array of the same size and the same depth as mv[0]; The number of channels will
844 be the total number of channels in the matrix array.
845 @sa mixChannels, split, Mat::reshape
847 CV_EXPORTS void merge(const Mat* mv, size_t count, OutputArray dst);
850 @param mv input vector of matrices to be merged; all the matrices in mv must have the same
851 size and the same depth.
852 @param dst output array of the same size and the same depth as mv[0]; The number of channels will
853 be the total number of channels in the matrix array.
855 CV_EXPORTS_W void merge(InputArrayOfArrays mv, OutputArray dst);
857 /** @brief Divides a multi-channel array into several single-channel arrays.
859 The functions split split a multi-channel array into separate single-channel arrays:
860 \f[\texttt{mv} [c](I) = \texttt{src} (I)_c\f]
861 If you need to extract a single channel or do some other sophisticated channel permutation, use
863 @param src input multi-channel array.
864 @param mvbegin output array; the number of arrays must match src.channels(); the arrays themselves are
865 reallocated, if needed.
866 @sa merge, mixChannels, cvtColor
868 CV_EXPORTS void split(const Mat& src, Mat* mvbegin);
871 @param m input multi-channel array.
872 @param mv output vector of arrays; the arrays themselves are reallocated, if needed.
874 CV_EXPORTS_W void split(InputArray m, OutputArrayOfArrays mv);
876 /** @brief Copies specified channels from input arrays to the specified channels of
879 The functions mixChannels provide an advanced mechanism for shuffling image channels.
881 split and merge and some forms of cvtColor are partial cases of mixChannels .
883 In the example below, the code splits a 4-channel RGBA image into a 3-channel BGR (with R and B
884 channels swapped) and a separate alpha-channel image:
886 Mat rgba( 100, 100, CV_8UC4, Scalar(1,2,3,4) );
887 Mat bgr( rgba.rows, rgba.cols, CV_8UC3 );
888 Mat alpha( rgba.rows, rgba.cols, CV_8UC1 );
890 // forming an array of matrices is a quite efficient operation,
891 // because the matrix data is not copied, only the headers
892 Mat out[] = { bgr, alpha };
893 // rgba[0] -> bgr[2], rgba[1] -> bgr[1],
894 // rgba[2] -> bgr[0], rgba[3] -> alpha[0]
895 int from_to[] = { 0,2, 1,1, 2,0, 3,3 };
896 mixChannels( &rgba, 1, out, 2, from_to, 4 );
898 @note Unlike many other new-style C++ functions in OpenCV (see the introduction section and
899 Mat::create ), mixChannels requires the output arrays to be pre-allocated before calling the
901 @param src input array or vector of matricesl; all of the matrices must have the same size and the
903 @param nsrcs number of matrices in src.
904 @param dst output array or vector of matrices; all the matrices *must be allocated*; their size and
905 depth must be the same as in src[0].
906 @param ndsts number of matrices in dst.
907 @param fromTo array of index pairs specifying which channels are copied and where; fromTo[k\*2] is
908 a 0-based index of the input channel in src, fromTo[k\*2+1] is an index of the output channel in
909 dst; the continuous channel numbering is used: the first input image channels are indexed from 0 to
910 src[0].channels()-1, the second input image channels are indexed from src[0].channels() to
911 src[0].channels() + src[1].channels()-1, and so on, the same scheme is used for the output image
912 channels; as a special case, when fromTo[k\*2] is negative, the corresponding output channel is
914 @param npairs number of index pairs in fromTo.
915 @sa split, merge, cvtColor
917 CV_EXPORTS void mixChannels(const Mat* src, size_t nsrcs, Mat* dst, size_t ndsts,
918 const int* fromTo, size_t npairs);
921 @param src input array or vector of matricesl; all of the matrices must have the same size and the
923 @param dst output array or vector of matrices; all the matrices *must be allocated*; their size and
924 depth must be the same as in src[0].
925 @param fromTo array of index pairs specifying which channels are copied and where; fromTo[k\*2] is
926 a 0-based index of the input channel in src, fromTo[k\*2+1] is an index of the output channel in
927 dst; the continuous channel numbering is used: the first input image channels are indexed from 0 to
928 src[0].channels()-1, the second input image channels are indexed from src[0].channels() to
929 src[0].channels() + src[1].channels()-1, and so on, the same scheme is used for the output image
930 channels; as a special case, when fromTo[k\*2] is negative, the corresponding output channel is
932 @param npairs number of index pairs in fromTo.
934 CV_EXPORTS void mixChannels(InputArrayOfArrays src, InputOutputArrayOfArrays dst,
935 const int* fromTo, size_t npairs);
938 @param src input array or vector of matricesl; all of the matrices must have the same size and the
940 @param dst output array or vector of matrices; all the matrices *must be allocated*; their size and
941 depth must be the same as in src[0].
942 @param fromTo array of index pairs specifying which channels are copied and where; fromTo[k\*2] is
943 a 0-based index of the input channel in src, fromTo[k\*2+1] is an index of the output channel in
944 dst; the continuous channel numbering is used: the first input image channels are indexed from 0 to
945 src[0].channels()-1, the second input image channels are indexed from src[0].channels() to
946 src[0].channels() + src[1].channels()-1, and so on, the same scheme is used for the output image
947 channels; as a special case, when fromTo[k\*2] is negative, the corresponding output channel is
950 CV_EXPORTS_W void mixChannels(InputArrayOfArrays src, InputOutputArrayOfArrays dst,
951 const std::vector<int>& fromTo);
953 /** @brief extracts a single channel from src (coi is 0-based index)
956 CV_EXPORTS_W void extractChannel(InputArray src, OutputArray dst, int coi);
958 /** @brief inserts a single channel to dst (coi is 0-based index)
961 CV_EXPORTS_W void insertChannel(InputArray src, InputOutputArray dst, int coi);
963 /** @brief Flips a 2D array around vertical, horizontal, or both axes.
965 The function flip flips the array in one of three different ways (row
966 and column indices are 0-based):
967 \f[\texttt{dst} _{ij} =
970 \texttt{src} _{\texttt{src.rows}-i-1,j} & if\; \texttt{flipCode} = 0 \\
971 \texttt{src} _{i, \texttt{src.cols} -j-1} & if\; \texttt{flipCode} > 0 \\
972 \texttt{src} _{ \texttt{src.rows} -i-1, \texttt{src.cols} -j-1} & if\; \texttt{flipCode} < 0 \\
975 The example scenarios of using the function are the following:
976 * Vertical flipping of the image (flipCode == 0) to switch between
977 top-left and bottom-left image origin. This is a typical operation
978 in video processing on Microsoft Windows\* OS.
979 * Horizontal flipping of the image with the subsequent horizontal
980 shift and absolute difference calculation to check for a
981 vertical-axis symmetry (flipCode \> 0).
982 * Simultaneous horizontal and vertical flipping of the image with
983 the subsequent shift and absolute difference calculation to check
984 for a central symmetry (flipCode \< 0).
985 * Reversing the order of point arrays (flipCode \> 0 or
987 @param src input array.
988 @param dst output array of the same size and type as src.
989 @param flipCode a flag to specify how to flip the array; 0 means
990 flipping around the x-axis and positive value (for example, 1) means
991 flipping around y-axis. Negative value (for example, -1) means flipping
993 @sa transpose , repeat , completeSymm
995 CV_EXPORTS_W void flip(InputArray src, OutputArray dst, int flipCode);
997 /** @brief Fills the output array with repeated copies of the input array.
999 The functions repeat duplicate the input array one or more times along each of the two axes:
1000 \f[\texttt{dst} _{ij}= \texttt{src} _{i\mod src.rows, \; j\mod src.cols }\f]
1001 The second variant of the function is more convenient to use with @ref MatrixExpressions.
1002 @param src input array to replicate.
1003 @param dst output array of the same type as src.
1004 @param ny Flag to specify how many times the src is repeated along the
1006 @param nx Flag to specify how many times the src is repeated along the
1010 CV_EXPORTS_W void repeat(InputArray src, int ny, int nx, OutputArray dst);
1013 @param src input array to replicate.
1014 @param ny Flag to specify how many times the src is repeated along the
1016 @param nx Flag to specify how many times the src is repeated along the
1019 CV_EXPORTS Mat repeat(const Mat& src, int ny, int nx);
1021 /** @brief Applies horizontal concatenation to given matrices.
1023 The function horizontally concatenates two or more cv::Mat matrices (with the same number of rows).
1025 cv::Mat matArray[] = { cv::Mat(4, 1, CV_8UC1, cv::Scalar(1)),
1026 cv::Mat(4, 1, CV_8UC1, cv::Scalar(2)),
1027 cv::Mat(4, 1, CV_8UC1, cv::Scalar(3)),};
1030 cv::hconcat( matArray, 3, out );
1037 @param src input array or vector of matrices. all of the matrices must have the same number of rows and the same depth.
1038 @param nsrc number of matrices in src.
1039 @param dst output array. It has the same number of rows and depth as the src, and the sum of cols of the src.
1040 @sa cv::vconcat(const Mat*, size_t, OutputArray), @sa cv::vconcat(InputArrayOfArrays, OutputArray) and @sa cv::vconcat(InputArray, InputArray, OutputArray)
1042 CV_EXPORTS void hconcat(const Mat* src, size_t nsrc, OutputArray dst);
1045 cv::Mat_<float> A = (cv::Mat_<float>(3, 2) << 1, 4,
1048 cv::Mat_<float> B = (cv::Mat_<float>(3, 2) << 7, 10,
1053 cv::hconcat(A, B, C);
1059 @param src1 first input array to be considered for horizontal concatenation.
1060 @param src2 second input array to be considered for horizontal concatenation.
1061 @param dst output array. It has the same number of rows and depth as the src1 and src2, and the sum of cols of the src1 and src2.
1063 CV_EXPORTS void hconcat(InputArray src1, InputArray src2, OutputArray dst);
1066 std::vector<cv::Mat> matrices = { cv::Mat(4, 1, CV_8UC1, cv::Scalar(1)),
1067 cv::Mat(4, 1, CV_8UC1, cv::Scalar(2)),
1068 cv::Mat(4, 1, CV_8UC1, cv::Scalar(3)),};
1071 cv::hconcat( matrices, out );
1078 @param src input array or vector of matrices. all of the matrices must have the same number of rows and the same depth.
1079 @param dst output array. It has the same number of rows and depth as the src, and the sum of cols of the src.
1082 CV_EXPORTS_W void hconcat(InputArrayOfArrays src, OutputArray dst);
1084 /** @brief Applies vertical concatenation to given matrices.
1086 The function vertically concatenates two or more cv::Mat matrices (with the same number of cols).
1088 cv::Mat matArray[] = { cv::Mat(1, 4, CV_8UC1, cv::Scalar(1)),
1089 cv::Mat(1, 4, CV_8UC1, cv::Scalar(2)),
1090 cv::Mat(1, 4, CV_8UC1, cv::Scalar(3)),};
1093 cv::vconcat( matArray, 3, out );
1099 @param src input array or vector of matrices. all of the matrices must have the same number of cols and the same depth.
1100 @param nsrc number of matrices in src.
1101 @param dst output array. It has the same number of cols and depth as the src, and the sum of rows of the src.
1102 @sa cv::hconcat(const Mat*, size_t, OutputArray), @sa cv::hconcat(InputArrayOfArrays, OutputArray) and @sa cv::hconcat(InputArray, InputArray, OutputArray)
1104 CV_EXPORTS void vconcat(const Mat* src, size_t nsrc, OutputArray dst);
1107 cv::Mat_<float> A = (cv::Mat_<float>(3, 2) << 1, 7,
1110 cv::Mat_<float> B = (cv::Mat_<float>(3, 2) << 4, 10,
1115 cv::vconcat(A, B, C);
1124 @param src1 first input array to be considered for vertical concatenation.
1125 @param src2 second input array to be considered for vertical concatenation.
1126 @param dst output array. It has the same number of cols and depth as the src1 and src2, and the sum of rows of the src1 and src2.
1128 CV_EXPORTS void vconcat(InputArray src1, InputArray src2, OutputArray dst);
1131 std::vector<cv::Mat> matrices = { cv::Mat(1, 4, CV_8UC1, cv::Scalar(1)),
1132 cv::Mat(1, 4, CV_8UC1, cv::Scalar(2)),
1133 cv::Mat(1, 4, CV_8UC1, cv::Scalar(3)),};
1136 cv::vconcat( matrices, out );
1142 @param src input array or vector of matrices. all of the matrices must have the same number of cols and the same depth
1143 @param dst output array. It has the same number of cols and depth as the src, and the sum of rows of the src.
1146 CV_EXPORTS_W void vconcat(InputArrayOfArrays src, OutputArray dst);
1148 /** @brief computes bitwise conjunction of the two arrays (dst = src1 & src2)
1149 Calculates the per-element bit-wise conjunction of two arrays or an
1152 The function calculates the per-element bit-wise logical conjunction for:
1153 * Two arrays when src1 and src2 have the same size:
1154 \f[\texttt{dst} (I) = \texttt{src1} (I) \wedge \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\f]
1155 * An array and a scalar when src2 is constructed from Scalar or has
1156 the same number of elements as `src1.channels()`:
1157 \f[\texttt{dst} (I) = \texttt{src1} (I) \wedge \texttt{src2} \quad \texttt{if mask} (I) \ne0\f]
1158 * A scalar and an array when src1 is constructed from Scalar or has
1159 the same number of elements as `src2.channels()`:
1160 \f[\texttt{dst} (I) = \texttt{src1} \wedge \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\f]
1161 In case of floating-point arrays, their machine-specific bit
1162 representations (usually IEEE754-compliant) are used for the operation.
1163 In case of multi-channel arrays, each channel is processed
1164 independently. In the second and third cases above, the scalar is first
1165 converted to the array type.
1166 @param src1 first input array or a scalar.
1167 @param src2 second input array or a scalar.
1168 @param dst output array that has the same size and type as the input
1170 @param mask optional operation mask, 8-bit single channel array, that
1171 specifies elements of the output array to be changed.
1173 CV_EXPORTS_W void bitwise_and(InputArray src1, InputArray src2,
1174 OutputArray dst, InputArray mask = noArray());
1176 /** @brief Calculates the per-element bit-wise disjunction of two arrays or an
1179 The function calculates the per-element bit-wise logical disjunction for:
1180 * Two arrays when src1 and src2 have the same size:
1181 \f[\texttt{dst} (I) = \texttt{src1} (I) \vee \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\f]
1182 * An array and a scalar when src2 is constructed from Scalar or has
1183 the same number of elements as `src1.channels()`:
1184 \f[\texttt{dst} (I) = \texttt{src1} (I) \vee \texttt{src2} \quad \texttt{if mask} (I) \ne0\f]
1185 * A scalar and an array when src1 is constructed from Scalar or has
1186 the same number of elements as `src2.channels()`:
1187 \f[\texttt{dst} (I) = \texttt{src1} \vee \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\f]
1188 In case of floating-point arrays, their machine-specific bit
1189 representations (usually IEEE754-compliant) are used for the operation.
1190 In case of multi-channel arrays, each channel is processed
1191 independently. In the second and third cases above, the scalar is first
1192 converted to the array type.
1193 @param src1 first input array or a scalar.
1194 @param src2 second input array or a scalar.
1195 @param dst output array that has the same size and type as the input
1197 @param mask optional operation mask, 8-bit single channel array, that
1198 specifies elements of the output array to be changed.
1200 CV_EXPORTS_W void bitwise_or(InputArray src1, InputArray src2,
1201 OutputArray dst, InputArray mask = noArray());
1203 /** @brief Calculates the per-element bit-wise "exclusive or" operation on two
1204 arrays or an array and a scalar.
1206 The function calculates the per-element bit-wise logical "exclusive-or"
1208 * Two arrays when src1 and src2 have the same size:
1209 \f[\texttt{dst} (I) = \texttt{src1} (I) \oplus \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\f]
1210 * An array and a scalar when src2 is constructed from Scalar or has
1211 the same number of elements as `src1.channels()`:
1212 \f[\texttt{dst} (I) = \texttt{src1} (I) \oplus \texttt{src2} \quad \texttt{if mask} (I) \ne0\f]
1213 * A scalar and an array when src1 is constructed from Scalar or has
1214 the same number of elements as `src2.channels()`:
1215 \f[\texttt{dst} (I) = \texttt{src1} \oplus \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\f]
1216 In case of floating-point arrays, their machine-specific bit
1217 representations (usually IEEE754-compliant) are used for the operation.
1218 In case of multi-channel arrays, each channel is processed
1219 independently. In the 2nd and 3rd cases above, the scalar is first
1220 converted to the array type.
1221 @param src1 first input array or a scalar.
1222 @param src2 second input array or a scalar.
1223 @param dst output array that has the same size and type as the input
1225 @param mask optional operation mask, 8-bit single channel array, that
1226 specifies elements of the output array to be changed.
1228 CV_EXPORTS_W void bitwise_xor(InputArray src1, InputArray src2,
1229 OutputArray dst, InputArray mask = noArray());
1231 /** @brief Inverts every bit of an array.
1233 The function calculates per-element bit-wise inversion of the input
1235 \f[\texttt{dst} (I) = \neg \texttt{src} (I)\f]
1236 In case of a floating-point input array, its machine-specific bit
1237 representation (usually IEEE754-compliant) is used for the operation. In
1238 case of multi-channel arrays, each channel is processed independently.
1239 @param src input array.
1240 @param dst output array that has the same size and type as the input
1242 @param mask optional operation mask, 8-bit single channel array, that
1243 specifies elements of the output array to be changed.
1245 CV_EXPORTS_W void bitwise_not(InputArray src, OutputArray dst,
1246 InputArray mask = noArray());
1248 /** @brief Calculates the per-element absolute difference between two arrays or between an array and a scalar.
1250 The function absdiff calculates:
1251 * Absolute difference between two arrays when they have the same
1253 \f[\texttt{dst}(I) = \texttt{saturate} (| \texttt{src1}(I) - \texttt{src2}(I)|)\f]
1254 * Absolute difference between an array and a scalar when the second
1255 array is constructed from Scalar or has as many elements as the
1256 number of channels in `src1`:
1257 \f[\texttt{dst}(I) = \texttt{saturate} (| \texttt{src1}(I) - \texttt{src2} |)\f]
1258 * Absolute difference between a scalar and an array when the first
1259 array is constructed from Scalar or has as many elements as the
1260 number of channels in `src2`:
1261 \f[\texttt{dst}(I) = \texttt{saturate} (| \texttt{src1} - \texttt{src2}(I) |)\f]
1262 where I is a multi-dimensional index of array elements. In case of
1263 multi-channel arrays, each channel is processed independently.
1264 @note Saturation is not applied when the arrays have the depth CV_32S.
1265 You may even get a negative value in the case of overflow.
1266 @param src1 first input array or a scalar.
1267 @param src2 second input array or a scalar.
1268 @param dst output array that has the same size and type as input arrays.
1269 @sa cv::abs(const Mat&)
1271 CV_EXPORTS_W void absdiff(InputArray src1, InputArray src2, OutputArray dst);
1273 /** @brief Checks if array elements lie between the elements of two other arrays.
1275 The function checks the range as follows:
1276 - For every element of a single-channel input array:
1277 \f[\texttt{dst} (I)= \texttt{lowerb} (I)_0 \leq \texttt{src} (I)_0 \leq \texttt{upperb} (I)_0\f]
1278 - For two-channel arrays:
1279 \f[\texttt{dst} (I)= \texttt{lowerb} (I)_0 \leq \texttt{src} (I)_0 \leq \texttt{upperb} (I)_0 \land \texttt{lowerb} (I)_1 \leq \texttt{src} (I)_1 \leq \texttt{upperb} (I)_1\f]
1282 That is, dst (I) is set to 255 (all 1 -bits) if src (I) is within the
1283 specified 1D, 2D, 3D, ... box and 0 otherwise.
1285 When the lower and/or upper boundary parameters are scalars, the indexes
1286 (I) at lowerb and upperb in the above formulas should be omitted.
1287 @param src first input array.
1288 @param lowerb inclusive lower boundary array or a scalar.
1289 @param upperb inclusive upper boundary array or a scalar.
1290 @param dst output array of the same size as src and CV_8U type.
1292 CV_EXPORTS_W void inRange(InputArray src, InputArray lowerb,
1293 InputArray upperb, OutputArray dst);
1295 /** @brief Performs the per-element comparison of two arrays or an array and scalar value.
1297 The function compares:
1298 * Elements of two arrays when src1 and src2 have the same size:
1299 \f[\texttt{dst} (I) = \texttt{src1} (I) \,\texttt{cmpop}\, \texttt{src2} (I)\f]
1300 * Elements of src1 with a scalar src2 when src2 is constructed from
1301 Scalar or has a single element:
1302 \f[\texttt{dst} (I) = \texttt{src1}(I) \,\texttt{cmpop}\, \texttt{src2}\f]
1303 * src1 with elements of src2 when src1 is constructed from Scalar or
1304 has a single element:
1305 \f[\texttt{dst} (I) = \texttt{src1} \,\texttt{cmpop}\, \texttt{src2} (I)\f]
1306 When the comparison result is true, the corresponding element of output
1307 array is set to 255. The comparison operations can be replaced with the
1308 equivalent matrix expressions:
1310 Mat dst1 = src1 >= src2;
1311 Mat dst2 = src1 < 8;
1314 @param src1 first input array or a scalar; when it is an array, it must have a single channel.
1315 @param src2 second input array or a scalar; when it is an array, it must have a single channel.
1316 @param dst output array of type ref CV_8U that has the same size and the same number of channels as
1318 @param cmpop a flag, that specifies correspondence between the arrays (cv::CmpTypes)
1319 @sa checkRange, min, max, threshold
1321 CV_EXPORTS_W void compare(InputArray src1, InputArray src2, OutputArray dst, int cmpop);
1323 /** @brief Calculates per-element minimum of two arrays or an array and a scalar.
1325 The functions min calculate the per-element minimum of two arrays:
1326 \f[\texttt{dst} (I)= \min ( \texttt{src1} (I), \texttt{src2} (I))\f]
1327 or array and a scalar:
1328 \f[\texttt{dst} (I)= \min ( \texttt{src1} (I), \texttt{value} )\f]
1329 @param src1 first input array.
1330 @param src2 second input array of the same size and type as src1.
1331 @param dst output array of the same size and type as src1.
1332 @sa max, compare, inRange, minMaxLoc
1334 CV_EXPORTS_W void min(InputArray src1, InputArray src2, OutputArray dst);
1336 needed to avoid conflicts with const _Tp& std::min(const _Tp&, const _Tp&, _Compare)
1338 CV_EXPORTS void min(const Mat& src1, const Mat& src2, Mat& dst);
1340 needed to avoid conflicts with const _Tp& std::min(const _Tp&, const _Tp&, _Compare)
1342 CV_EXPORTS void min(const UMat& src1, const UMat& src2, UMat& dst);
1344 /** @brief Calculates per-element maximum of two arrays or an array and a scalar.
1346 The functions max calculate the per-element maximum of two arrays:
1347 \f[\texttt{dst} (I)= \max ( \texttt{src1} (I), \texttt{src2} (I))\f]
1348 or array and a scalar:
1349 \f[\texttt{dst} (I)= \max ( \texttt{src1} (I), \texttt{value} )\f]
1350 @param src1 first input array.
1351 @param src2 second input array of the same size and type as src1 .
1352 @param dst output array of the same size and type as src1.
1353 @sa min, compare, inRange, minMaxLoc, @ref MatrixExpressions
1355 CV_EXPORTS_W void max(InputArray src1, InputArray src2, OutputArray dst);
1357 needed to avoid conflicts with const _Tp& std::min(const _Tp&, const _Tp&, _Compare)
1359 CV_EXPORTS void max(const Mat& src1, const Mat& src2, Mat& dst);
1361 needed to avoid conflicts with const _Tp& std::min(const _Tp&, const _Tp&, _Compare)
1363 CV_EXPORTS void max(const UMat& src1, const UMat& src2, UMat& dst);
1365 /** @brief Calculates a square root of array elements.
1367 The functions sqrt calculate a square root of each input array element.
1368 In case of multi-channel arrays, each channel is processed
1369 independently. The accuracy is approximately the same as of the built-in
1371 @param src input floating-point array.
1372 @param dst output array of the same size and type as src.
1374 CV_EXPORTS_W void sqrt(InputArray src, OutputArray dst);
1376 /** @brief Raises every array element to a power.
1378 The function pow raises every element of the input array to power :
1379 \f[\texttt{dst} (I) = \fork{\texttt{src}(I)^{power}}{if \(\texttt{power}\) is integer}{|\texttt{src}(I)|^{power}}{otherwise}\f]
1381 So, for a non-integer power exponent, the absolute values of input array
1382 elements are used. However, it is possible to get true values for
1383 negative values using some extra operations. In the example below,
1384 computing the 5th root of array src shows:
1387 pow(src, 1./5, dst);
1388 subtract(Scalar::all(0), dst, dst, mask);
1390 For some values of power, such as integer values, 0.5 and -0.5,
1391 specialized faster algorithms are used.
1393 Special values (NaN, Inf) are not handled.
1394 @param src input array.
1395 @param power exponent of power.
1396 @param dst output array of the same size and type as src.
1397 @sa sqrt, exp, log, cartToPolar, polarToCart
1399 CV_EXPORTS_W void pow(InputArray src, double power, OutputArray dst);
1401 /** @brief Calculates the exponent of every array element.
1403 The function exp calculates the exponent of every element of the input
1405 \f[\texttt{dst} [I] = e^{ src(I) }\f]
1407 The maximum relative error is about 7e-6 for single-precision input and
1408 less than 1e-10 for double-precision input. Currently, the function
1409 converts denormalized values to zeros on output. Special values (NaN,
1410 Inf) are not handled.
1411 @param src input array.
1412 @param dst output array of the same size and type as src.
1413 @sa log , cartToPolar , polarToCart , phase , pow , sqrt , magnitude
1415 CV_EXPORTS_W void exp(InputArray src, OutputArray dst);
1417 /** @brief Calculates the natural logarithm of every array element.
1419 The function log calculates the natural logarithm of the absolute value
1420 of every element of the input array:
1421 \f[\texttt{dst} (I) = \fork{\log |\texttt{src}(I)|}{if \(\texttt{src}(I) \ne 0\) }{\texttt{C}}{otherwise}\f]
1423 where C is a large negative number (about -700 in the current
1424 implementation). The maximum relative error is about 7e-6 for
1425 single-precision input and less than 1e-10 for double-precision input.
1426 Special values (NaN, Inf) are not handled.
1427 @param src input array.
1428 @param dst output array of the same size and type as src .
1429 @sa exp, cartToPolar, polarToCart, phase, pow, sqrt, magnitude
1431 CV_EXPORTS_W void log(InputArray src, OutputArray dst);
1433 /** @brief Calculates x and y coordinates of 2D vectors from their magnitude and angle.
1435 The function polarToCart calculates the Cartesian coordinates of each 2D
1436 vector represented by the corresponding elements of magnitude and angle:
1437 \f[\begin{array}{l} \texttt{x} (I) = \texttt{magnitude} (I) \cos ( \texttt{angle} (I)) \\ \texttt{y} (I) = \texttt{magnitude} (I) \sin ( \texttt{angle} (I)) \\ \end{array}\f]
1439 The relative accuracy of the estimated coordinates is about 1e-6.
1440 @param magnitude input floating-point array of magnitudes of 2D vectors;
1441 it can be an empty matrix (=Mat()), in this case, the function assumes
1442 that all the magnitudes are =1; if it is not empty, it must have the
1443 same size and type as angle.
1444 @param angle input floating-point array of angles of 2D vectors.
1445 @param x output array of x-coordinates of 2D vectors; it has the same
1446 size and type as angle.
1447 @param y output array of y-coordinates of 2D vectors; it has the same
1448 size and type as angle.
1449 @param angleInDegrees when true, the input angles are measured in
1450 degrees, otherwise, they are measured in radians.
1451 @sa cartToPolar, magnitude, phase, exp, log, pow, sqrt
1453 CV_EXPORTS_W void polarToCart(InputArray magnitude, InputArray angle,
1454 OutputArray x, OutputArray y, bool angleInDegrees = false);
1456 /** @brief Calculates the magnitude and angle of 2D vectors.
1458 The function cartToPolar calculates either the magnitude, angle, or both
1459 for every 2D vector (x(I),y(I)):
1460 \f[\begin{array}{l} \texttt{magnitude} (I)= \sqrt{\texttt{x}(I)^2+\texttt{y}(I)^2} , \\ \texttt{angle} (I)= \texttt{atan2} ( \texttt{y} (I), \texttt{x} (I))[ \cdot180 / \pi ] \end{array}\f]
1462 The angles are calculated with accuracy about 0.3 degrees. For the point
1463 (0,0), the angle is set to 0.
1464 @param x array of x-coordinates; this must be a single-precision or
1465 double-precision floating-point array.
1466 @param y array of y-coordinates, that must have the same size and same type as x.
1467 @param magnitude output array of magnitudes of the same size and type as x.
1468 @param angle output array of angles that has the same size and type as
1469 x; the angles are measured in radians (from 0 to 2\*Pi) or in degrees (0 to 360 degrees).
1470 @param angleInDegrees a flag, indicating whether the angles are measured
1471 in radians (which is by default), or in degrees.
1474 CV_EXPORTS_W void cartToPolar(InputArray x, InputArray y,
1475 OutputArray magnitude, OutputArray angle,
1476 bool angleInDegrees = false);
1478 /** @brief Calculates the rotation angle of 2D vectors.
1480 The function phase calculates the rotation angle of each 2D vector that
1481 is formed from the corresponding elements of x and y :
1482 \f[\texttt{angle} (I) = \texttt{atan2} ( \texttt{y} (I), \texttt{x} (I))\f]
1484 The angle estimation accuracy is about 0.3 degrees. When x(I)=y(I)=0 ,
1485 the corresponding angle(I) is set to 0.
1486 @param x input floating-point array of x-coordinates of 2D vectors.
1487 @param y input array of y-coordinates of 2D vectors; it must have the
1488 same size and the same type as x.
1489 @param angle output array of vector angles; it has the same size and
1491 @param angleInDegrees when true, the function calculates the angle in
1492 degrees, otherwise, they are measured in radians.
1494 CV_EXPORTS_W void phase(InputArray x, InputArray y, OutputArray angle,
1495 bool angleInDegrees = false);
1497 /** @brief Calculates the magnitude of 2D vectors.
1499 The function magnitude calculates the magnitude of 2D vectors formed
1500 from the corresponding elements of x and y arrays:
1501 \f[\texttt{dst} (I) = \sqrt{\texttt{x}(I)^2 + \texttt{y}(I)^2}\f]
1502 @param x floating-point array of x-coordinates of the vectors.
1503 @param y floating-point array of y-coordinates of the vectors; it must
1504 have the same size as x.
1505 @param magnitude output array of the same size and type as x.
1506 @sa cartToPolar, polarToCart, phase, sqrt
1508 CV_EXPORTS_W void magnitude(InputArray x, InputArray y, OutputArray magnitude);
1510 /** @brief Checks every element of an input array for invalid values.
1512 The functions checkRange check that every array element is neither NaN nor infinite. When minVal \<
1513 -DBL_MAX and maxVal \< DBL_MAX, the functions also check that each value is between minVal and
1514 maxVal. In case of multi-channel arrays, each channel is processed independently. If some values
1515 are out of range, position of the first outlier is stored in pos (when pos != NULL). Then, the
1516 functions either return false (when quiet=true) or throw an exception.
1517 @param a input array.
1518 @param quiet a flag, indicating whether the functions quietly return false when the array elements
1519 are out of range or they throw an exception.
1520 @param pos optional output parameter, when not NULL, must be a pointer to array of src.dims
1522 @param minVal inclusive lower boundary of valid values range.
1523 @param maxVal exclusive upper boundary of valid values range.
1525 CV_EXPORTS_W bool checkRange(InputArray a, bool quiet = true, CV_OUT Point* pos = 0,
1526 double minVal = -DBL_MAX, double maxVal = DBL_MAX);
1528 /** @brief converts NaN's to the given number
1530 CV_EXPORTS_W void patchNaNs(InputOutputArray a, double val = 0);
1532 /** @brief Performs generalized matrix multiplication.
1534 The function performs generalized matrix multiplication similar to the
1535 gemm functions in BLAS level 3. For example,
1536 `gemm(src1, src2, alpha, src3, beta, dst, GEMM_1_T + GEMM_3_T)`
1538 \f[\texttt{dst} = \texttt{alpha} \cdot \texttt{src1} ^T \cdot \texttt{src2} + \texttt{beta} \cdot \texttt{src3} ^T\f]
1540 In case of complex (two-channel) data, performed a complex matrix
1543 The function can be replaced with a matrix expression. For example, the
1544 above call can be replaced with:
1546 dst = alpha*src1.t()*src2 + beta*src3.t();
1548 @param src1 first multiplied input matrix that could be real(CV_32FC1,
1549 CV_64FC1) or complex(CV_32FC2, CV_64FC2).
1550 @param src2 second multiplied input matrix of the same type as src1.
1551 @param alpha weight of the matrix product.
1552 @param src3 third optional delta matrix added to the matrix product; it
1553 should have the same type as src1 and src2.
1554 @param beta weight of src3.
1555 @param dst output matrix; it has the proper size and the same type as
1557 @param flags operation flags (cv::GemmFlags)
1558 @sa mulTransposed , transform
1560 CV_EXPORTS_W void gemm(InputArray src1, InputArray src2, double alpha,
1561 InputArray src3, double beta, OutputArray dst, int flags = 0);
1563 /** @brief Calculates the product of a matrix and its transposition.
1565 The function mulTransposed calculates the product of src and its
1567 \f[\texttt{dst} = \texttt{scale} ( \texttt{src} - \texttt{delta} )^T ( \texttt{src} - \texttt{delta} )\f]
1569 \f[\texttt{dst} = \texttt{scale} ( \texttt{src} - \texttt{delta} ) ( \texttt{src} - \texttt{delta} )^T\f]
1570 otherwise. The function is used to calculate the covariance matrix. With
1571 zero delta, it can be used as a faster substitute for general matrix
1572 product A\*B when B=A'
1573 @param src input single-channel matrix. Note that unlike gemm, the
1574 function can multiply not only floating-point matrices.
1575 @param dst output square matrix.
1576 @param aTa Flag specifying the multiplication ordering. See the
1578 @param delta Optional delta matrix subtracted from src before the
1579 multiplication. When the matrix is empty ( delta=noArray() ), it is
1580 assumed to be zero, that is, nothing is subtracted. If it has the same
1581 size as src , it is simply subtracted. Otherwise, it is "repeated" (see
1582 repeat ) to cover the full src and then subtracted. Type of the delta
1583 matrix, when it is not empty, must be the same as the type of created
1584 output matrix. See the dtype parameter description below.
1585 @param scale Optional scale factor for the matrix product.
1586 @param dtype Optional type of the output matrix. When it is negative,
1587 the output matrix will have the same type as src . Otherwise, it will be
1588 type=CV_MAT_DEPTH(dtype) that should be either CV_32F or CV_64F .
1589 @sa calcCovarMatrix, gemm, repeat, reduce
1591 CV_EXPORTS_W void mulTransposed( InputArray src, OutputArray dst, bool aTa,
1592 InputArray delta = noArray(),
1593 double scale = 1, int dtype = -1 );
1595 /** @brief Transposes a matrix.
1597 The function transpose transposes the matrix src :
1598 \f[\texttt{dst} (i,j) = \texttt{src} (j,i)\f]
1599 @note No complex conjugation is done in case of a complex matrix. It it
1600 should be done separately if needed.
1601 @param src input array.
1602 @param dst output array of the same type as src.
1604 CV_EXPORTS_W void transpose(InputArray src, OutputArray dst);
1606 /** @brief Performs the matrix transformation of every array element.
1608 The function transform performs the matrix transformation of every
1609 element of the array src and stores the results in dst :
1610 \f[\texttt{dst} (I) = \texttt{m} \cdot \texttt{src} (I)\f]
1611 (when m.cols=src.channels() ), or
1612 \f[\texttt{dst} (I) = \texttt{m} \cdot [ \texttt{src} (I); 1]\f]
1613 (when m.cols=src.channels()+1 )
1615 Every element of the N -channel array src is interpreted as N -element
1616 vector that is transformed using the M x N or M x (N+1) matrix m to
1617 M-element vector - the corresponding element of the output array dst .
1619 The function may be used for geometrical transformation of
1620 N -dimensional points, arbitrary linear color space transformation (such
1621 as various kinds of RGB to YUV transforms), shuffling the image
1622 channels, and so forth.
1623 @param src input array that must have as many channels (1 to 4) as
1625 @param dst output array of the same size and depth as src; it has as
1626 many channels as m.rows.
1627 @param m transformation 2x2 or 2x3 floating-point matrix.
1628 @sa perspectiveTransform, getAffineTransform, estimateRigidTransform, warpAffine, warpPerspective
1630 CV_EXPORTS_W void transform(InputArray src, OutputArray dst, InputArray m );
1632 /** @brief Performs the perspective matrix transformation of vectors.
1634 The function perspectiveTransform transforms every element of src by
1635 treating it as a 2D or 3D vector, in the following way:
1636 \f[(x, y, z) \rightarrow (x'/w, y'/w, z'/w)\f]
1638 \f[(x', y', z', w') = \texttt{mat} \cdot \begin{bmatrix} x & y & z & 1 \end{bmatrix}\f]
1640 \f[w = \fork{w'}{if \(w' \ne 0\)}{\infty}{otherwise}\f]
1642 Here a 3D vector transformation is shown. In case of a 2D vector
1643 transformation, the z component is omitted.
1645 @note The function transforms a sparse set of 2D or 3D vectors. If you
1646 want to transform an image using perspective transformation, use
1647 warpPerspective . If you have an inverse problem, that is, you want to
1648 compute the most probable perspective transformation out of several
1649 pairs of corresponding points, you can use getPerspectiveTransform or
1651 @param src input two-channel or three-channel floating-point array; each
1652 element is a 2D/3D vector to be transformed.
1653 @param dst output array of the same size and type as src.
1654 @param m 3x3 or 4x4 floating-point transformation matrix.
1655 @sa transform, warpPerspective, getPerspectiveTransform, findHomography
1657 CV_EXPORTS_W void perspectiveTransform(InputArray src, OutputArray dst, InputArray m );
1659 /** @brief Copies the lower or the upper half of a square matrix to another half.
1661 The function completeSymm copies the lower half of a square matrix to
1662 its another half. The matrix diagonal remains unchanged:
1663 * \f$\texttt{mtx}_{ij}=\texttt{mtx}_{ji}\f$ for \f$i > j\f$ if
1665 * \f$\texttt{mtx}_{ij}=\texttt{mtx}_{ji}\f$ for \f$i < j\f$ if
1667 @param mtx input-output floating-point square matrix.
1668 @param lowerToUpper operation flag; if true, the lower half is copied to
1669 the upper half. Otherwise, the upper half is copied to the lower half.
1672 CV_EXPORTS_W void completeSymm(InputOutputArray mtx, bool lowerToUpper = false);
1674 /** @brief Initializes a scaled identity matrix.
1676 The function setIdentity initializes a scaled identity matrix:
1677 \f[\texttt{mtx} (i,j)= \fork{\texttt{value}}{ if \(i=j\)}{0}{otherwise}\f]
1679 The function can also be emulated using the matrix initializers and the
1682 Mat A = Mat::eye(4, 3, CV_32F)*5;
1683 // A will be set to [[5, 0, 0], [0, 5, 0], [0, 0, 5], [0, 0, 0]]
1685 @param mtx matrix to initialize (not necessarily square).
1686 @param s value to assign to diagonal elements.
1687 @sa Mat::zeros, Mat::ones, Mat::setTo, Mat::operator=
1689 CV_EXPORTS_W void setIdentity(InputOutputArray mtx, const Scalar& s = Scalar(1));
1691 /** @brief Returns the determinant of a square floating-point matrix.
1693 The function determinant calculates and returns the determinant of the
1694 specified matrix. For small matrices ( mtx.cols=mtx.rows\<=3 ), the
1695 direct method is used. For larger matrices, the function uses LU
1696 factorization with partial pivoting.
1698 For symmetric positively-determined matrices, it is also possible to use
1699 eigen decomposition to calculate the determinant.
1700 @param mtx input matrix that must have CV_32FC1 or CV_64FC1 type and
1702 @sa trace, invert, solve, eigen, @ref MatrixExpressions
1704 CV_EXPORTS_W double determinant(InputArray mtx);
1706 /** @brief Returns the trace of a matrix.
1708 The function trace returns the sum of the diagonal elements of the
1710 \f[\mathrm{tr} ( \texttt{mtx} ) = \sum _i \texttt{mtx} (i,i)\f]
1711 @param mtx input matrix.
1713 CV_EXPORTS_W Scalar trace(InputArray mtx);
1715 /** @brief Finds the inverse or pseudo-inverse of a matrix.
1717 The function invert inverts the matrix src and stores the result in dst
1718 . When the matrix src is singular or non-square, the function calculates
1719 the pseudo-inverse matrix (the dst matrix) so that norm(src\*dst - I) is
1720 minimal, where I is an identity matrix.
1722 In case of the DECOMP_LU method, the function returns non-zero value if
1723 the inverse has been successfully calculated and 0 if src is singular.
1725 In case of the DECOMP_SVD method, the function returns the inverse
1726 condition number of src (the ratio of the smallest singular value to the
1727 largest singular value) and 0 if src is singular. The SVD method
1728 calculates a pseudo-inverse matrix if src is singular.
1730 Similarly to DECOMP_LU, the method DECOMP_CHOLESKY works only with
1731 non-singular square matrices that should also be symmetrical and
1732 positively defined. In this case, the function stores the inverted
1733 matrix in dst and returns non-zero. Otherwise, it returns 0.
1735 @param src input floating-point M x N matrix.
1736 @param dst output matrix of N x M size and the same type as src.
1737 @param flags inversion method (cv::DecompTypes)
1740 CV_EXPORTS_W double invert(InputArray src, OutputArray dst, int flags = DECOMP_LU);
1742 /** @brief Solves one or more linear systems or least-squares problems.
1744 The function solve solves a linear system or least-squares problem (the
1745 latter is possible with SVD or QR methods, or by specifying the flag
1747 \f[\texttt{dst} = \arg \min _X \| \texttt{src1} \cdot \texttt{X} - \texttt{src2} \|\f]
1749 If DECOMP_LU or DECOMP_CHOLESKY method is used, the function returns 1
1750 if src1 (or \f$\texttt{src1}^T\texttt{src1}\f$ ) is non-singular. Otherwise,
1751 it returns 0. In the latter case, dst is not valid. Other methods find a
1752 pseudo-solution in case of a singular left-hand side part.
1754 @note If you want to find a unity-norm solution of an under-defined
1755 singular system \f$\texttt{src1}\cdot\texttt{dst}=0\f$ , the function solve
1756 will not do the work. Use SVD::solveZ instead.
1758 @param src1 input matrix on the left-hand side of the system.
1759 @param src2 input matrix on the right-hand side of the system.
1760 @param dst output solution.
1761 @param flags solution (matrix inversion) method (cv::DecompTypes)
1762 @sa invert, SVD, eigen
1764 CV_EXPORTS_W bool solve(InputArray src1, InputArray src2,
1765 OutputArray dst, int flags = DECOMP_LU);
1767 /** @brief Sorts each row or each column of a matrix.
1769 The function sort sorts each matrix row or each matrix column in
1770 ascending or descending order. So you should pass two operation flags to
1771 get desired behaviour. If you want to sort matrix rows or columns
1772 lexicographically, you can use STL std::sort generic function with the
1773 proper comparison predicate.
1775 @param src input single-channel array.
1776 @param dst output array of the same size and type as src.
1777 @param flags operation flags, a combination of cv::SortFlags
1778 @sa sortIdx, randShuffle
1780 CV_EXPORTS_W void sort(InputArray src, OutputArray dst, int flags);
1782 /** @brief Sorts each row or each column of a matrix.
1784 The function sortIdx sorts each matrix row or each matrix column in the
1785 ascending or descending order. So you should pass two operation flags to
1786 get desired behaviour. Instead of reordering the elements themselves, it
1787 stores the indices of sorted elements in the output array. For example:
1789 Mat A = Mat::eye(3,3,CV_32F), B;
1790 sortIdx(A, B, SORT_EVERY_ROW + SORT_ASCENDING);
1791 // B will probably contain
1792 // (because of equal elements in A some permutations are possible):
1793 // [[1, 2, 0], [0, 2, 1], [0, 1, 2]]
1795 @param src input single-channel array.
1796 @param dst output integer array of the same size as src.
1797 @param flags operation flags that could be a combination of cv::SortFlags
1798 @sa sort, randShuffle
1800 CV_EXPORTS_W void sortIdx(InputArray src, OutputArray dst, int flags);
1802 /** @brief Finds the real roots of a cubic equation.
1804 The function solveCubic finds the real roots of a cubic equation:
1805 - if coeffs is a 4-element vector:
1806 \f[\texttt{coeffs} [0] x^3 + \texttt{coeffs} [1] x^2 + \texttt{coeffs} [2] x + \texttt{coeffs} [3] = 0\f]
1807 - if coeffs is a 3-element vector:
1808 \f[x^3 + \texttt{coeffs} [0] x^2 + \texttt{coeffs} [1] x + \texttt{coeffs} [2] = 0\f]
1810 The roots are stored in the roots array.
1811 @param coeffs equation coefficients, an array of 3 or 4 elements.
1812 @param roots output array of real roots that has 1 or 3 elements.
1814 CV_EXPORTS_W int solveCubic(InputArray coeffs, OutputArray roots);
1816 /** @brief Finds the real or complex roots of a polynomial equation.
1818 The function solvePoly finds real and complex roots of a polynomial equation:
1819 \f[\texttt{coeffs} [n] x^{n} + \texttt{coeffs} [n-1] x^{n-1} + ... + \texttt{coeffs} [1] x + \texttt{coeffs} [0] = 0\f]
1820 @param coeffs array of polynomial coefficients.
1821 @param roots output (complex) array of roots.
1822 @param maxIters maximum number of iterations the algorithm does.
1824 CV_EXPORTS_W double solvePoly(InputArray coeffs, OutputArray roots, int maxIters = 300);
1826 /** @brief Calculates eigenvalues and eigenvectors of a symmetric matrix.
1828 The functions eigen calculate just eigenvalues, or eigenvalues and eigenvectors of the symmetric
1831 src*eigenvectors.row(i).t() = eigenvalues.at<srcType>(i)*eigenvectors.row(i).t()
1833 @note in the new and the old interfaces different ordering of eigenvalues and eigenvectors
1835 @param src input matrix that must have CV_32FC1 or CV_64FC1 type, square size and be symmetrical
1837 @param eigenvalues output vector of eigenvalues of the same type as src; the eigenvalues are stored
1838 in the descending order.
1839 @param eigenvectors output matrix of eigenvectors; it has the same size and type as src; the
1840 eigenvectors are stored as subsequent matrix rows, in the same order as the corresponding
1842 @sa completeSymm , PCA
1844 CV_EXPORTS_W bool eigen(InputArray src, OutputArray eigenvalues,
1845 OutputArray eigenvectors = noArray());
1847 /** @brief Calculates the covariance matrix of a set of vectors.
1849 The functions calcCovarMatrix calculate the covariance matrix and, optionally, the mean vector of
1850 the set of input vectors.
1851 @param samples samples stored as separate matrices
1852 @param nsamples number of samples
1853 @param covar output covariance matrix of the type ctype and square size.
1854 @param mean input or output (depending on the flags) array as the average value of the input vectors.
1855 @param flags operation flags as a combination of cv::CovarFlags
1856 @param ctype type of the matrixl; it equals 'CV_64F' by default.
1857 @sa PCA, mulTransposed, Mahalanobis
1858 @todo InputArrayOfArrays
1860 CV_EXPORTS void calcCovarMatrix( const Mat* samples, int nsamples, Mat& covar, Mat& mean,
1861 int flags, int ctype = CV_64F);
1864 @note use cv::COVAR_ROWS or cv::COVAR_COLS flag
1865 @param samples samples stored as rows/columns of a single matrix.
1866 @param covar output covariance matrix of the type ctype and square size.
1867 @param mean input or output (depending on the flags) array as the average value of the input vectors.
1868 @param flags operation flags as a combination of cv::CovarFlags
1869 @param ctype type of the matrixl; it equals 'CV_64F' by default.
1871 CV_EXPORTS_W void calcCovarMatrix( InputArray samples, OutputArray covar,
1872 InputOutputArray mean, int flags, int ctype = CV_64F);
1874 /** wrap PCA::operator() */
1875 CV_EXPORTS_W void PCACompute(InputArray data, InputOutputArray mean,
1876 OutputArray eigenvectors, int maxComponents = 0);
1878 /** wrap PCA::operator() */
1879 CV_EXPORTS_W void PCACompute(InputArray data, InputOutputArray mean,
1880 OutputArray eigenvectors, double retainedVariance);
1882 /** wrap PCA::project */
1883 CV_EXPORTS_W void PCAProject(InputArray data, InputArray mean,
1884 InputArray eigenvectors, OutputArray result);
1886 /** wrap PCA::backProject */
1887 CV_EXPORTS_W void PCABackProject(InputArray data, InputArray mean,
1888 InputArray eigenvectors, OutputArray result);
1890 /** wrap SVD::compute */
1891 CV_EXPORTS_W void SVDecomp( InputArray src, OutputArray w, OutputArray u, OutputArray vt, int flags = 0 );
1893 /** wrap SVD::backSubst */
1894 CV_EXPORTS_W void SVBackSubst( InputArray w, InputArray u, InputArray vt,
1895 InputArray rhs, OutputArray dst );
1897 /** @brief Calculates the Mahalanobis distance between two vectors.
1899 The function Mahalanobis calculates and returns the weighted distance between two vectors:
1900 \f[d( \texttt{vec1} , \texttt{vec2} )= \sqrt{\sum_{i,j}{\texttt{icovar(i,j)}\cdot(\texttt{vec1}(I)-\texttt{vec2}(I))\cdot(\texttt{vec1(j)}-\texttt{vec2(j)})} }\f]
1901 The covariance matrix may be calculated using the cv::calcCovarMatrix function and then inverted using
1902 the invert function (preferably using the cv::DECOMP_SVD method, as the most accurate).
1903 @param v1 first 1D input vector.
1904 @param v2 second 1D input vector.
1905 @param icovar inverse covariance matrix.
1907 CV_EXPORTS_W double Mahalanobis(InputArray v1, InputArray v2, InputArray icovar);
1909 /** @brief Performs a forward or inverse Discrete Fourier transform of a 1D or 2D floating-point array.
1911 The function performs one of the following:
1912 - Forward the Fourier transform of a 1D vector of N elements:
1913 \f[Y = F^{(N)} \cdot X,\f]
1914 where \f$F^{(N)}_{jk}=\exp(-2\pi i j k/N)\f$ and \f$i=\sqrt{-1}\f$
1915 - Inverse the Fourier transform of a 1D vector of N elements:
1916 \f[\begin{array}{l} X'= \left (F^{(N)} \right )^{-1} \cdot Y = \left (F^{(N)} \right )^* \cdot y \\ X = (1/N) \cdot X, \end{array}\f]
1917 where \f$F^*=\left(\textrm{Re}(F^{(N)})-\textrm{Im}(F^{(N)})\right)^T\f$
1918 - Forward the 2D Fourier transform of a M x N matrix:
1919 \f[Y = F^{(M)} \cdot X \cdot F^{(N)}\f]
1920 - Inverse the 2D Fourier transform of a M x N matrix:
1921 \f[\begin{array}{l} X'= \left (F^{(M)} \right )^* \cdot Y \cdot \left (F^{(N)} \right )^* \\ X = \frac{1}{M \cdot N} \cdot X' \end{array}\f]
1923 In case of real (single-channel) data, the output spectrum of the forward Fourier transform or input
1924 spectrum of the inverse Fourier transform can be represented in a packed format called *CCS*
1925 (complex-conjugate-symmetrical). It was borrowed from IPL (Intel\* Image Processing Library). Here
1926 is how 2D *CCS* spectrum looks:
1927 \f[\begin{bmatrix} Re Y_{0,0} & Re Y_{0,1} & Im Y_{0,1} & Re Y_{0,2} & Im Y_{0,2} & \cdots & Re Y_{0,N/2-1} & Im Y_{0,N/2-1} & Re Y_{0,N/2} \\ Re Y_{1,0} & Re Y_{1,1} & Im Y_{1,1} & Re Y_{1,2} & Im Y_{1,2} & \cdots & Re Y_{1,N/2-1} & Im Y_{1,N/2-1} & Re Y_{1,N/2} \\ Im Y_{1,0} & Re Y_{2,1} & Im Y_{2,1} & Re Y_{2,2} & Im Y_{2,2} & \cdots & Re Y_{2,N/2-1} & Im Y_{2,N/2-1} & Im Y_{1,N/2} \\ \hdotsfor{9} \\ Re Y_{M/2-1,0} & Re Y_{M-3,1} & Im Y_{M-3,1} & \hdotsfor{3} & Re Y_{M-3,N/2-1} & Im Y_{M-3,N/2-1}& Re Y_{M/2-1,N/2} \\ Im Y_{M/2-1,0} & Re Y_{M-2,1} & Im Y_{M-2,1} & \hdotsfor{3} & Re Y_{M-2,N/2-1} & Im Y_{M-2,N/2-1}& Im Y_{M/2-1,N/2} \\ Re Y_{M/2,0} & Re Y_{M-1,1} & Im Y_{M-1,1} & \hdotsfor{3} & Re Y_{M-1,N/2-1} & Im Y_{M-1,N/2-1}& Re Y_{M/2,N/2} \end{bmatrix}\f]
1929 In case of 1D transform of a real vector, the output looks like the first row of the matrix above.
1931 So, the function chooses an operation mode depending on the flags and size of the input array:
1932 - If DFT_ROWS is set or the input array has a single row or single column, the function
1933 performs a 1D forward or inverse transform of each row of a matrix when DFT_ROWS is set.
1934 Otherwise, it performs a 2D transform.
1935 - If the input array is real and DFT_INVERSE is not set, the function performs a forward 1D or
1937 - When DFT_COMPLEX_OUTPUT is set, the output is a complex matrix of the same size as
1939 - When DFT_COMPLEX_OUTPUT is not set, the output is a real matrix of the same size as
1940 input. In case of 2D transform, it uses the packed format as shown above. In case of a
1941 single 1D transform, it looks like the first row of the matrix above. In case of
1942 multiple 1D transforms (when using the DFT_ROWS flag), each row of the output matrix
1943 looks like the first row of the matrix above.
1944 - If the input array is complex and either DFT_INVERSE or DFT_REAL_OUTPUT are not set, the
1945 output is a complex array of the same size as input. The function performs a forward or
1946 inverse 1D or 2D transform of the whole input array or each row of the input array
1947 independently, depending on the flags DFT_INVERSE and DFT_ROWS.
1948 - When DFT_INVERSE is set and the input array is real, or it is complex but DFT_REAL_OUTPUT
1949 is set, the output is a real array of the same size as input. The function performs a 1D or 2D
1950 inverse transformation of the whole input array or each individual row, depending on the flags
1951 DFT_INVERSE and DFT_ROWS.
1953 If DFT_SCALE is set, the scaling is done after the transformation.
1955 Unlike dct , the function supports arrays of arbitrary size. But only those arrays are processed
1956 efficiently, whose sizes can be factorized in a product of small prime numbers (2, 3, and 5 in the
1957 current implementation). Such an efficient DFT size can be calculated using the getOptimalDFTSize
1960 The sample below illustrates how to calculate a DFT-based convolution of two 2D real arrays:
1962 void convolveDFT(InputArray A, InputArray B, OutputArray C)
1964 // reallocate the output array if needed
1965 C.create(abs(A.rows - B.rows)+1, abs(A.cols - B.cols)+1, A.type());
1967 // calculate the size of DFT transform
1968 dftSize.width = getOptimalDFTSize(A.cols + B.cols - 1);
1969 dftSize.height = getOptimalDFTSize(A.rows + B.rows - 1);
1971 // allocate temporary buffers and initialize them with 0's
1972 Mat tempA(dftSize, A.type(), Scalar::all(0));
1973 Mat tempB(dftSize, B.type(), Scalar::all(0));
1975 // copy A and B to the top-left corners of tempA and tempB, respectively
1976 Mat roiA(tempA, Rect(0,0,A.cols,A.rows));
1978 Mat roiB(tempB, Rect(0,0,B.cols,B.rows));
1981 // now transform the padded A & B in-place;
1982 // use "nonzeroRows" hint for faster processing
1983 dft(tempA, tempA, 0, A.rows);
1984 dft(tempB, tempB, 0, B.rows);
1986 // multiply the spectrums;
1987 // the function handles packed spectrum representations well
1988 mulSpectrums(tempA, tempB, tempA);
1990 // transform the product back from the frequency domain.
1991 // Even though all the result rows will be non-zero,
1992 // you need only the first C.rows of them, and thus you
1993 // pass nonzeroRows == C.rows
1994 dft(tempA, tempA, DFT_INVERSE + DFT_SCALE, C.rows);
1996 // now copy the result back to C.
1997 tempA(Rect(0, 0, C.cols, C.rows)).copyTo(C);
1999 // all the temporary buffers will be deallocated automatically
2002 To optimize this sample, consider the following approaches:
2003 - Since nonzeroRows != 0 is passed to the forward transform calls and since A and B are copied to
2004 the top-left corners of tempA and tempB, respectively, it is not necessary to clear the whole
2005 tempA and tempB. It is only necessary to clear the tempA.cols - A.cols ( tempB.cols - B.cols)
2006 rightmost columns of the matrices.
2007 - This DFT-based convolution does not have to be applied to the whole big arrays, especially if B
2008 is significantly smaller than A or vice versa. Instead, you can calculate convolution by parts.
2009 To do this, you need to split the output array C into multiple tiles. For each tile, estimate
2010 which parts of A and B are required to calculate convolution in this tile. If the tiles in C are
2011 too small, the speed will decrease a lot because of repeated work. In the ultimate case, when
2012 each tile in C is a single pixel, the algorithm becomes equivalent to the naive convolution
2013 algorithm. If the tiles are too big, the temporary arrays tempA and tempB become too big and
2014 there is also a slowdown because of bad cache locality. So, there is an optimal tile size
2015 somewhere in the middle.
2016 - If different tiles in C can be calculated in parallel and, thus, the convolution is done by
2017 parts, the loop can be threaded.
2019 All of the above improvements have been implemented in matchTemplate and filter2D . Therefore, by
2020 using them, you can get the performance even better than with the above theoretically optimal
2021 implementation. Though, those two functions actually calculate cross-correlation, not convolution,
2022 so you need to "flip" the second convolution operand B vertically and horizontally using flip .
2024 - An example using the discrete fourier transform can be found at
2025 opencv_source_code/samples/cpp/dft.cpp
2026 - (Python) An example using the dft functionality to perform Wiener deconvolution can be found
2027 at opencv_source/samples/python2/deconvolution.py
2028 - (Python) An example rearranging the quadrants of a Fourier image can be found at
2029 opencv_source/samples/python2/dft.py
2030 @param src input array that could be real or complex.
2031 @param dst output array whose size and type depends on the flags .
2032 @param flags transformation flags, representing a combination of the cv::DftFlags
2033 @param nonzeroRows when the parameter is not zero, the function assumes that only the first
2034 nonzeroRows rows of the input array (DFT_INVERSE is not set) or only the first nonzeroRows of the
2035 output array (DFT_INVERSE is set) contain non-zeros, thus, the function can handle the rest of the
2036 rows more efficiently and save some time; this technique is very useful for calculating array
2037 cross-correlation or convolution using DFT.
2038 @sa dct , getOptimalDFTSize , mulSpectrums, filter2D , matchTemplate , flip , cartToPolar ,
2041 CV_EXPORTS_W void dft(InputArray src, OutputArray dst, int flags = 0, int nonzeroRows = 0);
2043 /** @brief Calculates the inverse Discrete Fourier Transform of a 1D or 2D array.
2045 idft(src, dst, flags) is equivalent to dft(src, dst, flags | DFT_INVERSE) .
2046 @note None of dft and idft scales the result by default. So, you should pass DFT_SCALE to one of
2047 dft or idft explicitly to make these transforms mutually inverse.
2048 @sa dft, dct, idct, mulSpectrums, getOptimalDFTSize
2049 @param src input floating-point real or complex array.
2050 @param dst output array whose size and type depend on the flags.
2051 @param flags operation flags (see dft and cv::DftFlags).
2052 @param nonzeroRows number of dst rows to process; the rest of the rows have undefined content (see
2053 the convolution sample in dft description.
2055 CV_EXPORTS_W void idft(InputArray src, OutputArray dst, int flags = 0, int nonzeroRows = 0);
2057 /** @brief Performs a forward or inverse discrete Cosine transform of 1D or 2D array.
2059 The function dct performs a forward or inverse discrete Cosine transform (DCT) of a 1D or 2D
2060 floating-point array:
2061 - Forward Cosine transform of a 1D vector of N elements:
2062 \f[Y = C^{(N)} \cdot X\f]
2064 \f[C^{(N)}_{jk}= \sqrt{\alpha_j/N} \cos \left ( \frac{\pi(2k+1)j}{2N} \right )\f]
2066 \f$\alpha_0=1\f$, \f$\alpha_j=2\f$ for *j \> 0*.
2067 - Inverse Cosine transform of a 1D vector of N elements:
2068 \f[X = \left (C^{(N)} \right )^{-1} \cdot Y = \left (C^{(N)} \right )^T \cdot Y\f]
2069 (since \f$C^{(N)}\f$ is an orthogonal matrix, \f$C^{(N)} \cdot \left(C^{(N)}\right)^T = I\f$ )
2070 - Forward 2D Cosine transform of M x N matrix:
2071 \f[Y = C^{(N)} \cdot X \cdot \left (C^{(N)} \right )^T\f]
2072 - Inverse 2D Cosine transform of M x N matrix:
2073 \f[X = \left (C^{(N)} \right )^T \cdot X \cdot C^{(N)}\f]
2075 The function chooses the mode of operation by looking at the flags and size of the input array:
2076 - If (flags & DCT_INVERSE) == 0 , the function does a forward 1D or 2D transform. Otherwise, it
2077 is an inverse 1D or 2D transform.
2078 - If (flags & DCT_ROWS) != 0 , the function performs a 1D transform of each row.
2079 - If the array is a single column or a single row, the function performs a 1D transform.
2080 - If none of the above is true, the function performs a 2D transform.
2082 @note Currently dct supports even-size arrays (2, 4, 6 ...). For data analysis and approximation, you
2083 can pad the array when necessary.
2084 Also, the function performance depends very much, and not monotonically, on the array size (see
2085 getOptimalDFTSize ). In the current implementation DCT of a vector of size N is calculated via DFT
2086 of a vector of size N/2 . Thus, the optimal DCT size N1 \>= N can be calculated as:
2088 size_t getOptimalDCTSize(size_t N) { return 2*getOptimalDFTSize((N+1)/2); }
2089 N1 = getOptimalDCTSize(N);
2091 @param src input floating-point array.
2092 @param dst output array of the same size and type as src .
2093 @param flags transformation flags as a combination of cv::DftFlags (DCT_*)
2094 @sa dft , getOptimalDFTSize , idct
2096 CV_EXPORTS_W void dct(InputArray src, OutputArray dst, int flags = 0);
2098 /** @brief Calculates the inverse Discrete Cosine Transform of a 1D or 2D array.
2100 idct(src, dst, flags) is equivalent to dct(src, dst, flags | DCT_INVERSE).
2101 @param src input floating-point single-channel array.
2102 @param dst output array of the same size and type as src.
2103 @param flags operation flags.
2104 @sa dct, dft, idft, getOptimalDFTSize
2106 CV_EXPORTS_W void idct(InputArray src, OutputArray dst, int flags = 0);
2108 /** @brief Performs the per-element multiplication of two Fourier spectrums.
2110 The function mulSpectrums performs the per-element multiplication of the two CCS-packed or complex
2111 matrices that are results of a real or complex Fourier transform.
2113 The function, together with dft and idft , may be used to calculate convolution (pass conjB=false )
2114 or correlation (pass conjB=true ) of two arrays rapidly. When the arrays are complex, they are
2115 simply multiplied (per element) with an optional conjugation of the second-array elements. When the
2116 arrays are real, they are assumed to be CCS-packed (see dft for details).
2117 @param a first input array.
2118 @param b second input array of the same size and type as src1 .
2119 @param c output array of the same size and type as src1 .
2120 @param flags operation flags; currently, the only supported flag is cv::DFT_ROWS, which indicates that
2121 each row of src1 and src2 is an independent 1D Fourier spectrum. If you do not want to use this flag, then simply add a `0` as value.
2122 @param conjB optional flag that conjugates the second input array before the multiplication (true)
2125 CV_EXPORTS_W void mulSpectrums(InputArray a, InputArray b, OutputArray c,
2126 int flags, bool conjB = false);
2128 /** @brief Returns the optimal DFT size for a given vector size.
2130 DFT performance is not a monotonic function of a vector size. Therefore, when you calculate
2131 convolution of two arrays or perform the spectral analysis of an array, it usually makes sense to
2132 pad the input data with zeros to get a bit larger array that can be transformed much faster than the
2133 original one. Arrays whose size is a power-of-two (2, 4, 8, 16, 32, ...) are the fastest to process.
2134 Though, the arrays whose size is a product of 2's, 3's, and 5's (for example, 300 = 5\*5\*3\*2\*2)
2135 are also processed quite efficiently.
2137 The function getOptimalDFTSize returns the minimum number N that is greater than or equal to vecsize
2138 so that the DFT of a vector of size N can be processed efficiently. In the current implementation N
2139 = 2 ^p^ \* 3 ^q^ \* 5 ^r^ for some integer p, q, r.
2141 The function returns a negative number if vecsize is too large (very close to INT_MAX ).
2143 While the function cannot be used directly to estimate the optimal vector size for DCT transform
2144 (since the current DCT implementation supports only even-size vectors), it can be easily processed
2145 as getOptimalDFTSize((vecsize+1)/2)\*2.
2146 @param vecsize vector size.
2147 @sa dft , dct , idft , idct , mulSpectrums
2149 CV_EXPORTS_W int getOptimalDFTSize(int vecsize);
2151 /** @brief Returns the default random number generator.
2153 The function theRNG returns the default random number generator. For each thread, there is a
2154 separate random number generator, so you can use the function safely in multi-thread environments.
2155 If you just need to get a single random number using this generator or initialize an array, you can
2156 use randu or randn instead. But if you are going to generate many random numbers inside a loop, it
2157 is much faster to use this function to retrieve the generator and then use RNG::operator _Tp() .
2158 @sa RNG, randu, randn
2160 CV_EXPORTS RNG& theRNG();
2162 /** @brief Generates a single uniformly-distributed random number or an array of random numbers.
2164 Non-template variant of the function fills the matrix dst with uniformly-distributed
2165 random numbers from the specified range:
2166 \f[\texttt{low} _c \leq \texttt{dst} (I)_c < \texttt{high} _c\f]
2167 @param dst output array of random numbers; the array must be pre-allocated.
2168 @param low inclusive lower boundary of the generated random numbers.
2169 @param high exclusive upper boundary of the generated random numbers.
2170 @sa RNG, randn, theRNG
2172 CV_EXPORTS_W void randu(InputOutputArray dst, InputArray low, InputArray high);
2174 /** @brief Fills the array with normally distributed random numbers.
2176 The function randn fills the matrix dst with normally distributed random numbers with the specified
2177 mean vector and the standard deviation matrix. The generated random numbers are clipped to fit the
2178 value range of the output array data type.
2179 @param dst output array of random numbers; the array must be pre-allocated and have 1 to 4 channels.
2180 @param mean mean value (expectation) of the generated random numbers.
2181 @param stddev standard deviation of the generated random numbers; it can be either a vector (in
2182 which case a diagonal standard deviation matrix is assumed) or a square matrix.
2185 CV_EXPORTS_W void randn(InputOutputArray dst, InputArray mean, InputArray stddev);
2187 /** @brief Shuffles the array elements randomly.
2189 The function randShuffle shuffles the specified 1D array by randomly choosing pairs of elements and
2190 swapping them. The number of such swap operations will be dst.rows\*dst.cols\*iterFactor .
2191 @param dst input/output numerical 1D array.
2192 @param iterFactor scale factor that determines the number of random swap operations (see the details
2194 @param rng optional random number generator used for shuffling; if it is zero, theRNG () is used
2198 CV_EXPORTS_W void randShuffle(InputOutputArray dst, double iterFactor = 1., RNG* rng = 0);
2200 /** @brief Principal Component Analysis
2202 The class is used to calculate a special basis for a set of vectors. The
2203 basis will consist of eigenvectors of the covariance matrix calculated
2204 from the input set of vectors. The class %PCA can also transform
2205 vectors to/from the new coordinate space defined by the basis. Usually,
2206 in this new coordinate system, each vector from the original set (and
2207 any linear combination of such vectors) can be quite accurately
2208 approximated by taking its first few components, corresponding to the
2209 eigenvectors of the largest eigenvalues of the covariance matrix.
2210 Geometrically it means that you calculate a projection of the vector to
2211 a subspace formed by a few eigenvectors corresponding to the dominant
2212 eigenvalues of the covariance matrix. And usually such a projection is
2213 very close to the original vector. So, you can represent the original
2214 vector from a high-dimensional space with a much shorter vector
2215 consisting of the projected vector's coordinates in the subspace. Such a
2216 transformation is also known as Karhunen-Loeve Transform, or KLT.
2217 See http://en.wikipedia.org/wiki/Principal_component_analysis
2219 The sample below is the function that takes two matrices. The first
2220 function stores a set of vectors (a row per vector) that is used to
2221 calculate PCA. The second function stores another "test" set of vectors
2222 (a row per vector). First, these vectors are compressed with PCA, then
2223 reconstructed back, and then the reconstruction error norm is computed
2224 and printed for each vector. :
2229 PCA compressPCA(const Mat& pcaset, int maxComponents,
2230 const Mat& testset, Mat& compressed)
2232 PCA pca(pcaset, // pass the data
2233 Mat(), // we do not have a pre-computed mean vector,
2234 // so let the PCA engine to compute it
2235 PCA::DATA_AS_ROW, // indicate that the vectors
2236 // are stored as matrix rows
2237 // (use PCA::DATA_AS_COL if the vectors are
2238 // the matrix columns)
2239 maxComponents // specify, how many principal components to retain
2241 // if there is no test data, just return the computed basis, ready-to-use
2244 CV_Assert( testset.cols == pcaset.cols );
2246 compressed.create(testset.rows, maxComponents, testset.type());
2249 for( int i = 0; i < testset.rows; i++ )
2251 Mat vec = testset.row(i), coeffs = compressed.row(i), reconstructed;
2252 // compress the vector, the result will be stored
2253 // in the i-th row of the output matrix
2254 pca.project(vec, coeffs);
2255 // and then reconstruct it
2256 pca.backProject(coeffs, reconstructed);
2257 // and measure the error
2258 printf("%d. diff = %g\n", i, norm(vec, reconstructed, NORM_L2));
2263 @sa calcCovarMatrix, mulTransposed, SVD, dft, dct
2265 class CV_EXPORTS PCA
2268 enum Flags { DATA_AS_ROW = 0, //!< indicates that the input samples are stored as matrix rows
2269 DATA_AS_COL = 1, //!< indicates that the input samples are stored as matrix columns
2273 /** @brief default constructor
2275 The default constructor initializes an empty %PCA structure. The other
2276 constructors initialize the structure and call PCA::operator()().
2281 @param data input samples stored as matrix rows or matrix columns.
2282 @param mean optional mean value; if the matrix is empty (@c noArray()),
2283 the mean is computed from the data.
2284 @param flags operation flags; currently the parameter is only used to
2285 specify the data layout (PCA::Flags)
2286 @param maxComponents maximum number of components that %PCA should
2287 retain; by default, all the components are retained.
2289 PCA(InputArray data, InputArray mean, int flags, int maxComponents = 0);
2292 @param data input samples stored as matrix rows or matrix columns.
2293 @param mean optional mean value; if the matrix is empty (noArray()),
2294 the mean is computed from the data.
2295 @param flags operation flags; currently the parameter is only used to
2296 specify the data layout (PCA::Flags)
2297 @param retainedVariance Percentage of variance that PCA should retain.
2298 Using this parameter will let the PCA decided how many components to
2299 retain but it will always keep at least 2.
2301 PCA(InputArray data, InputArray mean, int flags, double retainedVariance);
2303 /** @brief performs %PCA
2305 The operator performs %PCA of the supplied dataset. It is safe to reuse
2306 the same PCA structure for multiple datasets. That is, if the structure
2307 has been previously used with another dataset, the existing internal
2308 data is reclaimed and the new eigenvalues, @ref eigenvectors , and @ref
2309 mean are allocated and computed.
2311 The computed eigenvalues are sorted from the largest to the smallest and
2312 the corresponding eigenvectors are stored as eigenvectors rows.
2314 @param data input samples stored as the matrix rows or as the matrix
2316 @param mean optional mean value; if the matrix is empty (noArray()),
2317 the mean is computed from the data.
2318 @param flags operation flags; currently the parameter is only used to
2319 specify the data layout. (Flags)
2320 @param maxComponents maximum number of components that PCA should
2321 retain; by default, all the components are retained.
2323 PCA& operator()(InputArray data, InputArray mean, int flags, int maxComponents = 0);
2326 @param data input samples stored as the matrix rows or as the matrix
2328 @param mean optional mean value; if the matrix is empty (noArray()),
2329 the mean is computed from the data.
2330 @param flags operation flags; currently the parameter is only used to
2331 specify the data layout. (PCA::Flags)
2332 @param retainedVariance Percentage of variance that %PCA should retain.
2333 Using this parameter will let the %PCA decided how many components to
2334 retain but it will always keep at least 2.
2336 PCA& operator()(InputArray data, InputArray mean, int flags, double retainedVariance);
2338 /** @brief Projects vector(s) to the principal component subspace.
2340 The methods project one or more vectors to the principal component
2341 subspace, where each vector projection is represented by coefficients in
2342 the principal component basis. The first form of the method returns the
2343 matrix that the second form writes to the result. So the first form can
2344 be used as a part of expression while the second form can be more
2345 efficient in a processing loop.
2346 @param vec input vector(s); must have the same dimensionality and the
2347 same layout as the input data used at %PCA phase, that is, if
2348 DATA_AS_ROW are specified, then `vec.cols==data.cols`
2349 (vector dimensionality) and `vec.rows` is the number of vectors to
2350 project, and the same is true for the PCA::DATA_AS_COL case.
2352 Mat project(InputArray vec) const;
2355 @param vec input vector(s); must have the same dimensionality and the
2356 same layout as the input data used at PCA phase, that is, if
2357 DATA_AS_ROW are specified, then `vec.cols==data.cols`
2358 (vector dimensionality) and `vec.rows` is the number of vectors to
2359 project, and the same is true for the PCA::DATA_AS_COL case.
2360 @param result output vectors; in case of PCA::DATA_AS_COL, the
2361 output matrix has as many columns as the number of input vectors, this
2362 means that `result.cols==vec.cols` and the number of rows match the
2363 number of principal components (for example, `maxComponents` parameter
2364 passed to the constructor).
2366 void project(InputArray vec, OutputArray result) const;
2368 /** @brief Reconstructs vectors from their PC projections.
2370 The methods are inverse operations to PCA::project. They take PC
2371 coordinates of projected vectors and reconstruct the original vectors.
2372 Unless all the principal components have been retained, the
2373 reconstructed vectors are different from the originals. But typically,
2374 the difference is small if the number of components is large enough (but
2375 still much smaller than the original vector dimensionality). As a
2376 result, PCA is used.
2377 @param vec coordinates of the vectors in the principal component
2378 subspace, the layout and size are the same as of PCA::project output
2381 Mat backProject(InputArray vec) const;
2384 @param vec coordinates of the vectors in the principal component
2385 subspace, the layout and size are the same as of PCA::project output
2387 @param result reconstructed vectors; the layout and size are the same as
2388 of PCA::project input vectors.
2390 void backProject(InputArray vec, OutputArray result) const;
2392 /** @brief write and load PCA matrix
2395 void write(FileStorage& fs ) const;
2396 void read(const FileNode& fs);
2398 Mat eigenvectors; //!< eigenvectors of the covariation matrix
2399 Mat eigenvalues; //!< eigenvalues of the covariation matrix
2400 Mat mean; //!< mean value subtracted before the projection and added after the back projection
2403 /** @example pca.cpp
2404 An example using %PCA for dimensionality reduction while maintaining an amount of variance
2408 @brief Linear Discriminant Analysis
2409 @todo document this class
2411 class CV_EXPORTS LDA
2414 /** @brief constructor
2415 Initializes a LDA with num_components (default 0).
2417 explicit LDA(int num_components = 0);
2419 /** Initializes and performs a Discriminant Analysis with Fisher's
2420 Optimization Criterion on given data in src and corresponding labels
2421 in labels. If 0 (or less) number of components are given, they are
2422 automatically determined for given data in computation.
2424 LDA(InputArrayOfArrays src, InputArray labels, int num_components = 0);
2426 /** Serializes this object to a given filename.
2428 void save(const String& filename) const;
2430 /** Deserializes this object from a given filename.
2432 void load(const String& filename);
2434 /** Serializes this object to a given cv::FileStorage.
2436 void save(FileStorage& fs) const;
2438 /** Deserializes this object from a given cv::FileStorage.
2440 void load(const FileStorage& node);
2446 /** Compute the discriminants for data in src (row aligned) and labels.
2448 void compute(InputArrayOfArrays src, InputArray labels);
2450 /** Projects samples into the LDA subspace.
2451 src may be one or more row aligned samples.
2453 Mat project(InputArray src);
2455 /** Reconstructs projections from the LDA subspace.
2456 src may be one or more row aligned projections.
2458 Mat reconstruct(InputArray src);
2460 /** Returns the eigenvectors of this LDA.
2462 Mat eigenvectors() const { return _eigenvectors; }
2464 /** Returns the eigenvalues of this LDA.
2466 Mat eigenvalues() const { return _eigenvalues; }
2468 static Mat subspaceProject(InputArray W, InputArray mean, InputArray src);
2469 static Mat subspaceReconstruct(InputArray W, InputArray mean, InputArray src);
2472 bool _dataAsRow; // unused, but needed for 3.0 ABI compatibility.
2473 int _num_components;
2476 void lda(InputArrayOfArrays src, InputArray labels);
2479 /** @brief Singular Value Decomposition
2481 Class for computing Singular Value Decomposition of a floating-point
2482 matrix. The Singular Value Decomposition is used to solve least-square
2483 problems, under-determined linear systems, invert matrices, compute
2484 condition numbers, and so on.
2486 If you want to compute a condition number of a matrix or an absolute value of
2487 its determinant, you do not need `u` and `vt`. You can pass
2488 flags=SVD::NO_UV|... . Another flag SVD::FULL_UV indicates that full-size u
2489 and vt must be computed, which is not necessary most of the time.
2491 @sa invert, solve, eigen, determinant
2493 class CV_EXPORTS SVD
2497 /** allow the algorithm to modify the decomposed matrix; it can save space and speed up
2498 processing. currently ignored. */
2500 /** indicates that only a vector of singular values `w` is to be processed, while u and vt
2501 will be set to empty matrices */
2503 /** when the matrix is not square, by default the algorithm produces u and vt matrices of
2504 sufficiently large size for the further A reconstruction; if, however, FULL_UV flag is
2505 specified, u and vt will be full-size square orthogonal matrices.*/
2509 /** @brief the default constructor
2511 initializes an empty SVD structure
2516 initializes an empty SVD structure and then calls SVD::operator()
2517 @param src decomposed matrix.
2518 @param flags operation flags (SVD::Flags)
2520 SVD( InputArray src, int flags = 0 );
2522 /** @brief the operator that performs SVD. The previously allocated u, w and vt are released.
2524 The operator performs the singular value decomposition of the supplied
2525 matrix. The u,`vt` , and the vector of singular values w are stored in
2526 the structure. The same SVD structure can be reused many times with
2527 different matrices. Each time, if needed, the previous u,`vt` , and w
2528 are reclaimed and the new matrices are created, which is all handled by
2530 @param src decomposed matrix.
2531 @param flags operation flags (SVD::Flags)
2533 SVD& operator ()( InputArray src, int flags = 0 );
2535 /** @brief decomposes matrix and stores the results to user-provided matrices
2537 The methods/functions perform SVD of matrix. Unlike SVD::SVD constructor
2538 and SVD::operator(), they store the results to the user-provided
2543 SVD::compute(A, w, u, vt);
2546 @param src decomposed matrix
2547 @param w calculated singular values
2548 @param u calculated left singular vectors
2549 @param vt transposed matrix of right singular values
2550 @param flags operation flags - see SVD::SVD.
2552 static void compute( InputArray src, OutputArray w,
2553 OutputArray u, OutputArray vt, int flags = 0 );
2556 computes singular values of a matrix
2557 @param src decomposed matrix
2558 @param w calculated singular values
2559 @param flags operation flags - see SVD::Flags.
2561 static void compute( InputArray src, OutputArray w, int flags = 0 );
2563 /** @brief performs back substitution
2565 static void backSubst( InputArray w, InputArray u,
2566 InputArray vt, InputArray rhs,
2569 /** @brief solves an under-determined singular linear system
2571 The method finds a unit-length solution x of a singular linear system
2572 A\*x = 0. Depending on the rank of A, there can be no solutions, a
2573 single solution or an infinite number of solutions. In general, the
2574 algorithm solves the following problem:
2575 \f[dst = \arg \min _{x: \| x \| =1} \| src \cdot x \|\f]
2576 @param src left-hand-side matrix.
2577 @param dst found solution.
2579 static void solveZ( InputArray src, OutputArray dst );
2581 /** @brief performs a singular value back substitution.
2583 The method calculates a back substitution for the specified right-hand
2586 \f[\texttt{x} = \texttt{vt} ^T \cdot diag( \texttt{w} )^{-1} \cdot \texttt{u} ^T \cdot \texttt{rhs} \sim \texttt{A} ^{-1} \cdot \texttt{rhs}\f]
2588 Using this technique you can either get a very accurate solution of the
2589 convenient linear system, or the best (in the least-squares terms)
2590 pseudo-solution of an overdetermined linear system.
2592 @param rhs right-hand side of a linear system (u\*w\*v')\*dst = rhs to
2593 be solved, where A has been previously decomposed.
2595 @param dst found solution of the system.
2597 @note Explicit SVD with the further back substitution only makes sense
2598 if you need to solve many linear systems with the same left-hand side
2599 (for example, src ). If all you need is to solve a single system
2600 (possibly with multiple rhs immediately available), simply call solve
2601 add pass DECOMP_SVD there. It does absolutely the same thing.
2603 void backSubst( InputArray rhs, OutputArray dst ) const;
2605 /** @todo document */
2606 template<typename _Tp, int m, int n, int nm> static
2607 void compute( const Matx<_Tp, m, n>& a, Matx<_Tp, nm, 1>& w, Matx<_Tp, m, nm>& u, Matx<_Tp, n, nm>& vt );
2609 /** @todo document */
2610 template<typename _Tp, int m, int n, int nm> static
2611 void compute( const Matx<_Tp, m, n>& a, Matx<_Tp, nm, 1>& w );
2613 /** @todo document */
2614 template<typename _Tp, int m, int n, int nm, int nb> static
2615 void backSubst( const Matx<_Tp, nm, 1>& w, const Matx<_Tp, m, nm>& u, const Matx<_Tp, n, nm>& vt, const Matx<_Tp, m, nb>& rhs, Matx<_Tp, n, nb>& dst );
2620 /** @brief Random Number Generator
2622 Random number generator. It encapsulates the state (currently, a 64-bit
2623 integer) and has methods to return scalar random values and to fill
2624 arrays with random values. Currently it supports uniform and Gaussian
2625 (normal) distributions. The generator uses Multiply-With-Carry
2626 algorithm, introduced by G. Marsaglia (
2627 <http://en.wikipedia.org/wiki/Multiply-with-carry> ).
2628 Gaussian-distribution random numbers are generated using the Ziggurat
2629 algorithm ( <http://en.wikipedia.org/wiki/Ziggurat_algorithm> ),
2630 introduced by G. Marsaglia and W. W. Tsang.
2632 class CV_EXPORTS RNG
2639 /** @brief constructor
2641 These are the RNG constructors. The first form sets the state to some
2642 pre-defined value, equal to 2\*\*32-1 in the current implementation. The
2643 second form sets the state to the specified value. If you passed state=0
2644 , the constructor uses the above default value instead to avoid the
2645 singular random number sequence, consisting of all zeros.
2649 @param state 64-bit value used to initialize the RNG.
2652 /**The method updates the state using the MWC algorithm and returns the
2653 next 32-bit random number.*/
2656 /**Each of the methods updates the state using the MWC algorithm and
2657 returns the next random number of the specified type. In case of integer
2658 types, the returned number is from the available value range for the
2659 specified type. In case of floating-point types, the returned value is
2670 operator unsigned();
2678 /** @brief returns a random integer sampled uniformly from [0, N).
2680 The methods transform the state using the MWC algorithm and return the
2681 next random number. The first form is equivalent to RNG::next . The
2682 second form returns the random number modulo N , which means that the
2683 result is in the range [0, N) .
2685 unsigned operator ()();
2687 @param N upper non-inclusive boundary of the returned random number.
2689 unsigned operator ()(unsigned N);
2691 /** @brief returns uniformly distributed integer random number from [a,b) range
2693 The methods transform the state using the MWC algorithm and return the
2694 next uniformly-distributed random number of the specified type, deduced
2695 from the input parameter type, from the range [a, b) . There is a nuance
2696 illustrated by the following sample:
2701 // always produces 0
2702 double a = rng.uniform(0, 1);
2704 // produces double from [0, 1)
2705 double a1 = rng.uniform((double)0, (double)1);
2707 // produces float from [0, 1)
2708 double b = rng.uniform(0.f, 1.f);
2710 // produces double from [0, 1)
2711 double c = rng.uniform(0., 1.);
2713 // may cause compiler error because of ambiguity:
2714 // RNG::uniform(0, (int)0.999999)? or RNG::uniform((double)0, 0.99999)?
2715 double d = rng.uniform(0, 0.999999);
2718 The compiler does not take into account the type of the variable to
2719 which you assign the result of RNG::uniform . The only thing that
2720 matters to the compiler is the type of a and b parameters. So, if you
2721 want a floating-point random number, but the range boundaries are
2722 integer numbers, either put dots in the end, if they are constants, or
2723 use explicit type cast operators, as in the a1 initialization above.
2724 @param a lower inclusive boundary of the returned random numbers.
2725 @param b upper non-inclusive boundary of the returned random numbers.
2727 int uniform(int a, int b);
2729 float uniform(float a, float b);
2731 double uniform(double a, double b);
2733 /** @brief Fills arrays with random numbers.
2735 @param mat 2D or N-dimensional matrix; currently matrices with more than
2736 4 channels are not supported by the methods, use Mat::reshape as a
2737 possible workaround.
2738 @param distType distribution type, RNG::UNIFORM or RNG::NORMAL.
2739 @param a first distribution parameter; in case of the uniform
2740 distribution, this is an inclusive lower boundary, in case of the normal
2741 distribution, this is a mean value.
2742 @param b second distribution parameter; in case of the uniform
2743 distribution, this is a non-inclusive upper boundary, in case of the
2744 normal distribution, this is a standard deviation (diagonal of the
2745 standard deviation matrix or the full standard deviation matrix).
2746 @param saturateRange pre-saturation flag; for uniform distribution only;
2747 if true, the method will first convert a and b to the acceptable value
2748 range (according to the mat datatype) and then will generate uniformly
2749 distributed random numbers within the range [saturate(a), saturate(b)),
2750 if saturateRange=false, the method will generate uniformly distributed
2751 random numbers in the original range [a, b) and then will saturate them,
2752 it means, for example, that
2753 <tt>theRNG().fill(mat_8u, RNG::UNIFORM, -DBL_MAX, DBL_MAX)</tt> will likely
2754 produce array mostly filled with 0's and 255's, since the range (0, 255)
2755 is significantly smaller than [-DBL_MAX, DBL_MAX).
2757 Each of the methods fills the matrix with the random values from the
2758 specified distribution. As the new numbers are generated, the RNG state
2759 is updated accordingly. In case of multiple-channel images, every
2760 channel is filled independently, which means that RNG cannot generate
2761 samples from the multi-dimensional Gaussian distribution with
2762 non-diagonal covariance matrix directly. To do that, the method
2763 generates samples from multi-dimensional standard Gaussian distribution
2764 with zero mean and identity covariation matrix, and then transforms them
2765 using transform to get samples from the specified Gaussian distribution.
2767 void fill( InputOutputArray mat, int distType, InputArray a, InputArray b, bool saturateRange = false );
2769 /** @brief Returns the next random number sampled from the Gaussian distribution
2770 @param sigma standard deviation of the distribution.
2772 The method transforms the state using the MWC algorithm and returns the
2773 next random number from the Gaussian distribution N(0,sigma) . That is,
2774 the mean value of the returned random numbers is zero and the standard
2775 deviation is the specified sigma .
2777 double gaussian(double sigma);
2782 /** @brief Mersenne Twister random number generator
2784 Inspired by http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MT2002/CODES/mt19937ar.c
2787 class CV_EXPORTS RNG_MT19937
2791 RNG_MT19937(unsigned s);
2792 void seed(unsigned s);
2797 operator unsigned();
2801 unsigned operator ()(unsigned N);
2802 unsigned operator ()();
2804 /** @brief returns uniformly distributed integer random number from [a,b) range
2807 int uniform(int a, int b);
2808 /** @brief returns uniformly distributed floating-point random number from [a,b) range
2811 float uniform(float a, float b);
2812 /** @brief returns uniformly distributed double-precision floating-point random number from [a,b) range
2815 double uniform(double a, double b);
2818 enum PeriodParameters {N = 624, M = 397};
2825 //! @addtogroup core_cluster
2828 /** @example kmeans.cpp
2829 An example on K-means clustering
2832 /** @brief Finds centers of clusters and groups input samples around the clusters.
2834 The function kmeans implements a k-means algorithm that finds the centers of cluster_count clusters
2835 and groups the input samples around the clusters. As an output, \f$\texttt{labels}_i\f$ contains a
2836 0-based cluster index for the sample stored in the \f$i^{th}\f$ row of the samples matrix.
2839 - (Python) An example on K-means clustering can be found at
2840 opencv_source_code/samples/python2/kmeans.py
2841 @param data Data for clustering. An array of N-Dimensional points with float coordinates is needed.
2842 Examples of this array can be:
2843 - Mat points(count, 2, CV_32F);
2844 - Mat points(count, 1, CV_32FC2);
2845 - Mat points(1, count, CV_32FC2);
2846 - std::vector\<cv::Point2f\> points(sampleCount);
2847 @param K Number of clusters to split the set by.
2848 @param bestLabels Input/output integer array that stores the cluster indices for every sample.
2849 @param criteria The algorithm termination criteria, that is, the maximum number of iterations and/or
2850 the desired accuracy. The accuracy is specified as criteria.epsilon. As soon as each of the cluster
2851 centers moves by less than criteria.epsilon on some iteration, the algorithm stops.
2852 @param attempts Flag to specify the number of times the algorithm is executed using different
2853 initial labellings. The algorithm returns the labels that yield the best compactness (see the last
2854 function parameter).
2855 @param flags Flag that can take values of cv::KmeansFlags
2856 @param centers Output matrix of the cluster centers, one row per each cluster center.
2857 @return The function returns the compactness measure that is computed as
2858 \f[\sum _i \| \texttt{samples} _i - \texttt{centers} _{ \texttt{labels} _i} \| ^2\f]
2859 after every attempt. The best (minimum) value is chosen and the corresponding labels and the
2860 compactness value are returned by the function. Basically, you can use only the core of the
2861 function, set the number of attempts to 1, initialize labels each time using a custom algorithm,
2862 pass them with the ( flags = KMEANS_USE_INITIAL_LABELS ) flag, and then choose the best
2863 (most-compact) clustering.
2865 CV_EXPORTS_W double kmeans( InputArray data, int K, InputOutputArray bestLabels,
2866 TermCriteria criteria, int attempts,
2867 int flags, OutputArray centers = noArray() );
2871 //! @addtogroup core_basic
2874 /////////////////////////////// Formatted output of cv::Mat ///////////////////////////
2876 /** @todo document */
2877 class CV_EXPORTS Formatted
2880 virtual const char* next() = 0;
2881 virtual void reset() = 0;
2882 virtual ~Formatted();
2885 /** @todo document */
2886 class CV_EXPORTS Formatter
2889 enum { FMT_DEFAULT = 0,
2897 virtual ~Formatter();
2899 virtual Ptr<Formatted> format(const Mat& mtx) const = 0;
2901 virtual void set32fPrecision(int p = 8) = 0;
2902 virtual void set64fPrecision(int p = 16) = 0;
2903 virtual void setMultiline(bool ml = true) = 0;
2905 static Ptr<Formatter> get(int fmt = FMT_DEFAULT);
2909 //////////////////////////////////////// Algorithm ////////////////////////////////////
2911 class CV_EXPORTS Algorithm;
2913 template<typename _Tp> struct ParamType {};
2916 /** @brief This is a base class for all more or less complex algorithms in OpenCV
2918 especially for classes of algorithms, for which there can be multiple implementations. The examples
2919 are stereo correspondence (for which there are algorithms like block matching, semi-global block
2920 matching, graph-cut etc.), background subtraction (which can be done using mixture-of-gaussians
2921 models, codebook-based algorithm etc.), optical flow (block matching, Lucas-Kanade, Horn-Schunck
2924 Here is example of SIFT use in your application via Algorithm interface:
2926 #include "opencv2/opencv.hpp"
2927 #include "opencv2/xfeatures2d.hpp"
2928 using namespace cv::xfeatures2d;
2930 Ptr<Feature2D> sift = SIFT::create();
2931 FileStorage fs("sift_params.xml", FileStorage::READ);
2932 if( fs.isOpened() ) // if we have file with parameters, read them
2934 sift->read(fs["sift_params"]);
2937 else // else modify the parameters and store them; user can later edit the file to use different parameters
2939 sift->setContrastThreshold(0.01f); // lower the contrast threshold, compared to the default value
2941 WriteStructContext ws(fs, "sift_params", CV_NODE_MAP);
2945 Mat image = imread("myimage.png", 0), descriptors;
2946 vector<KeyPoint> keypoints;
2947 sift->detectAndCompute(image, noArray(), keypoints, descriptors);
2950 class CV_EXPORTS_W Algorithm
2954 virtual ~Algorithm();
2956 /** @brief Clears the algorithm state
2958 CV_WRAP virtual void clear() {}
2960 /** @brief Stores algorithm parameters in a file storage
2962 virtual void write(FileStorage& fs) const { (void)fs; }
2964 /** @brief Reads algorithm parameters from a file storage
2966 virtual void read(const FileNode& fn) { (void)fn; }
2968 /** @brief Returns true if the Algorithm is empty (e.g. in the very beginning or after unsuccessful read
2970 virtual bool empty() const { return false; }
2972 /** @brief Reads algorithm from the file node
2974 This is static template method of Algorithm. It's usage is following (in the case of SVM):
2976 Ptr<SVM> svm = Algorithm::read<SVM>(fn);
2978 In order to make this method work, the derived class must overwrite Algorithm::read(const
2979 FileNode& fn) and also have static create() method without parameters
2980 (or with all the optional parameters)
2982 template<typename _Tp> static Ptr<_Tp> read(const FileNode& fn)
2984 Ptr<_Tp> obj = _Tp::create();
2986 return !obj->empty() ? obj : Ptr<_Tp>();
2989 /** @brief Loads algorithm from the file
2991 @param filename Name of the file to read.
2992 @param objname The optional name of the node to read (if empty, the first top-level node will be used)
2994 This is static template method of Algorithm. It's usage is following (in the case of SVM):
2996 Ptr<SVM> svm = Algorithm::load<SVM>("my_svm_model.xml");
2998 In order to make this method work, the derived class must overwrite Algorithm::read(const
3001 template<typename _Tp> static Ptr<_Tp> load(const String& filename, const String& objname=String())
3003 FileStorage fs(filename, FileStorage::READ);
3004 FileNode fn = objname.empty() ? fs.getFirstTopLevelNode() : fs[objname];
3005 Ptr<_Tp> obj = _Tp::create();
3007 return !obj->empty() ? obj : Ptr<_Tp>();
3010 /** @brief Loads algorithm from a String
3012 @param strModel The string variable containing the model you want to load.
3013 @param objname The optional name of the node to read (if empty, the first top-level node will be used)
3015 This is static template method of Algorithm. It's usage is following (in the case of SVM):
3017 Ptr<SVM> svm = Algorithm::loadFromString<SVM>(myStringModel);
3020 template<typename _Tp> static Ptr<_Tp> loadFromString(const String& strModel, const String& objname=String())
3022 FileStorage fs(strModel, FileStorage::READ + FileStorage::MEMORY);
3023 FileNode fn = objname.empty() ? fs.getFirstTopLevelNode() : fs[objname];
3024 Ptr<_Tp> obj = _Tp::create();
3026 return !obj->empty() ? obj : Ptr<_Tp>();
3029 /** Saves the algorithm to a file.
3030 In order to make this method work, the derived class must implement Algorithm::write(FileStorage& fs). */
3031 CV_WRAP virtual void save(const String& filename) const;
3033 /** Returns the algorithm string identifier.
3034 This string is used as top level xml/yml node tag when the object is saved to a file or string. */
3035 CV_WRAP virtual String getDefaultName() const;
3039 enum { INT=0, BOOLEAN=1, REAL=2, STRING=3, MAT=4, MAT_VECTOR=5, ALGORITHM=6, FLOAT=7,
3040 UNSIGNED_INT=8, UINT64=9, UCHAR=11 };
3045 template<> struct ParamType<bool>
3047 typedef bool const_param_type;
3048 typedef bool member_type;
3050 enum { type = Param::BOOLEAN };
3053 template<> struct ParamType<int>
3055 typedef int const_param_type;
3056 typedef int member_type;
3058 enum { type = Param::INT };
3061 template<> struct ParamType<double>
3063 typedef double const_param_type;
3064 typedef double member_type;
3066 enum { type = Param::REAL };
3069 template<> struct ParamType<String>
3071 typedef const String& const_param_type;
3072 typedef String member_type;
3074 enum { type = Param::STRING };
3077 template<> struct ParamType<Mat>
3079 typedef const Mat& const_param_type;
3080 typedef Mat member_type;
3082 enum { type = Param::MAT };
3085 template<> struct ParamType<std::vector<Mat> >
3087 typedef const std::vector<Mat>& const_param_type;
3088 typedef std::vector<Mat> member_type;
3090 enum { type = Param::MAT_VECTOR };
3093 template<> struct ParamType<Algorithm>
3095 typedef const Ptr<Algorithm>& const_param_type;
3096 typedef Ptr<Algorithm> member_type;
3098 enum { type = Param::ALGORITHM };
3101 template<> struct ParamType<float>
3103 typedef float const_param_type;
3104 typedef float member_type;
3106 enum { type = Param::FLOAT };
3109 template<> struct ParamType<unsigned>
3111 typedef unsigned const_param_type;
3112 typedef unsigned member_type;
3114 enum { type = Param::UNSIGNED_INT };
3117 template<> struct ParamType<uint64>
3119 typedef uint64 const_param_type;
3120 typedef uint64 member_type;
3122 enum { type = Param::UINT64 };
3125 template<> struct ParamType<uchar>
3127 typedef uchar const_param_type;
3128 typedef uchar member_type;
3130 enum { type = Param::UCHAR };
3137 #include "opencv2/core/operations.hpp"
3138 #include "opencv2/core/cvstd.inl.hpp"
3139 #include "opencv2/core/utility.hpp"
3140 #include "opencv2/core/optim.hpp"
3142 #endif /*__OPENCV_CORE_HPP__*/