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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_sse SSE utilities
76 @defgroup core_utils_neon NEON utilities
77 @defgroup core_utils_softfloat Softfloat support
79 @defgroup core_opengl OpenGL interoperability
80 @defgroup core_ipp Intel IPP Asynchronous C/C++ Converters
81 @defgroup core_optim Optimization Algorithms
82 @defgroup core_directx DirectX interoperability
83 @defgroup core_eigen Eigen support
84 @defgroup core_opencl OpenCL support
85 @defgroup core_va_intel Intel VA-API/OpenCL (CL-VA) interoperability
86 @defgroup core_hal Hardware Acceleration Layer
88 @defgroup core_hal_functions Functions
89 @defgroup core_hal_interface Interface
90 @defgroup core_hal_intrin Universal intrinsics
92 @defgroup core_hal_intrin_impl Private implementation helpers
100 //! @addtogroup core_utils
103 /*! @brief Class passed to an error.
105 This class encapsulates all or almost all necessary
106 information about the error happened in the program. The exception is
107 usually constructed and thrown implicitly via CV_Error and CV_Error_ macros.
110 class CV_EXPORTS Exception : public std::exception
118 Full constructor. Normally the constructor is not called explicitly.
119 Instead, the macros CV_Error(), CV_Error_() and CV_Assert() are used.
121 Exception(int _code, const String& _err, const String& _func, const String& _file, int _line);
122 virtual ~Exception() throw();
125 \return the error description and the context as a text string.
127 virtual const char *what() const throw() CV_OVERRIDE;
128 void formatMessage();
130 String msg; ///< the formatted error message
132 int code; ///< error code @see CVStatus
133 String err; ///< error description
134 String func; ///< function name. Available only when the compiler supports getting it
135 String file; ///< source file name where the error has occurred
136 int line; ///< line number in the source file where the error has occurred
139 /*! @brief Signals an error and raises the exception.
141 By default the function prints information about the error to stderr,
142 then it either stops if cv::setBreakOnError() had been called before or raises the exception.
143 It is possible to alternate error processing by using #redirectError().
144 @param exc the exception raisen.
145 @deprecated drop this version
147 CV_EXPORTS CV_NORETURN void error(const Exception& exc);
149 enum SortFlags { SORT_EVERY_ROW = 0, //!< each matrix row is sorted independently
150 SORT_EVERY_COLUMN = 1, //!< each matrix column is sorted
151 //!< independently; this flag and the previous one are
152 //!< mutually exclusive.
153 SORT_ASCENDING = 0, //!< each matrix row is sorted in the ascending
155 SORT_DESCENDING = 16 //!< each matrix row is sorted in the
156 //!< descending order; this flag and the previous one are also
157 //!< mutually exclusive.
165 //! Covariation flags
167 /** The output covariance matrix is calculated as:
168 \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]
169 The covariance matrix will be nsamples x nsamples. Such an unusual covariance matrix is used
170 for fast PCA of a set of very large vectors (see, for example, the EigenFaces technique for
171 face recognition). Eigenvalues of this "scrambled" matrix match the eigenvalues of the true
172 covariance matrix. The "true" eigenvectors can be easily calculated from the eigenvectors of
173 the "scrambled" covariance matrix. */
175 /**The output covariance matrix is calculated as:
176 \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]
177 covar will be a square matrix of the same size as the total number of elements in each input
178 vector. One and only one of #COVAR_SCRAMBLED and #COVAR_NORMAL must be specified.*/
180 /** If the flag is specified, the function does not calculate mean from
181 the input vectors but, instead, uses the passed mean vector. This is useful if mean has been
182 pre-calculated or known in advance, or if the covariance matrix is calculated by parts. In
183 this case, mean is not a mean vector of the input sub-set of vectors but rather the mean
184 vector of the whole set.*/
186 /** If the flag is specified, the covariance matrix is scaled. In the
187 "normal" mode, scale is 1./nsamples . In the "scrambled" mode, scale is the reciprocal of the
188 total number of elements in each input vector. By default (if the flag is not specified), the
189 covariance matrix is not scaled ( scale=1 ).*/
192 specified, all the input vectors are stored as rows of the samples matrix. mean should be a
193 single-row vector in this case.*/
196 specified, all the input vectors are stored as columns of the samples matrix. mean should be a
197 single-column vector in this case.*/
203 /** Select random initial centers in each attempt.*/
204 KMEANS_RANDOM_CENTERS = 0,
205 /** Use kmeans++ center initialization by Arthur and Vassilvitskii [Arthur2007].*/
206 KMEANS_PP_CENTERS = 2,
207 /** During the first (and possibly the only) attempt, use the
208 user-supplied labels instead of computing them from the initial centers. For the second and
209 further attempts, use the random or semi-random centers. Use one of KMEANS_\*_CENTERS flag
210 to specify the exact method.*/
211 KMEANS_USE_INITIAL_LABELS = 1
217 LINE_4 = 4, //!< 4-connected line
218 LINE_8 = 8, //!< 8-connected line
219 LINE_AA = 16 //!< antialiased line
222 //! Only a subset of Hershey fonts <https://en.wikipedia.org/wiki/Hershey_fonts> are supported
224 FONT_HERSHEY_SIMPLEX = 0, //!< normal size sans-serif font
225 FONT_HERSHEY_PLAIN = 1, //!< small size sans-serif font
226 FONT_HERSHEY_DUPLEX = 2, //!< normal size sans-serif font (more complex than FONT_HERSHEY_SIMPLEX)
227 FONT_HERSHEY_COMPLEX = 3, //!< normal size serif font
228 FONT_HERSHEY_TRIPLEX = 4, //!< normal size serif font (more complex than FONT_HERSHEY_COMPLEX)
229 FONT_HERSHEY_COMPLEX_SMALL = 5, //!< smaller version of FONT_HERSHEY_COMPLEX
230 FONT_HERSHEY_SCRIPT_SIMPLEX = 6, //!< hand-writing style font
231 FONT_HERSHEY_SCRIPT_COMPLEX = 7, //!< more complex variant of FONT_HERSHEY_SCRIPT_SIMPLEX
232 FONT_ITALIC = 16 //!< flag for italic font
235 enum ReduceTypes { REDUCE_SUM = 0, //!< the output is the sum of all rows/columns of the matrix.
236 REDUCE_AVG = 1, //!< the output is the mean vector of all rows/columns of the matrix.
237 REDUCE_MAX = 2, //!< the output is the maximum (column/row-wise) of all rows/columns of the matrix.
238 REDUCE_MIN = 3 //!< the output is the minimum (column/row-wise) of all rows/columns of the matrix.
242 /** @brief Swaps two matrices
244 CV_EXPORTS void swap(Mat& a, Mat& b);
246 CV_EXPORTS void swap( UMat& a, UMat& b );
250 //! @addtogroup core_array
253 /** @brief Computes the source location of an extrapolated pixel.
255 The function computes and returns the coordinate of a donor pixel corresponding to the specified
256 extrapolated pixel when using the specified extrapolation border mode. For example, if you use
257 cv::BORDER_WRAP mode in the horizontal direction, cv::BORDER_REFLECT_101 in the vertical direction and
258 want to compute value of the "virtual" pixel Point(-5, 100) in a floating-point image img , it
261 float val = img.at<float>(borderInterpolate(100, img.rows, cv::BORDER_REFLECT_101),
262 borderInterpolate(-5, img.cols, cv::BORDER_WRAP));
264 Normally, the function is not called directly. It is used inside filtering functions and also in
266 @param p 0-based coordinate of the extrapolated pixel along one of the axes, likely \<0 or \>= len
267 @param len Length of the array along the corresponding axis.
268 @param borderType Border type, one of the #BorderTypes, except for #BORDER_TRANSPARENT and
269 #BORDER_ISOLATED . When borderType==#BORDER_CONSTANT , the function always returns -1, regardless
274 CV_EXPORTS_W int borderInterpolate(int p, int len, int borderType);
276 /** @example copyMakeBorder_demo.cpp
277 An example using copyMakeBorder function
279 /** @brief Forms a border around an image.
281 The function copies the source image into the middle of the destination image. The areas to the
282 left, to the right, above and below the copied source image will be filled with extrapolated
283 pixels. This is not what filtering functions based on it do (they extrapolate pixels on-fly), but
284 what other more complex functions, including your own, may do to simplify image boundary handling.
286 The function supports the mode when src is already in the middle of dst . In this case, the
287 function does not copy src itself but simply constructs the border, for example:
290 // let border be the same in all directions
292 // constructs a larger image to fit both the image and the border
293 Mat gray_buf(rgb.rows + border*2, rgb.cols + border*2, rgb.depth());
294 // select the middle part of it w/o copying data
295 Mat gray(gray_canvas, Rect(border, border, rgb.cols, rgb.rows));
296 // convert image from RGB to grayscale
297 cvtColor(rgb, gray, COLOR_RGB2GRAY);
298 // form a border in-place
299 copyMakeBorder(gray, gray_buf, border, border,
300 border, border, BORDER_REPLICATE);
301 // now do some custom filtering ...
304 @note When the source image is a part (ROI) of a bigger image, the function will try to use the
305 pixels outside of the ROI to form a border. To disable this feature and always do extrapolation, as
306 if src was not a ROI, use borderType | #BORDER_ISOLATED.
308 @param src Source image.
309 @param dst Destination image of the same type as src and the size Size(src.cols+left+right,
310 src.rows+top+bottom) .
314 @param right Parameter specifying how many pixels in each direction from the source image rectangle
315 to extrapolate. For example, top=1, bottom=1, left=1, right=1 mean that 1 pixel-wide border needs
317 @param borderType Border type. See borderInterpolate for details.
318 @param value Border value if borderType==BORDER_CONSTANT .
320 @sa borderInterpolate
322 CV_EXPORTS_W void copyMakeBorder(InputArray src, OutputArray dst,
323 int top, int bottom, int left, int right,
324 int borderType, const Scalar& value = Scalar() );
326 /** @brief Calculates the per-element sum of two arrays or an array and a scalar.
328 The function add calculates:
329 - Sum of two arrays when both input arrays have the same size and the same number of channels:
330 \f[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1}(I) + \texttt{src2}(I)) \quad \texttt{if mask}(I) \ne0\f]
331 - Sum of an array and a scalar when src2 is constructed from Scalar or has the same number of
332 elements as `src1.channels()`:
333 \f[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1}(I) + \texttt{src2} ) \quad \texttt{if mask}(I) \ne0\f]
334 - Sum of a scalar and an array when src1 is constructed from Scalar or has the same number of
335 elements as `src2.channels()`:
336 \f[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1} + \texttt{src2}(I) ) \quad \texttt{if mask}(I) \ne0\f]
337 where `I` is a multi-dimensional index of array elements. In case of multi-channel arrays, each
338 channel is processed independently.
340 The first function in the list above can be replaced with matrix expressions:
343 dst += src1; // equivalent to add(dst, src1, dst);
345 The input arrays and the output array can all have the same or different depths. For example, you
346 can add a 16-bit unsigned array to a 8-bit signed array and store the sum as a 32-bit
347 floating-point array. Depth of the output array is determined by the dtype parameter. In the second
348 and third cases above, as well as in the first case, when src1.depth() == src2.depth(), dtype can
349 be set to the default -1. In this case, the output array will have the same depth as the input
350 array, be it src1, src2 or both.
351 @note Saturation is not applied when the output array has the depth CV_32S. You may even get
352 result of an incorrect sign in the case of overflow.
353 @param src1 first input array or a scalar.
354 @param src2 second input array or a scalar.
355 @param dst output array that has the same size and number of channels as the input array(s); the
356 depth is defined by dtype or src1/src2.
357 @param mask optional operation mask - 8-bit single channel array, that specifies elements of the
358 output array to be changed.
359 @param dtype optional depth of the output array (see the discussion below).
360 @sa subtract, addWeighted, scaleAdd, Mat::convertTo
362 CV_EXPORTS_W void add(InputArray src1, InputArray src2, OutputArray dst,
363 InputArray mask = noArray(), int dtype = -1);
365 /** @brief Calculates the per-element difference between two arrays or array and a scalar.
367 The function subtract calculates:
368 - Difference between two arrays, when both input arrays have the same size and the same number of
370 \f[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1}(I) - \texttt{src2}(I)) \quad \texttt{if mask}(I) \ne0\f]
371 - Difference between an array and a scalar, when src2 is constructed from Scalar or has the same
372 number of elements as `src1.channels()`:
373 \f[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1}(I) - \texttt{src2} ) \quad \texttt{if mask}(I) \ne0\f]
374 - Difference between a scalar and an array, when src1 is constructed from Scalar or has the same
375 number of elements as `src2.channels()`:
376 \f[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1} - \texttt{src2}(I) ) \quad \texttt{if mask}(I) \ne0\f]
377 - The reverse difference between a scalar and an array in the case of `SubRS`:
378 \f[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src2} - \texttt{src1}(I) ) \quad \texttt{if mask}(I) \ne0\f]
379 where I is a multi-dimensional index of array elements. In case of multi-channel arrays, each
380 channel is processed independently.
382 The first function in the list above can be replaced with matrix expressions:
385 dst -= src1; // equivalent to subtract(dst, src1, dst);
387 The input arrays and the output array can all have the same or different depths. For example, you
388 can subtract to 8-bit unsigned arrays and store the difference in a 16-bit signed array. Depth of
389 the output array is determined by dtype parameter. In the second and third cases above, as well as
390 in the first case, when src1.depth() == src2.depth(), dtype can be set to the default -1. In this
391 case the output array will have the same depth as the input array, be it src1, src2 or both.
392 @note Saturation is not applied when the output array has the depth CV_32S. You may even get
393 result of an incorrect sign in the case of overflow.
394 @param src1 first input array or a scalar.
395 @param src2 second input array or a scalar.
396 @param dst output array of the same size and the same number of channels as the input array.
397 @param mask optional operation mask; this is an 8-bit single channel array that specifies elements
398 of the output array to be changed.
399 @param dtype optional depth of the output array
400 @sa add, addWeighted, scaleAdd, Mat::convertTo
402 CV_EXPORTS_W void subtract(InputArray src1, InputArray src2, OutputArray dst,
403 InputArray mask = noArray(), int dtype = -1);
406 /** @brief Calculates the per-element scaled product of two arrays.
408 The function multiply calculates the per-element product of two arrays:
410 \f[\texttt{dst} (I)= \texttt{saturate} ( \texttt{scale} \cdot \texttt{src1} (I) \cdot \texttt{src2} (I))\f]
412 There is also a @ref MatrixExpressions -friendly variant of the first function. See Mat::mul .
414 For a not-per-element matrix product, see gemm .
416 @note Saturation is not applied when the output array has the depth
417 CV_32S. You may even get result of an incorrect sign in the case of
419 @param src1 first input array.
420 @param src2 second input array of the same size and the same type as src1.
421 @param dst output array of the same size and type as src1.
422 @param scale optional scale factor.
423 @param dtype optional depth of the output array
424 @sa add, subtract, divide, scaleAdd, addWeighted, accumulate, accumulateProduct, accumulateSquare,
427 CV_EXPORTS_W void multiply(InputArray src1, InputArray src2,
428 OutputArray dst, double scale = 1, int dtype = -1);
430 /** @brief Performs per-element division of two arrays or a scalar by an array.
432 The function cv::divide divides one array by another:
433 \f[\texttt{dst(I) = saturate(src1(I)*scale/src2(I))}\f]
434 or a scalar by an array when there is no src1 :
435 \f[\texttt{dst(I) = saturate(scale/src2(I))}\f]
437 When src2(I) is zero, dst(I) will also be zero. Different channels of
438 multi-channel arrays are processed independently.
440 @note Saturation is not applied when the output array has the depth CV_32S. You may even get
441 result of an incorrect sign in the case of overflow.
442 @param src1 first input array.
443 @param src2 second input array of the same size and type as src1.
444 @param scale scalar factor.
445 @param dst output array of the same size and type as src2.
446 @param dtype optional depth of the output array; if -1, dst will have depth src2.depth(), but in
447 case of an array-by-array division, you can only pass -1 when src1.depth()==src2.depth().
448 @sa multiply, add, subtract
450 CV_EXPORTS_W void divide(InputArray src1, InputArray src2, OutputArray dst,
451 double scale = 1, int dtype = -1);
454 CV_EXPORTS_W void divide(double scale, InputArray src2,
455 OutputArray dst, int dtype = -1);
457 /** @brief Calculates the sum of a scaled array and another array.
459 The function scaleAdd is one of the classical primitive linear algebra operations, known as DAXPY
460 or SAXPY in [BLAS](http://en.wikipedia.org/wiki/Basic_Linear_Algebra_Subprograms). It calculates
461 the sum of a scaled array and another array:
462 \f[\texttt{dst} (I)= \texttt{scale} \cdot \texttt{src1} (I) + \texttt{src2} (I)\f]
463 The function can also be emulated with a matrix expression, for example:
467 A.row(0) = A.row(1)*2 + A.row(2);
469 @param src1 first input array.
470 @param alpha scale factor for the first array.
471 @param src2 second input array of the same size and type as src1.
472 @param dst output array of the same size and type as src1.
473 @sa add, addWeighted, subtract, Mat::dot, Mat::convertTo
475 CV_EXPORTS_W void scaleAdd(InputArray src1, double alpha, InputArray src2, OutputArray dst);
477 /** @example AddingImagesTrackbar.cpp
480 /** @brief Calculates the weighted sum of two arrays.
482 The function addWeighted calculates the weighted sum of two arrays as follows:
483 \f[\texttt{dst} (I)= \texttt{saturate} ( \texttt{src1} (I)* \texttt{alpha} + \texttt{src2} (I)* \texttt{beta} + \texttt{gamma} )\f]
484 where I is a multi-dimensional index of array elements. In case of multi-channel arrays, each
485 channel is processed independently.
486 The function can be replaced with a matrix expression:
488 dst = src1*alpha + src2*beta + gamma;
490 @note Saturation is not applied when the output array has the depth CV_32S. You may even get
491 result of an incorrect sign in the case of overflow.
492 @param src1 first input array.
493 @param alpha weight of the first array elements.
494 @param src2 second input array of the same size and channel number as src1.
495 @param beta weight of the second array elements.
496 @param gamma scalar added to each sum.
497 @param dst output array that has the same size and number of channels as the input arrays.
498 @param dtype optional depth of the output array; when both input arrays have the same depth, dtype
499 can be set to -1, which will be equivalent to src1.depth().
500 @sa add, subtract, scaleAdd, Mat::convertTo
502 CV_EXPORTS_W void addWeighted(InputArray src1, double alpha, InputArray src2,
503 double beta, double gamma, OutputArray dst, int dtype = -1);
505 /** @brief Scales, calculates absolute values, and converts the result to 8-bit.
507 On each element of the input array, the function convertScaleAbs
508 performs three operations sequentially: scaling, taking an absolute
509 value, conversion to an unsigned 8-bit type:
510 \f[\texttt{dst} (I)= \texttt{saturate\_cast<uchar>} (| \texttt{src} (I)* \texttt{alpha} + \texttt{beta} |)\f]
511 In case of multi-channel arrays, the function processes each channel
512 independently. When the output is not 8-bit, the operation can be
513 emulated by calling the Mat::convertTo method (or by using matrix
514 expressions) and then by calculating an absolute value of the result.
517 Mat_<float> A(30,30);
518 randu(A, Scalar(-100), Scalar(100));
519 Mat_<float> B = A*5 + 3;
521 // Mat_<float> B = abs(A*5+3) will also do the job,
522 // but it will allocate a temporary matrix
524 @param src input array.
525 @param dst output array.
526 @param alpha optional scale factor.
527 @param beta optional delta added to the scaled values.
528 @sa Mat::convertTo, cv::abs(const Mat&)
530 CV_EXPORTS_W void convertScaleAbs(InputArray src, OutputArray dst,
531 double alpha = 1, double beta = 0);
533 /** @brief Converts an array to half precision floating number.
535 This function converts FP32 (single precision floating point) from/to FP16 (half precision floating point). CV_16S format is used to represent FP16 data.
536 There are two use modes (src -> dst): CV_32F -> CV_16S and CV_16S -> CV_32F. The input array has to have type of CV_32F or
537 CV_16S to represent the bit depth. If the input array is neither of them, the function will raise an error.
538 The format of half precision floating point is defined in IEEE 754-2008.
540 @param src input array.
541 @param dst output array.
543 CV_EXPORTS_W void convertFp16(InputArray src, OutputArray dst);
545 /** @brief Performs a look-up table transform of an array.
547 The function LUT fills the output array with values from the look-up table. Indices of the entries
548 are taken from the input array. That is, the function processes each element of src as follows:
549 \f[\texttt{dst} (I) \leftarrow \texttt{lut(src(I) + d)}\f]
551 \f[d = \fork{0}{if \(\texttt{src}\) has depth \(\texttt{CV_8U}\)}{128}{if \(\texttt{src}\) has depth \(\texttt{CV_8S}\)}\f]
552 @param src input array of 8-bit elements.
553 @param lut look-up table of 256 elements; in case of multi-channel input array, the table should
554 either have a single channel (in this case the same table is used for all channels) or the same
555 number of channels as in the input array.
556 @param dst output array of the same size and number of channels as src, and the same depth as lut.
557 @sa convertScaleAbs, Mat::convertTo
559 CV_EXPORTS_W void LUT(InputArray src, InputArray lut, OutputArray dst);
561 /** @brief Calculates the sum of array elements.
563 The function cv::sum calculates and returns the sum of array elements,
564 independently for each channel.
565 @param src input array that must have from 1 to 4 channels.
566 @sa countNonZero, mean, meanStdDev, norm, minMaxLoc, reduce
568 CV_EXPORTS_AS(sumElems) Scalar sum(InputArray src);
570 /** @brief Counts non-zero array elements.
572 The function returns the number of non-zero elements in src :
573 \f[\sum _{I: \; \texttt{src} (I) \ne0 } 1\f]
574 @param src single-channel array.
575 @sa mean, meanStdDev, norm, minMaxLoc, calcCovarMatrix
577 CV_EXPORTS_W int countNonZero( InputArray src );
579 /** @brief Returns the list of locations of non-zero pixels
581 Given a binary matrix (likely returned from an operation such
582 as threshold(), compare(), >, ==, etc, return all of
583 the non-zero indices as a cv::Mat or std::vector<cv::Point> (x,y)
586 cv::Mat binaryImage; // input, binary image
587 cv::Mat locations; // output, locations of non-zero pixels
588 cv::findNonZero(binaryImage, locations);
590 // access pixel coordinates
591 Point pnt = locations.at<Point>(i);
595 cv::Mat binaryImage; // input, binary image
596 vector<Point> locations; // output, locations of non-zero pixels
597 cv::findNonZero(binaryImage, locations);
599 // access pixel coordinates
600 Point pnt = locations[i];
602 @param src single-channel array
603 @param idx the output array, type of cv::Mat or std::vector<Point>, corresponding to non-zero indices in the input
605 CV_EXPORTS_W void findNonZero( InputArray src, OutputArray idx );
607 /** @brief Calculates an average (mean) of array elements.
609 The function cv::mean calculates the mean value M of array elements,
610 independently for each channel, and return it:
611 \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]
612 When all the mask elements are 0's, the function returns Scalar::all(0)
613 @param src input array that should have from 1 to 4 channels so that the result can be stored in
615 @param mask optional operation mask.
616 @sa countNonZero, meanStdDev, norm, minMaxLoc
618 CV_EXPORTS_W Scalar mean(InputArray src, InputArray mask = noArray());
620 /** Calculates a mean and standard deviation of array elements.
622 The function cv::meanStdDev calculates the mean and the standard deviation M
623 of array elements independently for each channel and returns it via the
625 \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]
626 When all the mask elements are 0's, the function returns
627 mean=stddev=Scalar::all(0).
628 @note The calculated standard deviation is only the diagonal of the
629 complete normalized covariance matrix. If the full matrix is needed, you
630 can reshape the multi-channel array M x N to the single-channel array
631 M\*N x mtx.channels() (only possible when the matrix is continuous) and
632 then pass the matrix to calcCovarMatrix .
633 @param src input array that should have from 1 to 4 channels so that the results can be stored in
635 @param mean output parameter: calculated mean value.
636 @param stddev output parameter: calculated standard deviation.
637 @param mask optional operation mask.
638 @sa countNonZero, mean, norm, minMaxLoc, calcCovarMatrix
640 CV_EXPORTS_W void meanStdDev(InputArray src, OutputArray mean, OutputArray stddev,
641 InputArray mask=noArray());
643 /** @brief Calculates the absolute norm of an array.
645 This version of #norm calculates the absolute norm of src1. The type of norm to calculate is specified using #NormTypes.
647 As example for one array consider the function \f$r(x)= \begin{pmatrix} x \\ 1-x \end{pmatrix}, x \in [-1;1]\f$.
648 The \f$ L_{1}, L_{2} \f$ and \f$ L_{\infty} \f$ norm for the sample value \f$r(-1) = \begin{pmatrix} -1 \\ 2 \end{pmatrix}\f$
649 is calculated as follows
651 \| r(-1) \|_{L_1} &= |-1| + |2| = 3 \\
652 \| r(-1) \|_{L_2} &= \sqrt{(-1)^{2} + (2)^{2}} = \sqrt{5} \\
653 \| r(-1) \|_{L_\infty} &= \max(|-1|,|2|) = 2
655 and for \f$r(0.5) = \begin{pmatrix} 0.5 \\ 0.5 \end{pmatrix}\f$ the calculation is
657 \| r(0.5) \|_{L_1} &= |0.5| + |0.5| = 1 \\
658 \| r(0.5) \|_{L_2} &= \sqrt{(0.5)^{2} + (0.5)^{2}} = \sqrt{0.5} \\
659 \| r(0.5) \|_{L_\infty} &= \max(|0.5|,|0.5|) = 0.5.
661 The following graphic shows all values for the three norm functions \f$\| r(x) \|_{L_1}, \| r(x) \|_{L_2}\f$ and \f$\| r(x) \|_{L_\infty}\f$.
662 It is notable that the \f$ L_{1} \f$ norm forms the upper and the \f$ L_{\infty} \f$ norm forms the lower border for the example function \f$ r(x) \f$.
663 ![Graphs for the different norm functions from the above example](pics/NormTypes_OneArray_1-2-INF.png)
665 When the mask parameter is specified and it is not empty, the norm is
667 If normType is not specified, #NORM_L2 is used.
668 calculated only over the region specified by the mask.
670 Multi-channel input arrays are treated as single-channel arrays, that is,
671 the results for all channels are combined.
673 Hamming norms can only be calculated with CV_8U depth arrays.
675 @param src1 first input array.
676 @param normType type of the norm (see #NormTypes).
677 @param mask optional operation mask; it must have the same size as src1 and CV_8UC1 type.
679 CV_EXPORTS_W double norm(InputArray src1, int normType = NORM_L2, InputArray mask = noArray());
681 /** @brief Calculates an absolute difference norm or a relative difference norm.
683 This version of cv::norm calculates the absolute difference norm
684 or the relative difference norm of arrays src1 and src2.
685 The type of norm to calculate is specified using #NormTypes.
687 @param src1 first input array.
688 @param src2 second input array of the same size and the same type as src1.
689 @param normType type of the norm (see #NormTypes).
690 @param mask optional operation mask; it must have the same size as src1 and CV_8UC1 type.
692 CV_EXPORTS_W double norm(InputArray src1, InputArray src2,
693 int normType = NORM_L2, InputArray mask = noArray());
695 @param src first input array.
696 @param normType type of the norm (see #NormTypes).
698 CV_EXPORTS double norm( const SparseMat& src, int normType );
700 /** @brief Computes the Peak Signal-to-Noise Ratio (PSNR) image quality metric.
702 This function calculates the Peak Signal-to-Noise Ratio (PSNR) image quality metric in decibels (dB),
703 between two input arrays src1 and src2. The arrays must have the same type.
705 The PSNR is calculated as follows:
708 \texttt{PSNR} = 10 \cdot \log_{10}{\left( \frac{R^2}{MSE} \right) }
711 where R is the maximum integer value of depth (e.g. 255 in the case of CV_8U data)
712 and MSE is the mean squared error between the two arrays.
714 @param src1 first input array.
715 @param src2 second input array of the same size as src1.
716 @param R the maximum pixel value (255 by default)
719 CV_EXPORTS_W double PSNR(InputArray src1, InputArray src2, double R=255.);
721 /** @brief naive nearest neighbor finder
723 see http://en.wikipedia.org/wiki/Nearest_neighbor_search
726 CV_EXPORTS_W void batchDistance(InputArray src1, InputArray src2,
727 OutputArray dist, int dtype, OutputArray nidx,
728 int normType = NORM_L2, int K = 0,
729 InputArray mask = noArray(), int update = 0,
730 bool crosscheck = false);
732 /** @brief Normalizes the norm or value range of an array.
734 The function cv::normalize normalizes scale and shift the input array elements so that
735 \f[\| \texttt{dst} \| _{L_p}= \texttt{alpha}\f]
736 (where p=Inf, 1 or 2) when normType=NORM_INF, NORM_L1, or NORM_L2, respectively; or so that
737 \f[\min _I \texttt{dst} (I)= \texttt{alpha} , \, \, \max _I \texttt{dst} (I)= \texttt{beta}\f]
739 when normType=NORM_MINMAX (for dense arrays only). The optional mask specifies a sub-array to be
740 normalized. This means that the norm or min-n-max are calculated over the sub-array, and then this
741 sub-array is modified to be normalized. If you want to only use the mask to calculate the norm or
742 min-max but modify the whole array, you can use norm and Mat::convertTo.
744 In case of sparse matrices, only the non-zero values are analyzed and transformed. Because of this,
745 the range transformation for sparse matrices is not allowed since it can shift the zero level.
747 Possible usage with some positive example data:
749 vector<double> positiveData = { 2.0, 8.0, 10.0 };
750 vector<double> normalizedData_l1, normalizedData_l2, normalizedData_inf, normalizedData_minmax;
752 // Norm to probability (total count)
753 // sum(numbers) = 20.0
754 // 2.0 0.1 (2.0/20.0)
755 // 8.0 0.4 (8.0/20.0)
756 // 10.0 0.5 (10.0/20.0)
757 normalize(positiveData, normalizedData_l1, 1.0, 0.0, NORM_L1);
759 // Norm to unit vector: ||positiveData|| = 1.0
763 normalize(positiveData, normalizedData_l2, 1.0, 0.0, NORM_L2);
765 // Norm to max element
766 // 2.0 0.2 (2.0/10.0)
767 // 8.0 0.8 (8.0/10.0)
768 // 10.0 1.0 (10.0/10.0)
769 normalize(positiveData, normalizedData_inf, 1.0, 0.0, NORM_INF);
771 // Norm to range [0.0;1.0]
772 // 2.0 0.0 (shift to left border)
773 // 8.0 0.75 (6.0/8.0)
774 // 10.0 1.0 (shift to right border)
775 normalize(positiveData, normalizedData_minmax, 1.0, 0.0, NORM_MINMAX);
778 @param src input array.
779 @param dst output array of the same size as src .
780 @param alpha norm value to normalize to or the lower range boundary in case of the range
782 @param beta upper range boundary in case of the range normalization; it is not used for the norm
784 @param norm_type normalization type (see cv::NormTypes).
785 @param dtype when negative, the output array has the same type as src; otherwise, it has the same
786 number of channels as src and the depth =CV_MAT_DEPTH(dtype).
787 @param mask optional operation mask.
788 @sa norm, Mat::convertTo, SparseMat::convertTo
790 CV_EXPORTS_W void normalize( InputArray src, InputOutputArray dst, double alpha = 1, double beta = 0,
791 int norm_type = NORM_L2, int dtype = -1, InputArray mask = noArray());
794 @param src input array.
795 @param dst output array of the same size as src .
796 @param alpha norm value to normalize to or the lower range boundary in case of the range
798 @param normType normalization type (see cv::NormTypes).
800 CV_EXPORTS void normalize( const SparseMat& src, SparseMat& dst, double alpha, int normType );
802 /** @brief Finds the global minimum and maximum in an array.
804 The function cv::minMaxLoc finds the minimum and maximum element values and their positions. The
805 extremums are searched across the whole array or, if mask is not an empty array, in the specified
808 The function do not work with multi-channel arrays. If you need to find minimum or maximum
809 elements across all the channels, use Mat::reshape first to reinterpret the array as
810 single-channel. Or you may extract the particular channel using either extractImageCOI , or
811 mixChannels , or split .
812 @param src input single-channel array.
813 @param minVal pointer to the returned minimum value; NULL is used if not required.
814 @param maxVal pointer to the returned maximum value; NULL is used if not required.
815 @param minLoc pointer to the returned minimum location (in 2D case); NULL is used if not required.
816 @param maxLoc pointer to the returned maximum location (in 2D case); NULL is used if not required.
817 @param mask optional mask used to select a sub-array.
818 @sa max, min, compare, inRange, extractImageCOI, mixChannels, split, Mat::reshape
820 CV_EXPORTS_W void minMaxLoc(InputArray src, CV_OUT double* minVal,
821 CV_OUT double* maxVal = 0, CV_OUT Point* minLoc = 0,
822 CV_OUT Point* maxLoc = 0, InputArray mask = noArray());
825 /** @brief Finds the global minimum and maximum in an array
827 The function cv::minMaxIdx finds the minimum and maximum element values and their positions. The
828 extremums are searched across the whole array or, if mask is not an empty array, in the specified
829 array region. The function does not work with multi-channel arrays. If you need to find minimum or
830 maximum elements across all the channels, use Mat::reshape first to reinterpret the array as
831 single-channel. Or you may extract the particular channel using either extractImageCOI , or
832 mixChannels , or split . In case of a sparse matrix, the minimum is found among non-zero elements
834 @note When minIdx is not NULL, it must have at least 2 elements (as well as maxIdx), even if src is
835 a single-row or single-column matrix. In OpenCV (following MATLAB) each array has at least 2
836 dimensions, i.e. single-column matrix is Mx1 matrix (and therefore minIdx/maxIdx will be
837 (i1,0)/(i2,0)) and single-row matrix is 1xN matrix (and therefore minIdx/maxIdx will be
839 @param src input single-channel array.
840 @param minVal pointer to the returned minimum value; NULL is used if not required.
841 @param maxVal pointer to the returned maximum value; NULL is used if not required.
842 @param minIdx pointer to the returned minimum location (in nD case); NULL is used if not required;
843 Otherwise, it must point to an array of src.dims elements, the coordinates of the minimum element
844 in each dimension are stored there sequentially.
845 @param maxIdx pointer to the returned maximum location (in nD case). NULL is used if not required.
846 @param mask specified array region
848 CV_EXPORTS void minMaxIdx(InputArray src, double* minVal, double* maxVal = 0,
849 int* minIdx = 0, int* maxIdx = 0, InputArray mask = noArray());
852 @param a input single-channel array.
853 @param minVal pointer to the returned minimum value; NULL is used if not required.
854 @param maxVal pointer to the returned maximum value; NULL is used if not required.
855 @param minIdx pointer to the returned minimum location (in nD case); NULL is used if not required;
856 Otherwise, it must point to an array of src.dims elements, the coordinates of the minimum element
857 in each dimension are stored there sequentially.
858 @param maxIdx pointer to the returned maximum location (in nD case). NULL is used if not required.
860 CV_EXPORTS void minMaxLoc(const SparseMat& a, double* minVal,
861 double* maxVal, int* minIdx = 0, int* maxIdx = 0);
863 /** @brief Reduces a matrix to a vector.
865 The function #reduce reduces the matrix to a vector by treating the matrix rows/columns as a set of
866 1D vectors and performing the specified operation on the vectors until a single row/column is
867 obtained. For example, the function can be used to compute horizontal and vertical projections of a
868 raster image. In case of #REDUCE_MAX and #REDUCE_MIN , the output image should have the same type as the source one.
869 In case of #REDUCE_SUM and #REDUCE_AVG , the output may have a larger element bit-depth to preserve accuracy.
870 And multi-channel arrays are also supported in these two reduction modes.
872 The following code demonstrates its usage for a single channel matrix.
873 @snippet snippets/core_reduce.cpp example
875 And the following code demonstrates its usage for a two-channel matrix.
876 @snippet snippets/core_reduce.cpp example2
878 @param src input 2D matrix.
879 @param dst output vector. Its size and type is defined by dim and dtype parameters.
880 @param dim dimension index along which the matrix is reduced. 0 means that the matrix is reduced to
881 a single row. 1 means that the matrix is reduced to a single column.
882 @param rtype reduction operation that could be one of #ReduceTypes
883 @param dtype when negative, the output vector will have the same type as the input matrix,
884 otherwise, its type will be CV_MAKE_TYPE(CV_MAT_DEPTH(dtype), src.channels()).
887 CV_EXPORTS_W void reduce(InputArray src, OutputArray dst, int dim, int rtype, int dtype = -1);
889 /** @brief Creates one multi-channel array out of several single-channel ones.
891 The function cv::merge merges several arrays to make a single multi-channel array. That is, each
892 element of the output array will be a concatenation of the elements of the input arrays, where
893 elements of i-th input array are treated as mv[i].channels()-element vectors.
895 The function cv::split does the reverse operation. If you need to shuffle channels in some other
896 advanced way, use cv::mixChannels.
898 The following example shows how to merge 3 single channel matrices into a single 3-channel matrix.
899 @snippet snippets/core_merge.cpp example
901 @param mv input array of matrices to be merged; all the matrices in mv must have the same
902 size and the same depth.
903 @param count number of input matrices when mv is a plain C array; it must be greater than zero.
904 @param dst output array of the same size and the same depth as mv[0]; The number of channels will
905 be equal to the parameter count.
906 @sa mixChannels, split, Mat::reshape
908 CV_EXPORTS void merge(const Mat* mv, size_t count, OutputArray dst);
911 @param mv input vector of matrices to be merged; all the matrices in mv must have the same
912 size and the same depth.
913 @param dst output array of the same size and the same depth as mv[0]; The number of channels will
914 be the total number of channels in the matrix array.
916 CV_EXPORTS_W void merge(InputArrayOfArrays mv, OutputArray dst);
918 /** @brief Divides a multi-channel array into several single-channel arrays.
920 The function cv::split splits a multi-channel array into separate single-channel arrays:
921 \f[\texttt{mv} [c](I) = \texttt{src} (I)_c\f]
922 If you need to extract a single channel or do some other sophisticated channel permutation, use
925 The following example demonstrates how to split a 3-channel matrix into 3 single channel matrices.
926 @snippet snippets/core_split.cpp example
928 @param src input multi-channel array.
929 @param mvbegin output array; the number of arrays must match src.channels(); the arrays themselves are
930 reallocated, if needed.
931 @sa merge, mixChannels, cvtColor
933 CV_EXPORTS void split(const Mat& src, Mat* mvbegin);
936 @param m input multi-channel array.
937 @param mv output vector of arrays; the arrays themselves are reallocated, if needed.
939 CV_EXPORTS_W void split(InputArray m, OutputArrayOfArrays mv);
941 /** @brief Copies specified channels from input arrays to the specified channels of
944 The function cv::mixChannels provides an advanced mechanism for shuffling image channels.
946 cv::split,cv::merge,cv::extractChannel,cv::insertChannel and some forms of cv::cvtColor are partial cases of cv::mixChannels.
948 In the example below, the code splits a 4-channel BGRA image into a 3-channel BGR (with B and R
949 channels swapped) and a separate alpha-channel image:
951 Mat bgra( 100, 100, CV_8UC4, Scalar(255,0,0,255) );
952 Mat bgr( bgra.rows, bgra.cols, CV_8UC3 );
953 Mat alpha( bgra.rows, bgra.cols, CV_8UC1 );
955 // forming an array of matrices is a quite efficient operation,
956 // because the matrix data is not copied, only the headers
957 Mat out[] = { bgr, alpha };
958 // bgra[0] -> bgr[2], bgra[1] -> bgr[1],
959 // bgra[2] -> bgr[0], bgra[3] -> alpha[0]
960 int from_to[] = { 0,2, 1,1, 2,0, 3,3 };
961 mixChannels( &bgra, 1, out, 2, from_to, 4 );
963 @note Unlike many other new-style C++ functions in OpenCV (see the introduction section and
964 Mat::create ), cv::mixChannels requires the output arrays to be pre-allocated before calling the
966 @param src input array or vector of matrices; all of the matrices must have the same size and the
968 @param nsrcs number of matrices in `src`.
969 @param dst output array or vector of matrices; all the matrices **must be allocated**; their size and
970 depth must be the same as in `src[0]`.
971 @param ndsts number of matrices in `dst`.
972 @param fromTo array of index pairs specifying which channels are copied and where; fromTo[k\*2] is
973 a 0-based index of the input channel in src, fromTo[k\*2+1] is an index of the output channel in
974 dst; the continuous channel numbering is used: the first input image channels are indexed from 0 to
975 src[0].channels()-1, the second input image channels are indexed from src[0].channels() to
976 src[0].channels() + src[1].channels()-1, and so on, the same scheme is used for the output image
977 channels; as a special case, when fromTo[k\*2] is negative, the corresponding output channel is
979 @param npairs number of index pairs in `fromTo`.
980 @sa split, merge, extractChannel, insertChannel, cvtColor
982 CV_EXPORTS void mixChannels(const Mat* src, size_t nsrcs, Mat* dst, size_t ndsts,
983 const int* fromTo, size_t npairs);
986 @param src input array or vector of matrices; all of the matrices must have the same size and the
988 @param dst output array or vector of matrices; all the matrices **must be allocated**; their size and
989 depth must be the same as in src[0].
990 @param fromTo array of index pairs specifying which channels are copied and where; fromTo[k\*2] is
991 a 0-based index of the input channel in src, fromTo[k\*2+1] is an index of the output channel in
992 dst; the continuous channel numbering is used: the first input image channels are indexed from 0 to
993 src[0].channels()-1, the second input image channels are indexed from src[0].channels() to
994 src[0].channels() + src[1].channels()-1, and so on, the same scheme is used for the output image
995 channels; as a special case, when fromTo[k\*2] is negative, the corresponding output channel is
997 @param npairs number of index pairs in fromTo.
999 CV_EXPORTS void mixChannels(InputArrayOfArrays src, InputOutputArrayOfArrays dst,
1000 const int* fromTo, size_t npairs);
1003 @param src input array or vector of matrices; all of the matrices must have the same size and the
1005 @param dst output array or vector of matrices; all the matrices **must be allocated**; their size and
1006 depth must be the same as in src[0].
1007 @param fromTo array of index pairs specifying which channels are copied and where; fromTo[k\*2] is
1008 a 0-based index of the input channel in src, fromTo[k\*2+1] is an index of the output channel in
1009 dst; the continuous channel numbering is used: the first input image channels are indexed from 0 to
1010 src[0].channels()-1, the second input image channels are indexed from src[0].channels() to
1011 src[0].channels() + src[1].channels()-1, and so on, the same scheme is used for the output image
1012 channels; as a special case, when fromTo[k\*2] is negative, the corresponding output channel is
1015 CV_EXPORTS_W void mixChannels(InputArrayOfArrays src, InputOutputArrayOfArrays dst,
1016 const std::vector<int>& fromTo);
1018 /** @brief Extracts a single channel from src (coi is 0-based index)
1019 @param src input array
1020 @param dst output array
1021 @param coi index of channel to extract
1022 @sa mixChannels, split
1024 CV_EXPORTS_W void extractChannel(InputArray src, OutputArray dst, int coi);
1026 /** @brief Inserts a single channel to dst (coi is 0-based index)
1027 @param src input array
1028 @param dst output array
1029 @param coi index of channel for insertion
1030 @sa mixChannels, merge
1032 CV_EXPORTS_W void insertChannel(InputArray src, InputOutputArray dst, int coi);
1034 /** @brief Flips a 2D array around vertical, horizontal, or both axes.
1036 The function cv::flip flips the array in one of three different ways (row
1037 and column indices are 0-based):
1038 \f[\texttt{dst} _{ij} =
1041 \texttt{src} _{\texttt{src.rows}-i-1,j} & if\; \texttt{flipCode} = 0 \\
1042 \texttt{src} _{i, \texttt{src.cols} -j-1} & if\; \texttt{flipCode} > 0 \\
1043 \texttt{src} _{ \texttt{src.rows} -i-1, \texttt{src.cols} -j-1} & if\; \texttt{flipCode} < 0 \\
1046 The example scenarios of using the function are the following:
1047 * Vertical flipping of the image (flipCode == 0) to switch between
1048 top-left and bottom-left image origin. This is a typical operation
1049 in video processing on Microsoft Windows\* OS.
1050 * Horizontal flipping of the image with the subsequent horizontal
1051 shift and absolute difference calculation to check for a
1052 vertical-axis symmetry (flipCode \> 0).
1053 * Simultaneous horizontal and vertical flipping of the image with
1054 the subsequent shift and absolute difference calculation to check
1055 for a central symmetry (flipCode \< 0).
1056 * Reversing the order of point arrays (flipCode \> 0 or
1058 @param src input array.
1059 @param dst output array of the same size and type as src.
1060 @param flipCode a flag to specify how to flip the array; 0 means
1061 flipping around the x-axis and positive value (for example, 1) means
1062 flipping around y-axis. Negative value (for example, -1) means flipping
1064 @sa transpose , repeat , completeSymm
1066 CV_EXPORTS_W void flip(InputArray src, OutputArray dst, int flipCode);
1069 ROTATE_90_CLOCKWISE = 0, //!<Rotate 90 degrees clockwise
1070 ROTATE_180 = 1, //!<Rotate 180 degrees clockwise
1071 ROTATE_90_COUNTERCLOCKWISE = 2, //!<Rotate 270 degrees clockwise
1073 /** @brief Rotates a 2D array in multiples of 90 degrees.
1074 The function cv::rotate rotates the array in one of three different ways:
1075 * Rotate by 90 degrees clockwise (rotateCode = ROTATE_90_CLOCKWISE).
1076 * Rotate by 180 degrees clockwise (rotateCode = ROTATE_180).
1077 * Rotate by 270 degrees clockwise (rotateCode = ROTATE_90_COUNTERCLOCKWISE).
1078 @param src input array.
1079 @param dst output array of the same type as src. The size is the same with ROTATE_180,
1080 and the rows and cols are switched for ROTATE_90_CLOCKWISE and ROTATE_90_COUNTERCLOCKWISE.
1081 @param rotateCode an enum to specify how to rotate the array; see the enum #RotateFlags
1082 @sa transpose , repeat , completeSymm, flip, RotateFlags
1084 CV_EXPORTS_W void rotate(InputArray src, OutputArray dst, int rotateCode);
1086 /** @brief Fills the output array with repeated copies of the input array.
1088 The function cv::repeat duplicates the input array one or more times along each of the two axes:
1089 \f[\texttt{dst} _{ij}= \texttt{src} _{i\mod src.rows, \; j\mod src.cols }\f]
1090 The second variant of the function is more convenient to use with @ref MatrixExpressions.
1091 @param src input array to replicate.
1092 @param ny Flag to specify how many times the `src` is repeated along the
1094 @param nx Flag to specify how many times the `src` is repeated along the
1096 @param dst output array of the same type as `src`.
1099 CV_EXPORTS_W void repeat(InputArray src, int ny, int nx, OutputArray dst);
1102 @param src input array to replicate.
1103 @param ny Flag to specify how many times the `src` is repeated along the
1105 @param nx Flag to specify how many times the `src` is repeated along the
1108 CV_EXPORTS Mat repeat(const Mat& src, int ny, int nx);
1110 /** @brief Applies horizontal concatenation to given matrices.
1112 The function horizontally concatenates two or more cv::Mat matrices (with the same number of rows).
1114 cv::Mat matArray[] = { cv::Mat(4, 1, CV_8UC1, cv::Scalar(1)),
1115 cv::Mat(4, 1, CV_8UC1, cv::Scalar(2)),
1116 cv::Mat(4, 1, CV_8UC1, cv::Scalar(3)),};
1119 cv::hconcat( matArray, 3, out );
1126 @param src input array or vector of matrices. all of the matrices must have the same number of rows and the same depth.
1127 @param nsrc number of matrices in src.
1128 @param dst output array. It has the same number of rows and depth as the src, and the sum of cols of the src.
1129 @sa cv::vconcat(const Mat*, size_t, OutputArray), @sa cv::vconcat(InputArrayOfArrays, OutputArray) and @sa cv::vconcat(InputArray, InputArray, OutputArray)
1131 CV_EXPORTS void hconcat(const Mat* src, size_t nsrc, OutputArray dst);
1134 cv::Mat_<float> A = (cv::Mat_<float>(3, 2) << 1, 4,
1137 cv::Mat_<float> B = (cv::Mat_<float>(3, 2) << 7, 10,
1142 cv::hconcat(A, B, C);
1148 @param src1 first input array to be considered for horizontal concatenation.
1149 @param src2 second input array to be considered for horizontal concatenation.
1150 @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.
1152 CV_EXPORTS void hconcat(InputArray src1, InputArray src2, OutputArray dst);
1155 std::vector<cv::Mat> matrices = { cv::Mat(4, 1, CV_8UC1, cv::Scalar(1)),
1156 cv::Mat(4, 1, CV_8UC1, cv::Scalar(2)),
1157 cv::Mat(4, 1, CV_8UC1, cv::Scalar(3)),};
1160 cv::hconcat( matrices, out );
1167 @param src input array or vector of matrices. all of the matrices must have the same number of rows and the same depth.
1168 @param dst output array. It has the same number of rows and depth as the src, and the sum of cols of the src.
1171 CV_EXPORTS_W void hconcat(InputArrayOfArrays src, OutputArray dst);
1173 /** @brief Applies vertical concatenation to given matrices.
1175 The function vertically concatenates two or more cv::Mat matrices (with the same number of cols).
1177 cv::Mat matArray[] = { cv::Mat(1, 4, CV_8UC1, cv::Scalar(1)),
1178 cv::Mat(1, 4, CV_8UC1, cv::Scalar(2)),
1179 cv::Mat(1, 4, CV_8UC1, cv::Scalar(3)),};
1182 cv::vconcat( matArray, 3, out );
1188 @param src input array or vector of matrices. all of the matrices must have the same number of cols and the same depth.
1189 @param nsrc number of matrices in src.
1190 @param dst output array. It has the same number of cols and depth as the src, and the sum of rows of the src.
1191 @sa cv::hconcat(const Mat*, size_t, OutputArray), @sa cv::hconcat(InputArrayOfArrays, OutputArray) and @sa cv::hconcat(InputArray, InputArray, OutputArray)
1193 CV_EXPORTS void vconcat(const Mat* src, size_t nsrc, OutputArray dst);
1196 cv::Mat_<float> A = (cv::Mat_<float>(3, 2) << 1, 7,
1199 cv::Mat_<float> B = (cv::Mat_<float>(3, 2) << 4, 10,
1204 cv::vconcat(A, B, C);
1213 @param src1 first input array to be considered for vertical concatenation.
1214 @param src2 second input array to be considered for vertical concatenation.
1215 @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.
1217 CV_EXPORTS void vconcat(InputArray src1, InputArray src2, OutputArray dst);
1220 std::vector<cv::Mat> matrices = { cv::Mat(1, 4, CV_8UC1, cv::Scalar(1)),
1221 cv::Mat(1, 4, CV_8UC1, cv::Scalar(2)),
1222 cv::Mat(1, 4, CV_8UC1, cv::Scalar(3)),};
1225 cv::vconcat( matrices, out );
1231 @param src input array or vector of matrices. all of the matrices must have the same number of cols and the same depth
1232 @param dst output array. It has the same number of cols and depth as the src, and the sum of rows of the src.
1235 CV_EXPORTS_W void vconcat(InputArrayOfArrays src, OutputArray dst);
1237 /** @brief computes bitwise conjunction of the two arrays (dst = src1 & src2)
1238 Calculates the per-element bit-wise conjunction of two arrays or an
1241 The function cv::bitwise_and calculates the per-element bit-wise logical conjunction for:
1242 * Two arrays when src1 and src2 have the same size:
1243 \f[\texttt{dst} (I) = \texttt{src1} (I) \wedge \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\f]
1244 * An array and a scalar when src2 is constructed from Scalar or has
1245 the same number of elements as `src1.channels()`:
1246 \f[\texttt{dst} (I) = \texttt{src1} (I) \wedge \texttt{src2} \quad \texttt{if mask} (I) \ne0\f]
1247 * A scalar and an array when src1 is constructed from Scalar or has
1248 the same number of elements as `src2.channels()`:
1249 \f[\texttt{dst} (I) = \texttt{src1} \wedge \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\f]
1250 In case of floating-point arrays, their machine-specific bit
1251 representations (usually IEEE754-compliant) are used for the operation.
1252 In case of multi-channel arrays, each channel is processed
1253 independently. In the second and third cases above, the scalar is first
1254 converted to the array type.
1255 @param src1 first input array or a scalar.
1256 @param src2 second input array or a scalar.
1257 @param dst output array that has the same size and type as the input
1259 @param mask optional operation mask, 8-bit single channel array, that
1260 specifies elements of the output array to be changed.
1262 CV_EXPORTS_W void bitwise_and(InputArray src1, InputArray src2,
1263 OutputArray dst, InputArray mask = noArray());
1265 /** @brief Calculates the per-element bit-wise disjunction of two arrays or an
1268 The function cv::bitwise_or calculates the per-element bit-wise logical disjunction for:
1269 * Two arrays when src1 and src2 have the same size:
1270 \f[\texttt{dst} (I) = \texttt{src1} (I) \vee \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\f]
1271 * An array and a scalar when src2 is constructed from Scalar or has
1272 the same number of elements as `src1.channels()`:
1273 \f[\texttt{dst} (I) = \texttt{src1} (I) \vee \texttt{src2} \quad \texttt{if mask} (I) \ne0\f]
1274 * A scalar and an array when src1 is constructed from Scalar or has
1275 the same number of elements as `src2.channels()`:
1276 \f[\texttt{dst} (I) = \texttt{src1} \vee \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\f]
1277 In case of floating-point arrays, their machine-specific bit
1278 representations (usually IEEE754-compliant) are used for the operation.
1279 In case of multi-channel arrays, each channel is processed
1280 independently. In the second and third cases above, the scalar is first
1281 converted to the array type.
1282 @param src1 first input array or a scalar.
1283 @param src2 second input array or a scalar.
1284 @param dst output array that has the same size and type as the input
1286 @param mask optional operation mask, 8-bit single channel array, that
1287 specifies elements of the output array to be changed.
1289 CV_EXPORTS_W void bitwise_or(InputArray src1, InputArray src2,
1290 OutputArray dst, InputArray mask = noArray());
1292 /** @brief Calculates the per-element bit-wise "exclusive or" operation on two
1293 arrays or an array and a scalar.
1295 The function cv::bitwise_xor calculates the per-element bit-wise logical "exclusive-or"
1297 * Two arrays when src1 and src2 have the same size:
1298 \f[\texttt{dst} (I) = \texttt{src1} (I) \oplus \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\f]
1299 * An array and a scalar when src2 is constructed from Scalar or has
1300 the same number of elements as `src1.channels()`:
1301 \f[\texttt{dst} (I) = \texttt{src1} (I) \oplus \texttt{src2} \quad \texttt{if mask} (I) \ne0\f]
1302 * A scalar and an array when src1 is constructed from Scalar or has
1303 the same number of elements as `src2.channels()`:
1304 \f[\texttt{dst} (I) = \texttt{src1} \oplus \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\f]
1305 In case of floating-point arrays, their machine-specific bit
1306 representations (usually IEEE754-compliant) are used for the operation.
1307 In case of multi-channel arrays, each channel is processed
1308 independently. In the 2nd and 3rd cases above, the scalar is first
1309 converted to the array type.
1310 @param src1 first input array or a scalar.
1311 @param src2 second input array or a scalar.
1312 @param dst output array that has the same size and type as the input
1314 @param mask optional operation mask, 8-bit single channel array, that
1315 specifies elements of the output array to be changed.
1317 CV_EXPORTS_W void bitwise_xor(InputArray src1, InputArray src2,
1318 OutputArray dst, InputArray mask = noArray());
1320 /** @brief Inverts every bit of an array.
1322 The function cv::bitwise_not calculates per-element bit-wise inversion of the input
1324 \f[\texttt{dst} (I) = \neg \texttt{src} (I)\f]
1325 In case of a floating-point input array, its machine-specific bit
1326 representation (usually IEEE754-compliant) is used for the operation. In
1327 case of multi-channel arrays, each channel is processed independently.
1328 @param src input array.
1329 @param dst output array that has the same size and type as the input
1331 @param mask optional operation mask, 8-bit single channel array, that
1332 specifies elements of the output array to be changed.
1334 CV_EXPORTS_W void bitwise_not(InputArray src, OutputArray dst,
1335 InputArray mask = noArray());
1337 /** @brief Calculates the per-element absolute difference between two arrays or between an array and a scalar.
1339 The function cv::absdiff calculates:
1340 * Absolute difference between two arrays when they have the same
1342 \f[\texttt{dst}(I) = \texttt{saturate} (| \texttt{src1}(I) - \texttt{src2}(I)|)\f]
1343 * Absolute difference between an array and a scalar when the second
1344 array is constructed from Scalar or has as many elements as the
1345 number of channels in `src1`:
1346 \f[\texttt{dst}(I) = \texttt{saturate} (| \texttt{src1}(I) - \texttt{src2} |)\f]
1347 * Absolute difference between a scalar and an array when the first
1348 array is constructed from Scalar or has as many elements as the
1349 number of channels in `src2`:
1350 \f[\texttt{dst}(I) = \texttt{saturate} (| \texttt{src1} - \texttt{src2}(I) |)\f]
1351 where I is a multi-dimensional index of array elements. In case of
1352 multi-channel arrays, each channel is processed independently.
1353 @note Saturation is not applied when the arrays have the depth CV_32S.
1354 You may even get a negative value in the case of overflow.
1355 @param src1 first input array or a scalar.
1356 @param src2 second input array or a scalar.
1357 @param dst output array that has the same size and type as input arrays.
1358 @sa cv::abs(const Mat&)
1360 CV_EXPORTS_W void absdiff(InputArray src1, InputArray src2, OutputArray dst);
1362 /** @brief Checks if array elements lie between the elements of two other arrays.
1364 The function checks the range as follows:
1365 - For every element of a single-channel input array:
1366 \f[\texttt{dst} (I)= \texttt{lowerb} (I)_0 \leq \texttt{src} (I)_0 \leq \texttt{upperb} (I)_0\f]
1367 - For two-channel arrays:
1368 \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]
1371 That is, dst (I) is set to 255 (all 1 -bits) if src (I) is within the
1372 specified 1D, 2D, 3D, ... box and 0 otherwise.
1374 When the lower and/or upper boundary parameters are scalars, the indexes
1375 (I) at lowerb and upperb in the above formulas should be omitted.
1376 @param src first input array.
1377 @param lowerb inclusive lower boundary array or a scalar.
1378 @param upperb inclusive upper boundary array or a scalar.
1379 @param dst output array of the same size as src and CV_8U type.
1381 CV_EXPORTS_W void inRange(InputArray src, InputArray lowerb,
1382 InputArray upperb, OutputArray dst);
1384 /** @brief Performs the per-element comparison of two arrays or an array and scalar value.
1386 The function compares:
1387 * Elements of two arrays when src1 and src2 have the same size:
1388 \f[\texttt{dst} (I) = \texttt{src1} (I) \,\texttt{cmpop}\, \texttt{src2} (I)\f]
1389 * Elements of src1 with a scalar src2 when src2 is constructed from
1390 Scalar or has a single element:
1391 \f[\texttt{dst} (I) = \texttt{src1}(I) \,\texttt{cmpop}\, \texttt{src2}\f]
1392 * src1 with elements of src2 when src1 is constructed from Scalar or
1393 has a single element:
1394 \f[\texttt{dst} (I) = \texttt{src1} \,\texttt{cmpop}\, \texttt{src2} (I)\f]
1395 When the comparison result is true, the corresponding element of output
1396 array is set to 255. The comparison operations can be replaced with the
1397 equivalent matrix expressions:
1399 Mat dst1 = src1 >= src2;
1400 Mat dst2 = src1 < 8;
1403 @param src1 first input array or a scalar; when it is an array, it must have a single channel.
1404 @param src2 second input array or a scalar; when it is an array, it must have a single channel.
1405 @param dst output array of type ref CV_8U that has the same size and the same number of channels as
1407 @param cmpop a flag, that specifies correspondence between the arrays (cv::CmpTypes)
1408 @sa checkRange, min, max, threshold
1410 CV_EXPORTS_W void compare(InputArray src1, InputArray src2, OutputArray dst, int cmpop);
1412 /** @brief Calculates per-element minimum of two arrays or an array and a scalar.
1414 The function cv::min calculates the per-element minimum of two arrays:
1415 \f[\texttt{dst} (I)= \min ( \texttt{src1} (I), \texttt{src2} (I))\f]
1416 or array and a scalar:
1417 \f[\texttt{dst} (I)= \min ( \texttt{src1} (I), \texttt{value} )\f]
1418 @param src1 first input array.
1419 @param src2 second input array of the same size and type as src1.
1420 @param dst output array of the same size and type as src1.
1421 @sa max, compare, inRange, minMaxLoc
1423 CV_EXPORTS_W void min(InputArray src1, InputArray src2, OutputArray dst);
1425 needed to avoid conflicts with const _Tp& std::min(const _Tp&, const _Tp&, _Compare)
1427 CV_EXPORTS void min(const Mat& src1, const Mat& src2, Mat& dst);
1429 needed to avoid conflicts with const _Tp& std::min(const _Tp&, const _Tp&, _Compare)
1431 CV_EXPORTS void min(const UMat& src1, const UMat& src2, UMat& dst);
1433 /** @brief Calculates per-element maximum of two arrays or an array and a scalar.
1435 The function cv::max calculates the per-element maximum of two arrays:
1436 \f[\texttt{dst} (I)= \max ( \texttt{src1} (I), \texttt{src2} (I))\f]
1437 or array and a scalar:
1438 \f[\texttt{dst} (I)= \max ( \texttt{src1} (I), \texttt{value} )\f]
1439 @param src1 first input array.
1440 @param src2 second input array of the same size and type as src1 .
1441 @param dst output array of the same size and type as src1.
1442 @sa min, compare, inRange, minMaxLoc, @ref MatrixExpressions
1444 CV_EXPORTS_W void max(InputArray src1, InputArray src2, OutputArray dst);
1446 needed to avoid conflicts with const _Tp& std::min(const _Tp&, const _Tp&, _Compare)
1448 CV_EXPORTS void max(const Mat& src1, const Mat& src2, Mat& dst);
1450 needed to avoid conflicts with const _Tp& std::min(const _Tp&, const _Tp&, _Compare)
1452 CV_EXPORTS void max(const UMat& src1, const UMat& src2, UMat& dst);
1454 /** @brief Calculates a square root of array elements.
1456 The function cv::sqrt calculates a square root of each input array element.
1457 In case of multi-channel arrays, each channel is processed
1458 independently. The accuracy is approximately the same as of the built-in
1460 @param src input floating-point array.
1461 @param dst output array of the same size and type as src.
1463 CV_EXPORTS_W void sqrt(InputArray src, OutputArray dst);
1465 /** @brief Raises every array element to a power.
1467 The function cv::pow raises every element of the input array to power :
1468 \f[\texttt{dst} (I) = \fork{\texttt{src}(I)^{power}}{if \(\texttt{power}\) is integer}{|\texttt{src}(I)|^{power}}{otherwise}\f]
1470 So, for a non-integer power exponent, the absolute values of input array
1471 elements are used. However, it is possible to get true values for
1472 negative values using some extra operations. In the example below,
1473 computing the 5th root of array src shows:
1476 pow(src, 1./5, dst);
1477 subtract(Scalar::all(0), dst, dst, mask);
1479 For some values of power, such as integer values, 0.5 and -0.5,
1480 specialized faster algorithms are used.
1482 Special values (NaN, Inf) are not handled.
1483 @param src input array.
1484 @param power exponent of power.
1485 @param dst output array of the same size and type as src.
1486 @sa sqrt, exp, log, cartToPolar, polarToCart
1488 CV_EXPORTS_W void pow(InputArray src, double power, OutputArray dst);
1490 /** @brief Calculates the exponent of every array element.
1492 The function cv::exp calculates the exponent of every element of the input
1494 \f[\texttt{dst} [I] = e^{ src(I) }\f]
1496 The maximum relative error is about 7e-6 for single-precision input and
1497 less than 1e-10 for double-precision input. Currently, the function
1498 converts denormalized values to zeros on output. Special values (NaN,
1499 Inf) are not handled.
1500 @param src input array.
1501 @param dst output array of the same size and type as src.
1502 @sa log , cartToPolar , polarToCart , phase , pow , sqrt , magnitude
1504 CV_EXPORTS_W void exp(InputArray src, OutputArray dst);
1506 /** @brief Calculates the natural logarithm of every array element.
1508 The function cv::log calculates the natural logarithm of every element of the input array:
1509 \f[\texttt{dst} (I) = \log (\texttt{src}(I)) \f]
1511 Output on zero, negative and special (NaN, Inf) values is undefined.
1513 @param src input array.
1514 @param dst output array of the same size and type as src .
1515 @sa exp, cartToPolar, polarToCart, phase, pow, sqrt, magnitude
1517 CV_EXPORTS_W void log(InputArray src, OutputArray dst);
1519 /** @brief Calculates x and y coordinates of 2D vectors from their magnitude and angle.
1521 The function cv::polarToCart calculates the Cartesian coordinates of each 2D
1522 vector represented by the corresponding elements of magnitude and angle:
1523 \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]
1525 The relative accuracy of the estimated coordinates is about 1e-6.
1526 @param magnitude input floating-point array of magnitudes of 2D vectors;
1527 it can be an empty matrix (=Mat()), in this case, the function assumes
1528 that all the magnitudes are =1; if it is not empty, it must have the
1529 same size and type as angle.
1530 @param angle input floating-point array of angles of 2D vectors.
1531 @param x output array of x-coordinates of 2D vectors; it has the same
1532 size and type as angle.
1533 @param y output array of y-coordinates of 2D vectors; it has the same
1534 size and type as angle.
1535 @param angleInDegrees when true, the input angles are measured in
1536 degrees, otherwise, they are measured in radians.
1537 @sa cartToPolar, magnitude, phase, exp, log, pow, sqrt
1539 CV_EXPORTS_W void polarToCart(InputArray magnitude, InputArray angle,
1540 OutputArray x, OutputArray y, bool angleInDegrees = false);
1542 /** @brief Calculates the magnitude and angle of 2D vectors.
1544 The function cv::cartToPolar calculates either the magnitude, angle, or both
1545 for every 2D vector (x(I),y(I)):
1546 \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]
1548 The angles are calculated with accuracy about 0.3 degrees. For the point
1549 (0,0), the angle is set to 0.
1550 @param x array of x-coordinates; this must be a single-precision or
1551 double-precision floating-point array.
1552 @param y array of y-coordinates, that must have the same size and same type as x.
1553 @param magnitude output array of magnitudes of the same size and type as x.
1554 @param angle output array of angles that has the same size and type as
1555 x; the angles are measured in radians (from 0 to 2\*Pi) or in degrees (0 to 360 degrees).
1556 @param angleInDegrees a flag, indicating whether the angles are measured
1557 in radians (which is by default), or in degrees.
1560 CV_EXPORTS_W void cartToPolar(InputArray x, InputArray y,
1561 OutputArray magnitude, OutputArray angle,
1562 bool angleInDegrees = false);
1564 /** @brief Calculates the rotation angle of 2D vectors.
1566 The function cv::phase calculates the rotation angle of each 2D vector that
1567 is formed from the corresponding elements of x and y :
1568 \f[\texttt{angle} (I) = \texttt{atan2} ( \texttt{y} (I), \texttt{x} (I))\f]
1570 The angle estimation accuracy is about 0.3 degrees. When x(I)=y(I)=0 ,
1571 the corresponding angle(I) is set to 0.
1572 @param x input floating-point array of x-coordinates of 2D vectors.
1573 @param y input array of y-coordinates of 2D vectors; it must have the
1574 same size and the same type as x.
1575 @param angle output array of vector angles; it has the same size and
1577 @param angleInDegrees when true, the function calculates the angle in
1578 degrees, otherwise, they are measured in radians.
1580 CV_EXPORTS_W void phase(InputArray x, InputArray y, OutputArray angle,
1581 bool angleInDegrees = false);
1583 /** @brief Calculates the magnitude of 2D vectors.
1585 The function cv::magnitude calculates the magnitude of 2D vectors formed
1586 from the corresponding elements of x and y arrays:
1587 \f[\texttt{dst} (I) = \sqrt{\texttt{x}(I)^2 + \texttt{y}(I)^2}\f]
1588 @param x floating-point array of x-coordinates of the vectors.
1589 @param y floating-point array of y-coordinates of the vectors; it must
1590 have the same size as x.
1591 @param magnitude output array of the same size and type as x.
1592 @sa cartToPolar, polarToCart, phase, sqrt
1594 CV_EXPORTS_W void magnitude(InputArray x, InputArray y, OutputArray magnitude);
1596 /** @brief Checks every element of an input array for invalid values.
1598 The function cv::checkRange checks that every array element is neither NaN nor infinite. When minVal \>
1599 -DBL_MAX and maxVal \< DBL_MAX, the function also checks that each value is between minVal and
1600 maxVal. In case of multi-channel arrays, each channel is processed independently. If some values
1601 are out of range, position of the first outlier is stored in pos (when pos != NULL). Then, the
1602 function either returns false (when quiet=true) or throws an exception.
1603 @param a input array.
1604 @param quiet a flag, indicating whether the functions quietly return false when the array elements
1605 are out of range or they throw an exception.
1606 @param pos optional output parameter, when not NULL, must be a pointer to array of src.dims
1608 @param minVal inclusive lower boundary of valid values range.
1609 @param maxVal exclusive upper boundary of valid values range.
1611 CV_EXPORTS_W bool checkRange(InputArray a, bool quiet = true, CV_OUT Point* pos = 0,
1612 double minVal = -DBL_MAX, double maxVal = DBL_MAX);
1614 /** @brief converts NaN's to the given number
1616 CV_EXPORTS_W void patchNaNs(InputOutputArray a, double val = 0);
1618 /** @brief Performs generalized matrix multiplication.
1620 The function cv::gemm performs generalized matrix multiplication similar to the
1621 gemm functions in BLAS level 3. For example,
1622 `gemm(src1, src2, alpha, src3, beta, dst, GEMM_1_T + GEMM_3_T)`
1624 \f[\texttt{dst} = \texttt{alpha} \cdot \texttt{src1} ^T \cdot \texttt{src2} + \texttt{beta} \cdot \texttt{src3} ^T\f]
1626 In case of complex (two-channel) data, performed a complex matrix
1629 The function can be replaced with a matrix expression. For example, the
1630 above call can be replaced with:
1632 dst = alpha*src1.t()*src2 + beta*src3.t();
1634 @param src1 first multiplied input matrix that could be real(CV_32FC1,
1635 CV_64FC1) or complex(CV_32FC2, CV_64FC2).
1636 @param src2 second multiplied input matrix of the same type as src1.
1637 @param alpha weight of the matrix product.
1638 @param src3 third optional delta matrix added to the matrix product; it
1639 should have the same type as src1 and src2.
1640 @param beta weight of src3.
1641 @param dst output matrix; it has the proper size and the same type as
1643 @param flags operation flags (cv::GemmFlags)
1644 @sa mulTransposed , transform
1646 CV_EXPORTS_W void gemm(InputArray src1, InputArray src2, double alpha,
1647 InputArray src3, double beta, OutputArray dst, int flags = 0);
1649 /** @brief Calculates the product of a matrix and its transposition.
1651 The function cv::mulTransposed calculates the product of src and its
1653 \f[\texttt{dst} = \texttt{scale} ( \texttt{src} - \texttt{delta} )^T ( \texttt{src} - \texttt{delta} )\f]
1655 \f[\texttt{dst} = \texttt{scale} ( \texttt{src} - \texttt{delta} ) ( \texttt{src} - \texttt{delta} )^T\f]
1656 otherwise. The function is used to calculate the covariance matrix. With
1657 zero delta, it can be used as a faster substitute for general matrix
1658 product A\*B when B=A'
1659 @param src input single-channel matrix. Note that unlike gemm, the
1660 function can multiply not only floating-point matrices.
1661 @param dst output square matrix.
1662 @param aTa Flag specifying the multiplication ordering. See the
1664 @param delta Optional delta matrix subtracted from src before the
1665 multiplication. When the matrix is empty ( delta=noArray() ), it is
1666 assumed to be zero, that is, nothing is subtracted. If it has the same
1667 size as src , it is simply subtracted. Otherwise, it is "repeated" (see
1668 repeat ) to cover the full src and then subtracted. Type of the delta
1669 matrix, when it is not empty, must be the same as the type of created
1670 output matrix. See the dtype parameter description below.
1671 @param scale Optional scale factor for the matrix product.
1672 @param dtype Optional type of the output matrix. When it is negative,
1673 the output matrix will have the same type as src . Otherwise, it will be
1674 type=CV_MAT_DEPTH(dtype) that should be either CV_32F or CV_64F .
1675 @sa calcCovarMatrix, gemm, repeat, reduce
1677 CV_EXPORTS_W void mulTransposed( InputArray src, OutputArray dst, bool aTa,
1678 InputArray delta = noArray(),
1679 double scale = 1, int dtype = -1 );
1681 /** @brief Transposes a matrix.
1683 The function cv::transpose transposes the matrix src :
1684 \f[\texttt{dst} (i,j) = \texttt{src} (j,i)\f]
1685 @note No complex conjugation is done in case of a complex matrix. It
1686 should be done separately if needed.
1687 @param src input array.
1688 @param dst output array of the same type as src.
1690 CV_EXPORTS_W void transpose(InputArray src, OutputArray dst);
1692 /** @brief Performs the matrix transformation of every array element.
1694 The function cv::transform performs the matrix transformation of every
1695 element of the array src and stores the results in dst :
1696 \f[\texttt{dst} (I) = \texttt{m} \cdot \texttt{src} (I)\f]
1697 (when m.cols=src.channels() ), or
1698 \f[\texttt{dst} (I) = \texttt{m} \cdot [ \texttt{src} (I); 1]\f]
1699 (when m.cols=src.channels()+1 )
1701 Every element of the N -channel array src is interpreted as N -element
1702 vector that is transformed using the M x N or M x (N+1) matrix m to
1703 M-element vector - the corresponding element of the output array dst .
1705 The function may be used for geometrical transformation of
1706 N -dimensional points, arbitrary linear color space transformation (such
1707 as various kinds of RGB to YUV transforms), shuffling the image
1708 channels, and so forth.
1709 @param src input array that must have as many channels (1 to 4) as
1711 @param dst output array of the same size and depth as src; it has as
1712 many channels as m.rows.
1713 @param m transformation 2x2 or 2x3 floating-point matrix.
1714 @sa perspectiveTransform, getAffineTransform, estimateAffine2D, warpAffine, warpPerspective
1716 CV_EXPORTS_W void transform(InputArray src, OutputArray dst, InputArray m );
1718 /** @brief Performs the perspective matrix transformation of vectors.
1720 The function cv::perspectiveTransform transforms every element of src by
1721 treating it as a 2D or 3D vector, in the following way:
1722 \f[(x, y, z) \rightarrow (x'/w, y'/w, z'/w)\f]
1724 \f[(x', y', z', w') = \texttt{mat} \cdot \begin{bmatrix} x & y & z & 1 \end{bmatrix}\f]
1726 \f[w = \fork{w'}{if \(w' \ne 0\)}{\infty}{otherwise}\f]
1728 Here a 3D vector transformation is shown. In case of a 2D vector
1729 transformation, the z component is omitted.
1731 @note The function transforms a sparse set of 2D or 3D vectors. If you
1732 want to transform an image using perspective transformation, use
1733 warpPerspective . If you have an inverse problem, that is, you want to
1734 compute the most probable perspective transformation out of several
1735 pairs of corresponding points, you can use getPerspectiveTransform or
1737 @param src input two-channel or three-channel floating-point array; each
1738 element is a 2D/3D vector to be transformed.
1739 @param dst output array of the same size and type as src.
1740 @param m 3x3 or 4x4 floating-point transformation matrix.
1741 @sa transform, warpPerspective, getPerspectiveTransform, findHomography
1743 CV_EXPORTS_W void perspectiveTransform(InputArray src, OutputArray dst, InputArray m );
1745 /** @brief Copies the lower or the upper half of a square matrix to its another half.
1747 The function cv::completeSymm copies the lower or the upper half of a square matrix to
1748 its another half. The matrix diagonal remains unchanged:
1749 - \f$\texttt{m}_{ij}=\texttt{m}_{ji}\f$ for \f$i > j\f$ if
1751 - \f$\texttt{m}_{ij}=\texttt{m}_{ji}\f$ for \f$i < j\f$ if
1754 @param m input-output floating-point square matrix.
1755 @param lowerToUpper operation flag; if true, the lower half is copied to
1756 the upper half. Otherwise, the upper half is copied to the lower half.
1759 CV_EXPORTS_W void completeSymm(InputOutputArray m, bool lowerToUpper = false);
1761 /** @brief Initializes a scaled identity matrix.
1763 The function cv::setIdentity initializes a scaled identity matrix:
1764 \f[\texttt{mtx} (i,j)= \fork{\texttt{value}}{ if \(i=j\)}{0}{otherwise}\f]
1766 The function can also be emulated using the matrix initializers and the
1769 Mat A = Mat::eye(4, 3, CV_32F)*5;
1770 // A will be set to [[5, 0, 0], [0, 5, 0], [0, 0, 5], [0, 0, 0]]
1772 @param mtx matrix to initialize (not necessarily square).
1773 @param s value to assign to diagonal elements.
1774 @sa Mat::zeros, Mat::ones, Mat::setTo, Mat::operator=
1776 CV_EXPORTS_W void setIdentity(InputOutputArray mtx, const Scalar& s = Scalar(1));
1778 /** @brief Returns the determinant of a square floating-point matrix.
1780 The function cv::determinant calculates and returns the determinant of the
1781 specified matrix. For small matrices ( mtx.cols=mtx.rows\<=3 ), the
1782 direct method is used. For larger matrices, the function uses LU
1783 factorization with partial pivoting.
1785 For symmetric positively-determined matrices, it is also possible to use
1786 eigen decomposition to calculate the determinant.
1787 @param mtx input matrix that must have CV_32FC1 or CV_64FC1 type and
1789 @sa trace, invert, solve, eigen, @ref MatrixExpressions
1791 CV_EXPORTS_W double determinant(InputArray mtx);
1793 /** @brief Returns the trace of a matrix.
1795 The function cv::trace returns the sum of the diagonal elements of the
1797 \f[\mathrm{tr} ( \texttt{mtx} ) = \sum _i \texttt{mtx} (i,i)\f]
1798 @param mtx input matrix.
1800 CV_EXPORTS_W Scalar trace(InputArray mtx);
1802 /** @brief Finds the inverse or pseudo-inverse of a matrix.
1804 The function cv::invert inverts the matrix src and stores the result in dst
1805 . When the matrix src is singular or non-square, the function calculates
1806 the pseudo-inverse matrix (the dst matrix) so that norm(src\*dst - I) is
1807 minimal, where I is an identity matrix.
1809 In case of the #DECOMP_LU method, the function returns non-zero value if
1810 the inverse has been successfully calculated and 0 if src is singular.
1812 In case of the #DECOMP_SVD method, the function returns the inverse
1813 condition number of src (the ratio of the smallest singular value to the
1814 largest singular value) and 0 if src is singular. The SVD method
1815 calculates a pseudo-inverse matrix if src is singular.
1817 Similarly to #DECOMP_LU, the method #DECOMP_CHOLESKY works only with
1818 non-singular square matrices that should also be symmetrical and
1819 positively defined. In this case, the function stores the inverted
1820 matrix in dst and returns non-zero. Otherwise, it returns 0.
1822 @param src input floating-point M x N matrix.
1823 @param dst output matrix of N x M size and the same type as src.
1824 @param flags inversion method (cv::DecompTypes)
1827 CV_EXPORTS_W double invert(InputArray src, OutputArray dst, int flags = DECOMP_LU);
1829 /** @brief Solves one or more linear systems or least-squares problems.
1831 The function cv::solve solves a linear system or least-squares problem (the
1832 latter is possible with SVD or QR methods, or by specifying the flag
1834 \f[\texttt{dst} = \arg \min _X \| \texttt{src1} \cdot \texttt{X} - \texttt{src2} \|\f]
1836 If #DECOMP_LU or #DECOMP_CHOLESKY method is used, the function returns 1
1837 if src1 (or \f$\texttt{src1}^T\texttt{src1}\f$ ) is non-singular. Otherwise,
1838 it returns 0. In the latter case, dst is not valid. Other methods find a
1839 pseudo-solution in case of a singular left-hand side part.
1841 @note If you want to find a unity-norm solution of an under-defined
1842 singular system \f$\texttt{src1}\cdot\texttt{dst}=0\f$ , the function solve
1843 will not do the work. Use SVD::solveZ instead.
1845 @param src1 input matrix on the left-hand side of the system.
1846 @param src2 input matrix on the right-hand side of the system.
1847 @param dst output solution.
1848 @param flags solution (matrix inversion) method (#DecompTypes)
1849 @sa invert, SVD, eigen
1851 CV_EXPORTS_W bool solve(InputArray src1, InputArray src2,
1852 OutputArray dst, int flags = DECOMP_LU);
1854 /** @brief Sorts each row or each column of a matrix.
1856 The function cv::sort sorts each matrix row or each matrix column in
1857 ascending or descending order. So you should pass two operation flags to
1858 get desired behaviour. If you want to sort matrix rows or columns
1859 lexicographically, you can use STL std::sort generic function with the
1860 proper comparison predicate.
1862 @param src input single-channel array.
1863 @param dst output array of the same size and type as src.
1864 @param flags operation flags, a combination of #SortFlags
1865 @sa sortIdx, randShuffle
1867 CV_EXPORTS_W void sort(InputArray src, OutputArray dst, int flags);
1869 /** @brief Sorts each row or each column of a matrix.
1871 The function cv::sortIdx sorts each matrix row or each matrix column in the
1872 ascending or descending order. So you should pass two operation flags to
1873 get desired behaviour. Instead of reordering the elements themselves, it
1874 stores the indices of sorted elements in the output array. For example:
1876 Mat A = Mat::eye(3,3,CV_32F), B;
1877 sortIdx(A, B, SORT_EVERY_ROW + SORT_ASCENDING);
1878 // B will probably contain
1879 // (because of equal elements in A some permutations are possible):
1880 // [[1, 2, 0], [0, 2, 1], [0, 1, 2]]
1882 @param src input single-channel array.
1883 @param dst output integer array of the same size as src.
1884 @param flags operation flags that could be a combination of cv::SortFlags
1885 @sa sort, randShuffle
1887 CV_EXPORTS_W void sortIdx(InputArray src, OutputArray dst, int flags);
1889 /** @brief Finds the real roots of a cubic equation.
1891 The function solveCubic finds the real roots of a cubic equation:
1892 - if coeffs is a 4-element vector:
1893 \f[\texttt{coeffs} [0] x^3 + \texttt{coeffs} [1] x^2 + \texttt{coeffs} [2] x + \texttt{coeffs} [3] = 0\f]
1894 - if coeffs is a 3-element vector:
1895 \f[x^3 + \texttt{coeffs} [0] x^2 + \texttt{coeffs} [1] x + \texttt{coeffs} [2] = 0\f]
1897 The roots are stored in the roots array.
1898 @param coeffs equation coefficients, an array of 3 or 4 elements.
1899 @param roots output array of real roots that has 1 or 3 elements.
1900 @return number of real roots. It can be 0, 1 or 2.
1902 CV_EXPORTS_W int solveCubic(InputArray coeffs, OutputArray roots);
1904 /** @brief Finds the real or complex roots of a polynomial equation.
1906 The function cv::solvePoly finds real and complex roots of a polynomial equation:
1907 \f[\texttt{coeffs} [n] x^{n} + \texttt{coeffs} [n-1] x^{n-1} + ... + \texttt{coeffs} [1] x + \texttt{coeffs} [0] = 0\f]
1908 @param coeffs array of polynomial coefficients.
1909 @param roots output (complex) array of roots.
1910 @param maxIters maximum number of iterations the algorithm does.
1912 CV_EXPORTS_W double solvePoly(InputArray coeffs, OutputArray roots, int maxIters = 300);
1914 /** @brief Calculates eigenvalues and eigenvectors of a symmetric matrix.
1916 The function cv::eigen calculates just eigenvalues, or eigenvalues and eigenvectors of the symmetric
1919 src*eigenvectors.row(i).t() = eigenvalues.at<srcType>(i)*eigenvectors.row(i).t()
1922 @note Use cv::eigenNonSymmetric for calculation of real eigenvalues and eigenvectors of non-symmetric matrix.
1924 @param src input matrix that must have CV_32FC1 or CV_64FC1 type, square size and be symmetrical
1926 @param eigenvalues output vector of eigenvalues of the same type as src; the eigenvalues are stored
1927 in the descending order.
1928 @param eigenvectors output matrix of eigenvectors; it has the same size and type as src; the
1929 eigenvectors are stored as subsequent matrix rows, in the same order as the corresponding
1931 @sa eigenNonSymmetric, completeSymm , PCA
1933 CV_EXPORTS_W bool eigen(InputArray src, OutputArray eigenvalues,
1934 OutputArray eigenvectors = noArray());
1936 /** @brief Calculates eigenvalues and eigenvectors of a non-symmetric matrix (real eigenvalues only).
1938 @note Assumes real eigenvalues.
1940 The function calculates eigenvalues and eigenvectors (optional) of the square matrix src:
1942 src*eigenvectors.row(i).t() = eigenvalues.at<srcType>(i)*eigenvectors.row(i).t()
1945 @param src input matrix (CV_32FC1 or CV_64FC1 type).
1946 @param eigenvalues output vector of eigenvalues (type is the same type as src).
1947 @param eigenvectors output matrix of eigenvectors (type is the same type as src). The eigenvectors are stored as subsequent matrix rows, in the same order as the corresponding eigenvalues.
1950 CV_EXPORTS_W void eigenNonSymmetric(InputArray src, OutputArray eigenvalues,
1951 OutputArray eigenvectors);
1953 /** @brief Calculates the covariance matrix of a set of vectors.
1955 The function cv::calcCovarMatrix calculates the covariance matrix and, optionally, the mean vector of
1956 the set of input vectors.
1957 @param samples samples stored as separate matrices
1958 @param nsamples number of samples
1959 @param covar output covariance matrix of the type ctype and square size.
1960 @param mean input or output (depending on the flags) array as the average value of the input vectors.
1961 @param flags operation flags as a combination of #CovarFlags
1962 @param ctype type of the matrixl; it equals 'CV_64F' by default.
1963 @sa PCA, mulTransposed, Mahalanobis
1964 @todo InputArrayOfArrays
1966 CV_EXPORTS void calcCovarMatrix( const Mat* samples, int nsamples, Mat& covar, Mat& mean,
1967 int flags, int ctype = CV_64F);
1970 @note use #COVAR_ROWS or #COVAR_COLS flag
1971 @param samples samples stored as rows/columns of a single matrix.
1972 @param covar output covariance matrix of the type ctype and square size.
1973 @param mean input or output (depending on the flags) array as the average value of the input vectors.
1974 @param flags operation flags as a combination of #CovarFlags
1975 @param ctype type of the matrixl; it equals 'CV_64F' by default.
1977 CV_EXPORTS_W void calcCovarMatrix( InputArray samples, OutputArray covar,
1978 InputOutputArray mean, int flags, int ctype = CV_64F);
1980 /** wrap PCA::operator() */
1981 CV_EXPORTS_W void PCACompute(InputArray data, InputOutputArray mean,
1982 OutputArray eigenvectors, int maxComponents = 0);
1984 /** wrap PCA::operator() and add eigenvalues output parameter */
1985 CV_EXPORTS_AS(PCACompute2) void PCACompute(InputArray data, InputOutputArray mean,
1986 OutputArray eigenvectors, OutputArray eigenvalues,
1987 int maxComponents = 0);
1989 /** wrap PCA::operator() */
1990 CV_EXPORTS_W void PCACompute(InputArray data, InputOutputArray mean,
1991 OutputArray eigenvectors, double retainedVariance);
1993 /** wrap PCA::operator() and add eigenvalues output parameter */
1994 CV_EXPORTS_AS(PCACompute2) void PCACompute(InputArray data, InputOutputArray mean,
1995 OutputArray eigenvectors, OutputArray eigenvalues,
1996 double retainedVariance);
1998 /** wrap PCA::project */
1999 CV_EXPORTS_W void PCAProject(InputArray data, InputArray mean,
2000 InputArray eigenvectors, OutputArray result);
2002 /** wrap PCA::backProject */
2003 CV_EXPORTS_W void PCABackProject(InputArray data, InputArray mean,
2004 InputArray eigenvectors, OutputArray result);
2006 /** wrap SVD::compute */
2007 CV_EXPORTS_W void SVDecomp( InputArray src, OutputArray w, OutputArray u, OutputArray vt, int flags = 0 );
2009 /** wrap SVD::backSubst */
2010 CV_EXPORTS_W void SVBackSubst( InputArray w, InputArray u, InputArray vt,
2011 InputArray rhs, OutputArray dst );
2013 /** @brief Calculates the Mahalanobis distance between two vectors.
2015 The function cv::Mahalanobis calculates and returns the weighted distance between two vectors:
2016 \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]
2017 The covariance matrix may be calculated using the #calcCovarMatrix function and then inverted using
2018 the invert function (preferably using the #DECOMP_SVD method, as the most accurate).
2019 @param v1 first 1D input vector.
2020 @param v2 second 1D input vector.
2021 @param icovar inverse covariance matrix.
2023 CV_EXPORTS_W double Mahalanobis(InputArray v1, InputArray v2, InputArray icovar);
2025 /** @brief Performs a forward or inverse Discrete Fourier transform of a 1D or 2D floating-point array.
2027 The function cv::dft performs one of the following:
2028 - Forward the Fourier transform of a 1D vector of N elements:
2029 \f[Y = F^{(N)} \cdot X,\f]
2030 where \f$F^{(N)}_{jk}=\exp(-2\pi i j k/N)\f$ and \f$i=\sqrt{-1}\f$
2031 - Inverse the Fourier transform of a 1D vector of N elements:
2032 \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]
2033 where \f$F^*=\left(\textrm{Re}(F^{(N)})-\textrm{Im}(F^{(N)})\right)^T\f$
2034 - Forward the 2D Fourier transform of a M x N matrix:
2035 \f[Y = F^{(M)} \cdot X \cdot F^{(N)}\f]
2036 - Inverse the 2D Fourier transform of a M x N matrix:
2037 \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]
2039 In case of real (single-channel) data, the output spectrum of the forward Fourier transform or input
2040 spectrum of the inverse Fourier transform can be represented in a packed format called *CCS*
2041 (complex-conjugate-symmetrical). It was borrowed from IPL (Intel\* Image Processing Library). Here
2042 is how 2D *CCS* spectrum looks:
2043 \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]
2045 In case of 1D transform of a real vector, the output looks like the first row of the matrix above.
2047 So, the function chooses an operation mode depending on the flags and size of the input array:
2048 - If #DFT_ROWS is set or the input array has a single row or single column, the function
2049 performs a 1D forward or inverse transform of each row of a matrix when #DFT_ROWS is set.
2050 Otherwise, it performs a 2D transform.
2051 - If the input array is real and #DFT_INVERSE is not set, the function performs a forward 1D or
2053 - When #DFT_COMPLEX_OUTPUT is set, the output is a complex matrix of the same size as
2055 - When #DFT_COMPLEX_OUTPUT is not set, the output is a real matrix of the same size as
2056 input. In case of 2D transform, it uses the packed format as shown above. In case of a
2057 single 1D transform, it looks like the first row of the matrix above. In case of
2058 multiple 1D transforms (when using the #DFT_ROWS flag), each row of the output matrix
2059 looks like the first row of the matrix above.
2060 - If the input array is complex and either #DFT_INVERSE or #DFT_REAL_OUTPUT are not set, the
2061 output is a complex array of the same size as input. The function performs a forward or
2062 inverse 1D or 2D transform of the whole input array or each row of the input array
2063 independently, depending on the flags DFT_INVERSE and DFT_ROWS.
2064 - When #DFT_INVERSE is set and the input array is real, or it is complex but #DFT_REAL_OUTPUT
2065 is set, the output is a real array of the same size as input. The function performs a 1D or 2D
2066 inverse transformation of the whole input array or each individual row, depending on the flags
2067 #DFT_INVERSE and #DFT_ROWS.
2069 If #DFT_SCALE is set, the scaling is done after the transformation.
2071 Unlike dct , the function supports arrays of arbitrary size. But only those arrays are processed
2072 efficiently, whose sizes can be factorized in a product of small prime numbers (2, 3, and 5 in the
2073 current implementation). Such an efficient DFT size can be calculated using the getOptimalDFTSize
2076 The sample below illustrates how to calculate a DFT-based convolution of two 2D real arrays:
2078 void convolveDFT(InputArray A, InputArray B, OutputArray C)
2080 // reallocate the output array if needed
2081 C.create(abs(A.rows - B.rows)+1, abs(A.cols - B.cols)+1, A.type());
2083 // calculate the size of DFT transform
2084 dftSize.width = getOptimalDFTSize(A.cols + B.cols - 1);
2085 dftSize.height = getOptimalDFTSize(A.rows + B.rows - 1);
2087 // allocate temporary buffers and initialize them with 0's
2088 Mat tempA(dftSize, A.type(), Scalar::all(0));
2089 Mat tempB(dftSize, B.type(), Scalar::all(0));
2091 // copy A and B to the top-left corners of tempA and tempB, respectively
2092 Mat roiA(tempA, Rect(0,0,A.cols,A.rows));
2094 Mat roiB(tempB, Rect(0,0,B.cols,B.rows));
2097 // now transform the padded A & B in-place;
2098 // use "nonzeroRows" hint for faster processing
2099 dft(tempA, tempA, 0, A.rows);
2100 dft(tempB, tempB, 0, B.rows);
2102 // multiply the spectrums;
2103 // the function handles packed spectrum representations well
2104 mulSpectrums(tempA, tempB, tempA);
2106 // transform the product back from the frequency domain.
2107 // Even though all the result rows will be non-zero,
2108 // you need only the first C.rows of them, and thus you
2109 // pass nonzeroRows == C.rows
2110 dft(tempA, tempA, DFT_INVERSE + DFT_SCALE, C.rows);
2112 // now copy the result back to C.
2113 tempA(Rect(0, 0, C.cols, C.rows)).copyTo(C);
2115 // all the temporary buffers will be deallocated automatically
2118 To optimize this sample, consider the following approaches:
2119 - Since nonzeroRows != 0 is passed to the forward transform calls and since A and B are copied to
2120 the top-left corners of tempA and tempB, respectively, it is not necessary to clear the whole
2121 tempA and tempB. It is only necessary to clear the tempA.cols - A.cols ( tempB.cols - B.cols)
2122 rightmost columns of the matrices.
2123 - This DFT-based convolution does not have to be applied to the whole big arrays, especially if B
2124 is significantly smaller than A or vice versa. Instead, you can calculate convolution by parts.
2125 To do this, you need to split the output array C into multiple tiles. For each tile, estimate
2126 which parts of A and B are required to calculate convolution in this tile. If the tiles in C are
2127 too small, the speed will decrease a lot because of repeated work. In the ultimate case, when
2128 each tile in C is a single pixel, the algorithm becomes equivalent to the naive convolution
2129 algorithm. If the tiles are too big, the temporary arrays tempA and tempB become too big and
2130 there is also a slowdown because of bad cache locality. So, there is an optimal tile size
2131 somewhere in the middle.
2132 - If different tiles in C can be calculated in parallel and, thus, the convolution is done by
2133 parts, the loop can be threaded.
2135 All of the above improvements have been implemented in #matchTemplate and #filter2D . Therefore, by
2136 using them, you can get the performance even better than with the above theoretically optimal
2137 implementation. Though, those two functions actually calculate cross-correlation, not convolution,
2138 so you need to "flip" the second convolution operand B vertically and horizontally using flip .
2140 - An example using the discrete fourier transform can be found at
2141 opencv_source_code/samples/cpp/dft.cpp
2142 - (Python) An example using the dft functionality to perform Wiener deconvolution can be found
2143 at opencv_source/samples/python/deconvolution.py
2144 - (Python) An example rearranging the quadrants of a Fourier image can be found at
2145 opencv_source/samples/python/dft.py
2146 @param src input array that could be real or complex.
2147 @param dst output array whose size and type depends on the flags .
2148 @param flags transformation flags, representing a combination of the #DftFlags
2149 @param nonzeroRows when the parameter is not zero, the function assumes that only the first
2150 nonzeroRows rows of the input array (#DFT_INVERSE is not set) or only the first nonzeroRows of the
2151 output array (#DFT_INVERSE is set) contain non-zeros, thus, the function can handle the rest of the
2152 rows more efficiently and save some time; this technique is very useful for calculating array
2153 cross-correlation or convolution using DFT.
2154 @sa dct , getOptimalDFTSize , mulSpectrums, filter2D , matchTemplate , flip , cartToPolar ,
2157 CV_EXPORTS_W void dft(InputArray src, OutputArray dst, int flags = 0, int nonzeroRows = 0);
2159 /** @brief Calculates the inverse Discrete Fourier Transform of a 1D or 2D array.
2161 idft(src, dst, flags) is equivalent to dft(src, dst, flags | #DFT_INVERSE) .
2162 @note None of dft and idft scales the result by default. So, you should pass #DFT_SCALE to one of
2163 dft or idft explicitly to make these transforms mutually inverse.
2164 @sa dft, dct, idct, mulSpectrums, getOptimalDFTSize
2165 @param src input floating-point real or complex array.
2166 @param dst output array whose size and type depend on the flags.
2167 @param flags operation flags (see dft and #DftFlags).
2168 @param nonzeroRows number of dst rows to process; the rest of the rows have undefined content (see
2169 the convolution sample in dft description.
2171 CV_EXPORTS_W void idft(InputArray src, OutputArray dst, int flags = 0, int nonzeroRows = 0);
2173 /** @brief Performs a forward or inverse discrete Cosine transform of 1D or 2D array.
2175 The function cv::dct performs a forward or inverse discrete Cosine transform (DCT) of a 1D or 2D
2176 floating-point array:
2177 - Forward Cosine transform of a 1D vector of N elements:
2178 \f[Y = C^{(N)} \cdot X\f]
2180 \f[C^{(N)}_{jk}= \sqrt{\alpha_j/N} \cos \left ( \frac{\pi(2k+1)j}{2N} \right )\f]
2182 \f$\alpha_0=1\f$, \f$\alpha_j=2\f$ for *j \> 0*.
2183 - Inverse Cosine transform of a 1D vector of N elements:
2184 \f[X = \left (C^{(N)} \right )^{-1} \cdot Y = \left (C^{(N)} \right )^T \cdot Y\f]
2185 (since \f$C^{(N)}\f$ is an orthogonal matrix, \f$C^{(N)} \cdot \left(C^{(N)}\right)^T = I\f$ )
2186 - Forward 2D Cosine transform of M x N matrix:
2187 \f[Y = C^{(N)} \cdot X \cdot \left (C^{(N)} \right )^T\f]
2188 - Inverse 2D Cosine transform of M x N matrix:
2189 \f[X = \left (C^{(N)} \right )^T \cdot X \cdot C^{(N)}\f]
2191 The function chooses the mode of operation by looking at the flags and size of the input array:
2192 - If (flags & #DCT_INVERSE) == 0 , the function does a forward 1D or 2D transform. Otherwise, it
2193 is an inverse 1D or 2D transform.
2194 - If (flags & #DCT_ROWS) != 0 , the function performs a 1D transform of each row.
2195 - If the array is a single column or a single row, the function performs a 1D transform.
2196 - If none of the above is true, the function performs a 2D transform.
2198 @note Currently dct supports even-size arrays (2, 4, 6 ...). For data analysis and approximation, you
2199 can pad the array when necessary.
2200 Also, the function performance depends very much, and not monotonically, on the array size (see
2201 getOptimalDFTSize ). In the current implementation DCT of a vector of size N is calculated via DFT
2202 of a vector of size N/2 . Thus, the optimal DCT size N1 \>= N can be calculated as:
2204 size_t getOptimalDCTSize(size_t N) { return 2*getOptimalDFTSize((N+1)/2); }
2205 N1 = getOptimalDCTSize(N);
2207 @param src input floating-point array.
2208 @param dst output array of the same size and type as src .
2209 @param flags transformation flags as a combination of cv::DftFlags (DCT_*)
2210 @sa dft , getOptimalDFTSize , idct
2212 CV_EXPORTS_W void dct(InputArray src, OutputArray dst, int flags = 0);
2214 /** @brief Calculates the inverse Discrete Cosine Transform of a 1D or 2D array.
2216 idct(src, dst, flags) is equivalent to dct(src, dst, flags | DCT_INVERSE).
2217 @param src input floating-point single-channel array.
2218 @param dst output array of the same size and type as src.
2219 @param flags operation flags.
2220 @sa dct, dft, idft, getOptimalDFTSize
2222 CV_EXPORTS_W void idct(InputArray src, OutputArray dst, int flags = 0);
2224 /** @brief Performs the per-element multiplication of two Fourier spectrums.
2226 The function cv::mulSpectrums performs the per-element multiplication of the two CCS-packed or complex
2227 matrices that are results of a real or complex Fourier transform.
2229 The function, together with dft and idft , may be used to calculate convolution (pass conjB=false )
2230 or correlation (pass conjB=true ) of two arrays rapidly. When the arrays are complex, they are
2231 simply multiplied (per element) with an optional conjugation of the second-array elements. When the
2232 arrays are real, they are assumed to be CCS-packed (see dft for details).
2233 @param a first input array.
2234 @param b second input array of the same size and type as src1 .
2235 @param c output array of the same size and type as src1 .
2236 @param flags operation flags; currently, the only supported flag is cv::DFT_ROWS, which indicates that
2237 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.
2238 @param conjB optional flag that conjugates the second input array before the multiplication (true)
2241 CV_EXPORTS_W void mulSpectrums(InputArray a, InputArray b, OutputArray c,
2242 int flags, bool conjB = false);
2244 /** @brief Returns the optimal DFT size for a given vector size.
2246 DFT performance is not a monotonic function of a vector size. Therefore, when you calculate
2247 convolution of two arrays or perform the spectral analysis of an array, it usually makes sense to
2248 pad the input data with zeros to get a bit larger array that can be transformed much faster than the
2249 original one. Arrays whose size is a power-of-two (2, 4, 8, 16, 32, ...) are the fastest to process.
2250 Though, the arrays whose size is a product of 2's, 3's, and 5's (for example, 300 = 5\*5\*3\*2\*2)
2251 are also processed quite efficiently.
2253 The function cv::getOptimalDFTSize returns the minimum number N that is greater than or equal to vecsize
2254 so that the DFT of a vector of size N can be processed efficiently. In the current implementation N
2255 = 2 ^p^ \* 3 ^q^ \* 5 ^r^ for some integer p, q, r.
2257 The function returns a negative number if vecsize is too large (very close to INT_MAX ).
2259 While the function cannot be used directly to estimate the optimal vector size for DCT transform
2260 (since the current DCT implementation supports only even-size vectors), it can be easily processed
2261 as getOptimalDFTSize((vecsize+1)/2)\*2.
2262 @param vecsize vector size.
2263 @sa dft , dct , idft , idct , mulSpectrums
2265 CV_EXPORTS_W int getOptimalDFTSize(int vecsize);
2267 /** @brief Returns the default random number generator.
2269 The function cv::theRNG returns the default random number generator. For each thread, there is a
2270 separate random number generator, so you can use the function safely in multi-thread environments.
2271 If you just need to get a single random number using this generator or initialize an array, you can
2272 use randu or randn instead. But if you are going to generate many random numbers inside a loop, it
2273 is much faster to use this function to retrieve the generator and then use RNG::operator _Tp() .
2274 @sa RNG, randu, randn
2276 CV_EXPORTS RNG& theRNG();
2278 /** @brief Sets state of default random number generator.
2280 The function cv::setRNGSeed sets state of default random number generator to custom value.
2281 @param seed new state for default random number generator
2282 @sa RNG, randu, randn
2284 CV_EXPORTS_W void setRNGSeed(int seed);
2286 /** @brief Generates a single uniformly-distributed random number or an array of random numbers.
2288 Non-template variant of the function fills the matrix dst with uniformly-distributed
2289 random numbers from the specified range:
2290 \f[\texttt{low} _c \leq \texttt{dst} (I)_c < \texttt{high} _c\f]
2291 @param dst output array of random numbers; the array must be pre-allocated.
2292 @param low inclusive lower boundary of the generated random numbers.
2293 @param high exclusive upper boundary of the generated random numbers.
2294 @sa RNG, randn, theRNG
2296 CV_EXPORTS_W void randu(InputOutputArray dst, InputArray low, InputArray high);
2298 /** @brief Fills the array with normally distributed random numbers.
2300 The function cv::randn fills the matrix dst with normally distributed random numbers with the specified
2301 mean vector and the standard deviation matrix. The generated random numbers are clipped to fit the
2302 value range of the output array data type.
2303 @param dst output array of random numbers; the array must be pre-allocated and have 1 to 4 channels.
2304 @param mean mean value (expectation) of the generated random numbers.
2305 @param stddev standard deviation of the generated random numbers; it can be either a vector (in
2306 which case a diagonal standard deviation matrix is assumed) or a square matrix.
2309 CV_EXPORTS_W void randn(InputOutputArray dst, InputArray mean, InputArray stddev);
2311 /** @brief Shuffles the array elements randomly.
2313 The function cv::randShuffle shuffles the specified 1D array by randomly choosing pairs of elements and
2314 swapping them. The number of such swap operations will be dst.rows\*dst.cols\*iterFactor .
2315 @param dst input/output numerical 1D array.
2316 @param iterFactor scale factor that determines the number of random swap operations (see the details
2318 @param rng optional random number generator used for shuffling; if it is zero, theRNG () is used
2322 CV_EXPORTS_W void randShuffle(InputOutputArray dst, double iterFactor = 1., RNG* rng = 0);
2324 /** @brief Principal Component Analysis
2326 The class is used to calculate a special basis for a set of vectors. The
2327 basis will consist of eigenvectors of the covariance matrix calculated
2328 from the input set of vectors. The class %PCA can also transform
2329 vectors to/from the new coordinate space defined by the basis. Usually,
2330 in this new coordinate system, each vector from the original set (and
2331 any linear combination of such vectors) can be quite accurately
2332 approximated by taking its first few components, corresponding to the
2333 eigenvectors of the largest eigenvalues of the covariance matrix.
2334 Geometrically it means that you calculate a projection of the vector to
2335 a subspace formed by a few eigenvectors corresponding to the dominant
2336 eigenvalues of the covariance matrix. And usually such a projection is
2337 very close to the original vector. So, you can represent the original
2338 vector from a high-dimensional space with a much shorter vector
2339 consisting of the projected vector's coordinates in the subspace. Such a
2340 transformation is also known as Karhunen-Loeve Transform, or KLT.
2341 See http://en.wikipedia.org/wiki/Principal_component_analysis
2343 The sample below is the function that takes two matrices. The first
2344 function stores a set of vectors (a row per vector) that is used to
2345 calculate PCA. The second function stores another "test" set of vectors
2346 (a row per vector). First, these vectors are compressed with PCA, then
2347 reconstructed back, and then the reconstruction error norm is computed
2348 and printed for each vector. :
2353 PCA compressPCA(const Mat& pcaset, int maxComponents,
2354 const Mat& testset, Mat& compressed)
2356 PCA pca(pcaset, // pass the data
2357 Mat(), // we do not have a pre-computed mean vector,
2358 // so let the PCA engine to compute it
2359 PCA::DATA_AS_ROW, // indicate that the vectors
2360 // are stored as matrix rows
2361 // (use PCA::DATA_AS_COL if the vectors are
2362 // the matrix columns)
2363 maxComponents // specify, how many principal components to retain
2365 // if there is no test data, just return the computed basis, ready-to-use
2368 CV_Assert( testset.cols == pcaset.cols );
2370 compressed.create(testset.rows, maxComponents, testset.type());
2373 for( int i = 0; i < testset.rows; i++ )
2375 Mat vec = testset.row(i), coeffs = compressed.row(i), reconstructed;
2376 // compress the vector, the result will be stored
2377 // in the i-th row of the output matrix
2378 pca.project(vec, coeffs);
2379 // and then reconstruct it
2380 pca.backProject(coeffs, reconstructed);
2381 // and measure the error
2382 printf("%d. diff = %g\n", i, norm(vec, reconstructed, NORM_L2));
2387 @sa calcCovarMatrix, mulTransposed, SVD, dft, dct
2389 class CV_EXPORTS PCA
2392 enum Flags { DATA_AS_ROW = 0, //!< indicates that the input samples are stored as matrix rows
2393 DATA_AS_COL = 1, //!< indicates that the input samples are stored as matrix columns
2397 /** @brief default constructor
2399 The default constructor initializes an empty %PCA structure. The other
2400 constructors initialize the structure and call PCA::operator()().
2405 @param data input samples stored as matrix rows or matrix columns.
2406 @param mean optional mean value; if the matrix is empty (@c noArray()),
2407 the mean is computed from the data.
2408 @param flags operation flags; currently the parameter is only used to
2409 specify the data layout (PCA::Flags)
2410 @param maxComponents maximum number of components that %PCA should
2411 retain; by default, all the components are retained.
2413 PCA(InputArray data, InputArray mean, int flags, int maxComponents = 0);
2416 @param data input samples stored as matrix rows or matrix columns.
2417 @param mean optional mean value; if the matrix is empty (noArray()),
2418 the mean is computed from the data.
2419 @param flags operation flags; currently the parameter is only used to
2420 specify the data layout (PCA::Flags)
2421 @param retainedVariance Percentage of variance that PCA should retain.
2422 Using this parameter will let the PCA decided how many components to
2423 retain but it will always keep at least 2.
2425 PCA(InputArray data, InputArray mean, int flags, double retainedVariance);
2427 /** @brief performs %PCA
2429 The operator performs %PCA of the supplied dataset. It is safe to reuse
2430 the same PCA structure for multiple datasets. That is, if the structure
2431 has been previously used with another dataset, the existing internal
2432 data is reclaimed and the new @ref eigenvalues, @ref eigenvectors and @ref
2433 mean are allocated and computed.
2435 The computed @ref eigenvalues are sorted from the largest to the smallest and
2436 the corresponding @ref eigenvectors are stored as eigenvectors rows.
2438 @param data input samples stored as the matrix rows or as the matrix
2440 @param mean optional mean value; if the matrix is empty (noArray()),
2441 the mean is computed from the data.
2442 @param flags operation flags; currently the parameter is only used to
2443 specify the data layout. (Flags)
2444 @param maxComponents maximum number of components that PCA should
2445 retain; by default, all the components are retained.
2447 PCA& operator()(InputArray data, InputArray mean, int flags, int maxComponents = 0);
2450 @param data input samples stored as the matrix rows or as the matrix
2452 @param mean optional mean value; if the matrix is empty (noArray()),
2453 the mean is computed from the data.
2454 @param flags operation flags; currently the parameter is only used to
2455 specify the data layout. (PCA::Flags)
2456 @param retainedVariance Percentage of variance that %PCA should retain.
2457 Using this parameter will let the %PCA decided how many components to
2458 retain but it will always keep at least 2.
2460 PCA& operator()(InputArray data, InputArray mean, int flags, double retainedVariance);
2462 /** @brief Projects vector(s) to the principal component subspace.
2464 The methods project one or more vectors to the principal component
2465 subspace, where each vector projection is represented by coefficients in
2466 the principal component basis. The first form of the method returns the
2467 matrix that the second form writes to the result. So the first form can
2468 be used as a part of expression while the second form can be more
2469 efficient in a processing loop.
2470 @param vec input vector(s); must have the same dimensionality and the
2471 same layout as the input data used at %PCA phase, that is, if
2472 DATA_AS_ROW are specified, then `vec.cols==data.cols`
2473 (vector dimensionality) and `vec.rows` is the number of vectors to
2474 project, and the same is true for the PCA::DATA_AS_COL case.
2476 Mat project(InputArray vec) const;
2479 @param vec input vector(s); must have the same dimensionality and the
2480 same layout as the input data used at PCA phase, that is, if
2481 DATA_AS_ROW are specified, then `vec.cols==data.cols`
2482 (vector dimensionality) and `vec.rows` is the number of vectors to
2483 project, and the same is true for the PCA::DATA_AS_COL case.
2484 @param result output vectors; in case of PCA::DATA_AS_COL, the
2485 output matrix has as many columns as the number of input vectors, this
2486 means that `result.cols==vec.cols` and the number of rows match the
2487 number of principal components (for example, `maxComponents` parameter
2488 passed to the constructor).
2490 void project(InputArray vec, OutputArray result) const;
2492 /** @brief Reconstructs vectors from their PC projections.
2494 The methods are inverse operations to PCA::project. They take PC
2495 coordinates of projected vectors and reconstruct the original vectors.
2496 Unless all the principal components have been retained, the
2497 reconstructed vectors are different from the originals. But typically,
2498 the difference is small if the number of components is large enough (but
2499 still much smaller than the original vector dimensionality). As a
2500 result, PCA is used.
2501 @param vec coordinates of the vectors in the principal component
2502 subspace, the layout and size are the same as of PCA::project output
2505 Mat backProject(InputArray vec) const;
2508 @param vec coordinates of the vectors in the principal component
2509 subspace, the layout and size are the same as of PCA::project output
2511 @param result reconstructed vectors; the layout and size are the same as
2512 of PCA::project input vectors.
2514 void backProject(InputArray vec, OutputArray result) const;
2516 /** @brief write PCA objects
2518 Writes @ref eigenvalues @ref eigenvectors and @ref mean to specified FileStorage
2520 void write(FileStorage& fs) const;
2522 /** @brief load PCA objects
2524 Loads @ref eigenvalues @ref eigenvectors and @ref mean from specified FileNode
2526 void read(const FileNode& fn);
2528 Mat eigenvectors; //!< eigenvectors of the covariation matrix
2529 Mat eigenvalues; //!< eigenvalues of the covariation matrix
2530 Mat mean; //!< mean value subtracted before the projection and added after the back projection
2533 /** @example pca.cpp
2534 An example using %PCA for dimensionality reduction while maintaining an amount of variance
2538 @brief Linear Discriminant Analysis
2539 @todo document this class
2541 class CV_EXPORTS LDA
2544 /** @brief constructor
2545 Initializes a LDA with num_components (default 0).
2547 explicit LDA(int num_components = 0);
2549 /** Initializes and performs a Discriminant Analysis with Fisher's
2550 Optimization Criterion on given data in src and corresponding labels
2551 in labels. If 0 (or less) number of components are given, they are
2552 automatically determined for given data in computation.
2554 LDA(InputArrayOfArrays src, InputArray labels, int num_components = 0);
2556 /** Serializes this object to a given filename.
2558 void save(const String& filename) const;
2560 /** Deserializes this object from a given filename.
2562 void load(const String& filename);
2564 /** Serializes this object to a given cv::FileStorage.
2566 void save(FileStorage& fs) const;
2568 /** Deserializes this object from a given cv::FileStorage.
2570 void load(const FileStorage& node);
2576 /** Compute the discriminants for data in src (row aligned) and labels.
2578 void compute(InputArrayOfArrays src, InputArray labels);
2580 /** Projects samples into the LDA subspace.
2581 src may be one or more row aligned samples.
2583 Mat project(InputArray src);
2585 /** Reconstructs projections from the LDA subspace.
2586 src may be one or more row aligned projections.
2588 Mat reconstruct(InputArray src);
2590 /** Returns the eigenvectors of this LDA.
2592 Mat eigenvectors() const { return _eigenvectors; }
2594 /** Returns the eigenvalues of this LDA.
2596 Mat eigenvalues() const { return _eigenvalues; }
2598 static Mat subspaceProject(InputArray W, InputArray mean, InputArray src);
2599 static Mat subspaceReconstruct(InputArray W, InputArray mean, InputArray src);
2602 int _num_components;
2605 void lda(InputArrayOfArrays src, InputArray labels);
2608 /** @brief Singular Value Decomposition
2610 Class for computing Singular Value Decomposition of a floating-point
2611 matrix. The Singular Value Decomposition is used to solve least-square
2612 problems, under-determined linear systems, invert matrices, compute
2613 condition numbers, and so on.
2615 If you want to compute a condition number of a matrix or an absolute value of
2616 its determinant, you do not need `u` and `vt`. You can pass
2617 flags=SVD::NO_UV|... . Another flag SVD::FULL_UV indicates that full-size u
2618 and vt must be computed, which is not necessary most of the time.
2620 @sa invert, solve, eigen, determinant
2622 class CV_EXPORTS SVD
2626 /** allow the algorithm to modify the decomposed matrix; it can save space and speed up
2627 processing. currently ignored. */
2629 /** indicates that only a vector of singular values `w` is to be processed, while u and vt
2630 will be set to empty matrices */
2632 /** when the matrix is not square, by default the algorithm produces u and vt matrices of
2633 sufficiently large size for the further A reconstruction; if, however, FULL_UV flag is
2634 specified, u and vt will be full-size square orthogonal matrices.*/
2638 /** @brief the default constructor
2640 initializes an empty SVD structure
2645 initializes an empty SVD structure and then calls SVD::operator()
2646 @param src decomposed matrix. The depth has to be CV_32F or CV_64F.
2647 @param flags operation flags (SVD::Flags)
2649 SVD( InputArray src, int flags = 0 );
2651 /** @brief the operator that performs SVD. The previously allocated u, w and vt are released.
2653 The operator performs the singular value decomposition of the supplied
2654 matrix. The u,`vt` , and the vector of singular values w are stored in
2655 the structure. The same SVD structure can be reused many times with
2656 different matrices. Each time, if needed, the previous u,`vt` , and w
2657 are reclaimed and the new matrices are created, which is all handled by
2659 @param src decomposed matrix. The depth has to be CV_32F or CV_64F.
2660 @param flags operation flags (SVD::Flags)
2662 SVD& operator ()( InputArray src, int flags = 0 );
2664 /** @brief decomposes matrix and stores the results to user-provided matrices
2666 The methods/functions perform SVD of matrix. Unlike SVD::SVD constructor
2667 and SVD::operator(), they store the results to the user-provided
2672 SVD::compute(A, w, u, vt);
2675 @param src decomposed matrix. The depth has to be CV_32F or CV_64F.
2676 @param w calculated singular values
2677 @param u calculated left singular vectors
2678 @param vt transposed matrix of right singular vectors
2679 @param flags operation flags - see SVD::Flags.
2681 static void compute( InputArray src, OutputArray w,
2682 OutputArray u, OutputArray vt, int flags = 0 );
2685 computes singular values of a matrix
2686 @param src decomposed matrix. The depth has to be CV_32F or CV_64F.
2687 @param w calculated singular values
2688 @param flags operation flags - see SVD::Flags.
2690 static void compute( InputArray src, OutputArray w, int flags = 0 );
2692 /** @brief performs back substitution
2694 static void backSubst( InputArray w, InputArray u,
2695 InputArray vt, InputArray rhs,
2698 /** @brief solves an under-determined singular linear system
2700 The method finds a unit-length solution x of a singular linear system
2701 A\*x = 0. Depending on the rank of A, there can be no solutions, a
2702 single solution or an infinite number of solutions. In general, the
2703 algorithm solves the following problem:
2704 \f[dst = \arg \min _{x: \| x \| =1} \| src \cdot x \|\f]
2705 @param src left-hand-side matrix.
2706 @param dst found solution.
2708 static void solveZ( InputArray src, OutputArray dst );
2710 /** @brief performs a singular value back substitution.
2712 The method calculates a back substitution for the specified right-hand
2715 \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]
2717 Using this technique you can either get a very accurate solution of the
2718 convenient linear system, or the best (in the least-squares terms)
2719 pseudo-solution of an overdetermined linear system.
2721 @param rhs right-hand side of a linear system (u\*w\*v')\*dst = rhs to
2722 be solved, where A has been previously decomposed.
2724 @param dst found solution of the system.
2726 @note Explicit SVD with the further back substitution only makes sense
2727 if you need to solve many linear systems with the same left-hand side
2728 (for example, src ). If all you need is to solve a single system
2729 (possibly with multiple rhs immediately available), simply call solve
2730 add pass #DECOMP_SVD there. It does absolutely the same thing.
2732 void backSubst( InputArray rhs, OutputArray dst ) const;
2734 /** @todo document */
2735 template<typename _Tp, int m, int n, int nm> static
2736 void compute( const Matx<_Tp, m, n>& a, Matx<_Tp, nm, 1>& w, Matx<_Tp, m, nm>& u, Matx<_Tp, n, nm>& vt );
2738 /** @todo document */
2739 template<typename _Tp, int m, int n, int nm> static
2740 void compute( const Matx<_Tp, m, n>& a, Matx<_Tp, nm, 1>& w );
2742 /** @todo document */
2743 template<typename _Tp, int m, int n, int nm, int nb> static
2744 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 );
2749 /** @brief Random Number Generator
2751 Random number generator. It encapsulates the state (currently, a 64-bit
2752 integer) and has methods to return scalar random values and to fill
2753 arrays with random values. Currently it supports uniform and Gaussian
2754 (normal) distributions. The generator uses Multiply-With-Carry
2755 algorithm, introduced by G. Marsaglia (
2756 <http://en.wikipedia.org/wiki/Multiply-with-carry> ).
2757 Gaussian-distribution random numbers are generated using the Ziggurat
2758 algorithm ( <http://en.wikipedia.org/wiki/Ziggurat_algorithm> ),
2759 introduced by G. Marsaglia and W. W. Tsang.
2761 class CV_EXPORTS RNG
2768 /** @brief constructor
2770 These are the RNG constructors. The first form sets the state to some
2771 pre-defined value, equal to 2\*\*32-1 in the current implementation. The
2772 second form sets the state to the specified value. If you passed state=0
2773 , the constructor uses the above default value instead to avoid the
2774 singular random number sequence, consisting of all zeros.
2778 @param state 64-bit value used to initialize the RNG.
2781 /**The method updates the state using the MWC algorithm and returns the
2782 next 32-bit random number.*/
2785 /**Each of the methods updates the state using the MWC algorithm and
2786 returns the next random number of the specified type. In case of integer
2787 types, the returned number is from the available value range for the
2788 specified type. In case of floating-point types, the returned value is
2799 operator unsigned();
2807 /** @brief returns a random integer sampled uniformly from [0, N).
2809 The methods transform the state using the MWC algorithm and return the
2810 next random number. The first form is equivalent to RNG::next . The
2811 second form returns the random number modulo N , which means that the
2812 result is in the range [0, N) .
2814 unsigned operator ()();
2816 @param N upper non-inclusive boundary of the returned random number.
2818 unsigned operator ()(unsigned N);
2820 /** @brief returns uniformly distributed integer random number from [a,b) range
2822 The methods transform the state using the MWC algorithm and return the
2823 next uniformly-distributed random number of the specified type, deduced
2824 from the input parameter type, from the range [a, b) . There is a nuance
2825 illustrated by the following sample:
2830 // always produces 0
2831 double a = rng.uniform(0, 1);
2833 // produces double from [0, 1)
2834 double a1 = rng.uniform((double)0, (double)1);
2836 // produces float from [0, 1)
2837 float b = rng.uniform(0.f, 1.f);
2839 // produces double from [0, 1)
2840 double c = rng.uniform(0., 1.);
2842 // may cause compiler error because of ambiguity:
2843 // RNG::uniform(0, (int)0.999999)? or RNG::uniform((double)0, 0.99999)?
2844 double d = rng.uniform(0, 0.999999);
2847 The compiler does not take into account the type of the variable to
2848 which you assign the result of RNG::uniform . The only thing that
2849 matters to the compiler is the type of a and b parameters. So, if you
2850 want a floating-point random number, but the range boundaries are
2851 integer numbers, either put dots in the end, if they are constants, or
2852 use explicit type cast operators, as in the a1 initialization above.
2853 @param a lower inclusive boundary of the returned random number.
2854 @param b upper non-inclusive boundary of the returned random number.
2856 int uniform(int a, int b);
2858 float uniform(float a, float b);
2860 double uniform(double a, double b);
2862 /** @brief Fills arrays with random numbers.
2864 @param mat 2D or N-dimensional matrix; currently matrices with more than
2865 4 channels are not supported by the methods, use Mat::reshape as a
2866 possible workaround.
2867 @param distType distribution type, RNG::UNIFORM or RNG::NORMAL.
2868 @param a first distribution parameter; in case of the uniform
2869 distribution, this is an inclusive lower boundary, in case of the normal
2870 distribution, this is a mean value.
2871 @param b second distribution parameter; in case of the uniform
2872 distribution, this is a non-inclusive upper boundary, in case of the
2873 normal distribution, this is a standard deviation (diagonal of the
2874 standard deviation matrix or the full standard deviation matrix).
2875 @param saturateRange pre-saturation flag; for uniform distribution only;
2876 if true, the method will first convert a and b to the acceptable value
2877 range (according to the mat datatype) and then will generate uniformly
2878 distributed random numbers within the range [saturate(a), saturate(b)),
2879 if saturateRange=false, the method will generate uniformly distributed
2880 random numbers in the original range [a, b) and then will saturate them,
2881 it means, for example, that
2882 <tt>theRNG().fill(mat_8u, RNG::UNIFORM, -DBL_MAX, DBL_MAX)</tt> will likely
2883 produce array mostly filled with 0's and 255's, since the range (0, 255)
2884 is significantly smaller than [-DBL_MAX, DBL_MAX).
2886 Each of the methods fills the matrix with the random values from the
2887 specified distribution. As the new numbers are generated, the RNG state
2888 is updated accordingly. In case of multiple-channel images, every
2889 channel is filled independently, which means that RNG cannot generate
2890 samples from the multi-dimensional Gaussian distribution with
2891 non-diagonal covariance matrix directly. To do that, the method
2892 generates samples from multi-dimensional standard Gaussian distribution
2893 with zero mean and identity covariation matrix, and then transforms them
2894 using transform to get samples from the specified Gaussian distribution.
2896 void fill( InputOutputArray mat, int distType, InputArray a, InputArray b, bool saturateRange = false );
2898 /** @brief Returns the next random number sampled from the Gaussian distribution
2899 @param sigma standard deviation of the distribution.
2901 The method transforms the state using the MWC algorithm and returns the
2902 next random number from the Gaussian distribution N(0,sigma) . That is,
2903 the mean value of the returned random numbers is zero and the standard
2904 deviation is the specified sigma .
2906 double gaussian(double sigma);
2910 bool operator ==(const RNG& other) const;
2913 /** @brief Mersenne Twister random number generator
2915 Inspired by http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MT2002/CODES/mt19937ar.c
2918 class CV_EXPORTS RNG_MT19937
2922 RNG_MT19937(unsigned s);
2923 void seed(unsigned s);
2928 operator unsigned();
2932 unsigned operator ()(unsigned N);
2933 unsigned operator ()();
2935 /** @brief returns uniformly distributed integer random number from [a,b) range
2938 int uniform(int a, int b);
2939 /** @brief returns uniformly distributed floating-point random number from [a,b) range
2942 float uniform(float a, float b);
2943 /** @brief returns uniformly distributed double-precision floating-point random number from [a,b) range
2946 double uniform(double a, double b);
2949 enum PeriodParameters {N = 624, M = 397};
2956 //! @addtogroup core_cluster
2959 /** @example kmeans.cpp
2960 An example on K-means clustering
2963 /** @brief Finds centers of clusters and groups input samples around the clusters.
2965 The function kmeans implements a k-means algorithm that finds the centers of cluster_count clusters
2966 and groups the input samples around the clusters. As an output, \f$\texttt{labels}_i\f$ contains a
2967 0-based cluster index for the sample stored in the \f$i^{th}\f$ row of the samples matrix.
2970 - (Python) An example on K-means clustering can be found at
2971 opencv_source_code/samples/python/kmeans.py
2972 @param data Data for clustering. An array of N-Dimensional points with float coordinates is needed.
2973 Examples of this array can be:
2974 - Mat points(count, 2, CV_32F);
2975 - Mat points(count, 1, CV_32FC2);
2976 - Mat points(1, count, CV_32FC2);
2977 - std::vector\<cv::Point2f\> points(sampleCount);
2978 @param K Number of clusters to split the set by.
2979 @param bestLabels Input/output integer array that stores the cluster indices for every sample.
2980 @param criteria The algorithm termination criteria, that is, the maximum number of iterations and/or
2981 the desired accuracy. The accuracy is specified as criteria.epsilon. As soon as each of the cluster
2982 centers moves by less than criteria.epsilon on some iteration, the algorithm stops.
2983 @param attempts Flag to specify the number of times the algorithm is executed using different
2984 initial labellings. The algorithm returns the labels that yield the best compactness (see the last
2985 function parameter).
2986 @param flags Flag that can take values of cv::KmeansFlags
2987 @param centers Output matrix of the cluster centers, one row per each cluster center.
2988 @return The function returns the compactness measure that is computed as
2989 \f[\sum _i \| \texttt{samples} _i - \texttt{centers} _{ \texttt{labels} _i} \| ^2\f]
2990 after every attempt. The best (minimum) value is chosen and the corresponding labels and the
2991 compactness value are returned by the function. Basically, you can use only the core of the
2992 function, set the number of attempts to 1, initialize labels each time using a custom algorithm,
2993 pass them with the ( flags = #KMEANS_USE_INITIAL_LABELS ) flag, and then choose the best
2994 (most-compact) clustering.
2996 CV_EXPORTS_W double kmeans( InputArray data, int K, InputOutputArray bestLabels,
2997 TermCriteria criteria, int attempts,
2998 int flags, OutputArray centers = noArray() );
3002 //! @addtogroup core_basic
3005 /////////////////////////////// Formatted output of cv::Mat ///////////////////////////
3007 /** @todo document */
3008 class CV_EXPORTS Formatted
3011 virtual const char* next() = 0;
3012 virtual void reset() = 0;
3013 virtual ~Formatted();
3016 /** @todo document */
3017 class CV_EXPORTS Formatter
3020 enum { FMT_DEFAULT = 0,
3028 virtual ~Formatter();
3030 virtual Ptr<Formatted> format(const Mat& mtx) const = 0;
3032 virtual void set32fPrecision(int p = 8) = 0;
3033 virtual void set64fPrecision(int p = 16) = 0;
3034 virtual void setMultiline(bool ml = true) = 0;
3036 static Ptr<Formatter> get(int fmt = FMT_DEFAULT);
3041 String& operator << (String& out, Ptr<Formatted> fmtd)
3044 for(const char* str = fmtd->next(); str; str = fmtd->next())
3045 out += cv::String(str);
3050 String& operator << (String& out, const Mat& mtx)
3052 return out << Formatter::get()->format(mtx);
3055 //////////////////////////////////////// Algorithm ////////////////////////////////////
3057 class CV_EXPORTS Algorithm;
3059 template<typename _Tp> struct ParamType {};
3062 /** @brief This is a base class for all more or less complex algorithms in OpenCV
3064 especially for classes of algorithms, for which there can be multiple implementations. The examples
3065 are stereo correspondence (for which there are algorithms like block matching, semi-global block
3066 matching, graph-cut etc.), background subtraction (which can be done using mixture-of-gaussians
3067 models, codebook-based algorithm etc.), optical flow (block matching, Lucas-Kanade, Horn-Schunck
3070 Here is example of SimpleBlobDetector use in your application via Algorithm interface:
3071 @snippet snippets/core_various.cpp Algorithm
3073 class CV_EXPORTS_W Algorithm
3077 virtual ~Algorithm();
3079 /** @brief Clears the algorithm state
3081 CV_WRAP virtual void clear() {}
3083 /** @brief Stores algorithm parameters in a file storage
3085 virtual void write(FileStorage& fs) const { (void)fs; }
3087 /** @brief simplified API for language bindings
3090 CV_WRAP void write(const Ptr<FileStorage>& fs, const String& name = String()) const;
3092 /** @brief Reads algorithm parameters from a file storage
3094 CV_WRAP virtual void read(const FileNode& fn) { (void)fn; }
3096 /** @brief Returns true if the Algorithm is empty (e.g. in the very beginning or after unsuccessful read
3098 CV_WRAP virtual bool empty() const { return false; }
3100 /** @brief Reads algorithm from the file node
3102 This is static template method of Algorithm. It's usage is following (in the case of SVM):
3104 cv::FileStorage fsRead("example.xml", FileStorage::READ);
3105 Ptr<SVM> svm = Algorithm::read<SVM>(fsRead.root());
3107 In order to make this method work, the derived class must overwrite Algorithm::read(const
3108 FileNode& fn) and also have static create() method without parameters
3109 (or with all the optional parameters)
3111 template<typename _Tp> static Ptr<_Tp> read(const FileNode& fn)
3113 Ptr<_Tp> obj = _Tp::create();
3115 return !obj->empty() ? obj : Ptr<_Tp>();
3118 /** @brief Loads algorithm from the file
3120 @param filename Name of the file to read.
3121 @param objname The optional name of the node to read (if empty, the first top-level node will be used)
3123 This is static template method of Algorithm. It's usage is following (in the case of SVM):
3125 Ptr<SVM> svm = Algorithm::load<SVM>("my_svm_model.xml");
3127 In order to make this method work, the derived class must overwrite Algorithm::read(const
3130 template<typename _Tp> static Ptr<_Tp> load(const String& filename, const String& objname=String())
3132 FileStorage fs(filename, FileStorage::READ);
3133 CV_Assert(fs.isOpened());
3134 FileNode fn = objname.empty() ? fs.getFirstTopLevelNode() : fs[objname];
3135 if (fn.empty()) return Ptr<_Tp>();
3136 Ptr<_Tp> obj = _Tp::create();
3138 return !obj->empty() ? obj : Ptr<_Tp>();
3141 /** @brief Loads algorithm from a String
3143 @param strModel The string variable containing the model you want to load.
3144 @param objname The optional name of the node to read (if empty, the first top-level node will be used)
3146 This is static template method of Algorithm. It's usage is following (in the case of SVM):
3148 Ptr<SVM> svm = Algorithm::loadFromString<SVM>(myStringModel);
3151 template<typename _Tp> static Ptr<_Tp> loadFromString(const String& strModel, const String& objname=String())
3153 FileStorage fs(strModel, FileStorage::READ + FileStorage::MEMORY);
3154 FileNode fn = objname.empty() ? fs.getFirstTopLevelNode() : fs[objname];
3155 Ptr<_Tp> obj = _Tp::create();
3157 return !obj->empty() ? obj : Ptr<_Tp>();
3160 /** Saves the algorithm to a file.
3161 In order to make this method work, the derived class must implement Algorithm::write(FileStorage& fs). */
3162 CV_WRAP virtual void save(const String& filename) const;
3164 /** Returns the algorithm string identifier.
3165 This string is used as top level xml/yml node tag when the object is saved to a file or string. */
3166 CV_WRAP virtual String getDefaultName() const;
3169 void writeFormat(FileStorage& fs) const;
3173 enum { INT=0, BOOLEAN=1, REAL=2, STRING=3, MAT=4, MAT_VECTOR=5, ALGORITHM=6, FLOAT=7,
3174 UNSIGNED_INT=8, UINT64=9, UCHAR=11, SCALAR=12 };
3179 template<> struct ParamType<bool>
3181 typedef bool const_param_type;
3182 typedef bool member_type;
3184 enum { type = Param::BOOLEAN };
3187 template<> struct ParamType<int>
3189 typedef int const_param_type;
3190 typedef int member_type;
3192 enum { type = Param::INT };
3195 template<> struct ParamType<double>
3197 typedef double const_param_type;
3198 typedef double member_type;
3200 enum { type = Param::REAL };
3203 template<> struct ParamType<String>
3205 typedef const String& const_param_type;
3206 typedef String member_type;
3208 enum { type = Param::STRING };
3211 template<> struct ParamType<Mat>
3213 typedef const Mat& const_param_type;
3214 typedef Mat member_type;
3216 enum { type = Param::MAT };
3219 template<> struct ParamType<std::vector<Mat> >
3221 typedef const std::vector<Mat>& const_param_type;
3222 typedef std::vector<Mat> member_type;
3224 enum { type = Param::MAT_VECTOR };
3227 template<> struct ParamType<Algorithm>
3229 typedef const Ptr<Algorithm>& const_param_type;
3230 typedef Ptr<Algorithm> member_type;
3232 enum { type = Param::ALGORITHM };
3235 template<> struct ParamType<float>
3237 typedef float const_param_type;
3238 typedef float member_type;
3240 enum { type = Param::FLOAT };
3243 template<> struct ParamType<unsigned>
3245 typedef unsigned const_param_type;
3246 typedef unsigned member_type;
3248 enum { type = Param::UNSIGNED_INT };
3251 template<> struct ParamType<uint64>
3253 typedef uint64 const_param_type;
3254 typedef uint64 member_type;
3256 enum { type = Param::UINT64 };
3259 template<> struct ParamType<uchar>
3261 typedef uchar const_param_type;
3262 typedef uchar member_type;
3264 enum { type = Param::UCHAR };
3267 template<> struct ParamType<Scalar>
3269 typedef const Scalar& const_param_type;
3270 typedef Scalar member_type;
3272 enum { type = Param::SCALAR };
3279 #include "opencv2/core/operations.hpp"
3280 #include "opencv2/core/cvstd.inl.hpp"
3281 #include "opencv2/core/utility.hpp"
3282 #include "opencv2/core/optim.hpp"
3283 #include "opencv2/core/ovx.hpp"
3285 #endif /*OPENCV_CORE_HPP*/