OpenCV: Operations on arrays

| OpenCV 3.4.2 Open Source Computer Vision

Classes | Enumerations | Functions
Operations on arrays
Core functionality

## Classes
class | cv::LDA
| Linear Discriminant Analysis. More...
class | cv::PCA
| Principal Component Analysis. More...
class | cv::RNG
| Random Number Generator. More...
class | cv::RNG_MT19937
| Mersenne Twister random number generator. More...
class | cv::SVD
| Singular Value Decomposition. More...

## Enumerations
enum | cv::BorderTypes { cv::BORDER_CONSTANT = 0, cv::BORDER_REPLICATE = 1, cv::BORDER_REFLECT = 2, cv::BORDER_WRAP = 3, cv::BORDER_REFLECT_101 = 4, cv::BORDER_TRANSPARENT = 5, cv::BORDER_REFLECT101 = BORDER_REFLECT_101, cv::BORDER_DEFAULT = BORDER_REFLECT_101, cv::BORDER_ISOLATED = 16 }
enum | cv::CmpTypes { cv::CMP_EQ = 0, cv::CMP_GT = 1, cv::CMP_GE = 2, cv::CMP_LT = 3, cv::CMP_LE = 4, cv::CMP_NE = 5 }
| comparison types More...
enum | cv::DecompTypes { cv::DECOMP_LU = 0, cv::DECOMP_SVD = 1, cv::DECOMP_EIG = 2, cv::DECOMP_CHOLESKY = 3, cv::DECOMP_QR = 4, cv::DECOMP_NORMAL = 16 }
| matrix decomposition types More...
enum | cv::DftFlags { cv::DFT_INVERSE = 1, cv::DFT_SCALE = 2, cv::DFT_ROWS = 4, cv::DFT_COMPLEX_OUTPUT = 16, cv::DFT_REAL_OUTPUT = 32, cv::DFT_COMPLEX_INPUT = 64, cv::DCT_INVERSE = DFT_INVERSE, cv::DCT_ROWS = DFT_ROWS }
enum | cv::GemmFlags { cv::GEMM_1_T = 1, cv::GEMM_2_T = 2, cv::GEMM_3_T = 4 }
| generalized matrix multiplication flags More...
enum | cv::NormTypes { cv::NORM_INF = 1, cv::NORM_L1 = 2, cv::NORM_L2 = 4, cv::NORM_L2SQR = 5, cv::NORM_HAMMING = 6, cv::NORM_HAMMING2 = 7, cv::NORM_TYPE_MASK = 7, cv::NORM_RELATIVE = 8, cv::NORM_MINMAX = 32 }
enum | cv::RotateFlags { cv::ROTATE_90_CLOCKWISE = 0, cv::ROTATE_180 = 1, cv::ROTATE_90_COUNTERCLOCKWISE = 2 }

## Functions
void | cv::absdiff (InputArray src1, InputArray src2, OutputArray dst)
| Calculates the per-element absolute difference between two arrays or between an array and a scalar. More...
void | cv::add (InputArray src1, InputArray src2, OutputArray dst, InputArray mask=noArray(), int dtype=-1)
| Calculates the per-element sum of two arrays or an array and a scalar. More...
void | cv::addWeighted (InputArray src1, double alpha, InputArray src2, double beta, double gamma, OutputArray dst, int dtype=-1)
| Calculates the weighted sum of two arrays. More...
void | cv::batchDistance (InputArray src1, InputArray src2, OutputArray dist, int dtype, OutputArray nidx, int normType=NORM_L2, int K=0, InputArray mask=noArray(), int update=0, bool crosscheck=false)
| naive nearest neighbor finder More...
void | cv::bitwise_and (InputArray src1, InputArray src2, OutputArray dst, InputArray mask=noArray())
| computes bitwise conjunction of the two arrays (dst = src1 & src2) Calculates the per-element bit-wise conjunction of two arrays or an array and a scalar. More...
void | cv::bitwise_not (InputArray src, OutputArray dst, InputArray mask=noArray())
| Inverts every bit of an array. More...
void | cv::bitwise_or (InputArray src1, InputArray src2, OutputArray dst, InputArray mask=noArray())
| Calculates the per-element bit-wise disjunction of two arrays or an array and a scalar. More...
void | cv::bitwise_xor (InputArray src1, InputArray src2, OutputArray dst, InputArray mask=noArray())
| Calculates the per-element bit-wise "exclusive or" operation on two arrays or an array and a scalar. More...
int | cv::borderInterpolate (int p, int len, int borderType)
| Computes the source location of an extrapolated pixel. More...
void | cv::calcCovarMatrix (const Mat *samples, int nsamples, Mat &covar, Mat &mean, int flags, int ctype=CV_64F)
| Calculates the covariance matrix of a set of vectors. More...
void | cv::calcCovarMatrix (InputArray samples, OutputArray covar, InputOutputArray mean, int flags, int ctype=CV_64F)
void | cv::cartToPolar (InputArray x, InputArray y, OutputArray magnitude, OutputArray angle, bool angleInDegrees=false)
| Calculates the magnitude and angle of 2D vectors. More...
bool | cv::checkRange (InputArray a, bool quiet=true, Point *pos=0, double minVal=-DBL_MAX, double maxVal=DBL_MAX)
| Checks every element of an input array for invalid values. More...
void | cv::compare (InputArray src1, InputArray src2, OutputArray dst, int cmpop)
| Performs the per-element comparison of two arrays or an array and scalar value. More...
void | cv::completeSymm (InputOutputArray m, bool lowerToUpper=false)
| Copies the lower or the upper half of a square matrix to its another half. More...
void | cv::convertFp16 (InputArray src, OutputArray dst)
| Converts an array to half precision floating number. More...
void | cv::convertScaleAbs (InputArray src, OutputArray dst, double alpha=1, double beta=0)
| Scales, calculates absolute values, and converts the result to 8-bit. More...
void | cv::copyMakeBorder (InputArray src, OutputArray dst, int top, int bottom, int left, int right, int borderType, const Scalar &value=Scalar())
| Forms a border around an image. More...
int | cv::countNonZero (InputArray src)
| Counts non-zero array elements. More...
void | cv::dct (InputArray src, OutputArray dst, int flags=0)
| Performs a forward or inverse discrete Cosine transform of 1D or 2D array. More...
double | cv::determinant (InputArray mtx)
| Returns the determinant of a square floating-point matrix. More...
void | cv::dft (InputArray src, OutputArray dst, int flags=0, int nonzeroRows=0)
| Performs a forward or inverse Discrete Fourier transform of a 1D or 2D floating-point array. More...
void | cv::divide (InputArray src1, InputArray src2, OutputArray dst, double scale=1, int dtype=-1)
| Performs per-element division of two arrays or a scalar by an array. More...
void | cv::divide (double scale, InputArray src2, OutputArray dst, int dtype=-1)
bool | cv::eigen (InputArray src, OutputArray eigenvalues, OutputArray eigenvectors=noArray())
| Calculates eigenvalues and eigenvectors of a symmetric matrix. More...
void | cv::eigenNonSymmetric (InputArray src, OutputArray eigenvalues, OutputArray eigenvectors)
| Calculates eigenvalues and eigenvectors of a non-symmetric matrix (real eigenvalues only). More...
void | cv::exp (InputArray src, OutputArray dst)
| Calculates the exponent of every array element. More...
void | cv::extractChannel (InputArray src, OutputArray dst, int coi)
| Extracts a single channel from src (coi is 0-based index) More...
void | cv::findNonZero (InputArray src, OutputArray idx)
| Returns the list of locations of non-zero pixels. More...
void | cv::flip (InputArray src, OutputArray dst, int flipCode)
| Flips a 2D array around vertical, horizontal, or both axes. More...
void | cv::gemm (InputArray src1, InputArray src2, double alpha, InputArray src3, double beta, OutputArray dst, int flags=0)
| Performs generalized matrix multiplication. More...
int | cv::getOptimalDFTSize (int vecsize)
| Returns the optimal DFT size for a given vector size. More...
void | cv::hconcat (const Mat *src, size_t nsrc, OutputArray dst)
| Applies horizontal concatenation to given matrices. More...
void | cv::hconcat (InputArray src1, InputArray src2, OutputArray dst)
void | cv::hconcat (InputArrayOfArrays src, OutputArray dst)
void | cv::idct (InputArray src, OutputArray dst, int flags=0)
| Calculates the inverse Discrete Cosine Transform of a 1D or 2D array. More...
void | cv::idft (InputArray src, OutputArray dst, int flags=0, int nonzeroRows=0)
| Calculates the inverse Discrete Fourier Transform of a 1D or 2D array. More...
void | cv::inRange (InputArray src, InputArray lowerb, InputArray upperb, OutputArray dst)
| Checks if array elements lie between the elements of two other arrays. More...
void | cv::insertChannel (InputArray src, InputOutputArray dst, int coi)
| Inserts a single channel to dst (coi is 0-based index) More...
double | cv::invert (InputArray src, OutputArray dst, int flags=DECOMP_LU)
| Finds the inverse or pseudo-inverse of a matrix. More...
void | cv::log (InputArray src, OutputArray dst)
| Calculates the natural logarithm of every array element. More...
void | cv::LUT (InputArray src, InputArray lut, OutputArray dst)
| Performs a look-up table transform of an array. More...
void | cv::magnitude (InputArray x, InputArray y, OutputArray magnitude)
| Calculates the magnitude of 2D vectors. More...
double | cv::Mahalanobis (InputArray v1, InputArray v2, InputArray icovar)
| Calculates the Mahalanobis distance between two vectors. More...
void | cv::max (InputArray src1, InputArray src2, OutputArray dst)
| Calculates per-element maximum of two arrays or an array and a scalar. More...
void | cv::max (const Mat &src1, const Mat &src2, Mat &dst)
void | cv::max (const UMat &src1, const UMat &src2, UMat &dst)
Scalar | cv::mean (InputArray src, InputArray mask=noArray())
| Calculates an average (mean) of array elements. More...
void | cv::meanStdDev (InputArray src, OutputArray mean, OutputArray stddev, InputArray mask=noArray())
void | cv::merge (const Mat *mv, size_t count, OutputArray dst)
| Creates one multi-channel array out of several single-channel ones. More...
void | cv::merge (InputArrayOfArrays mv, OutputArray dst)
void | cv::min (InputArray src1, InputArray src2, OutputArray dst)
| Calculates per-element minimum of two arrays or an array and a scalar. More...
void | cv::min (const Mat &src1, const Mat &src2, Mat &dst)
void | cv::min (const UMat &src1, const UMat &src2, UMat &dst)
void | cv::minMaxIdx (InputArray src, double *minVal, double *maxVal=0, int *minIdx=0, int *maxIdx=0, InputArray mask=noArray())
| Finds the global minimum and maximum in an array. More...
void | cv::minMaxLoc (InputArray src, double *minVal, double *maxVal=0, Point *minLoc=0, Point *maxLoc=0, InputArray mask=noArray())
| Finds the global minimum and maximum in an array. More...
void | cv::minMaxLoc (const SparseMat &a, double *minVal, double *maxVal, int *minIdx=0, int *maxIdx=0)
void | cv::mixChannels (const Mat *src, size_t nsrcs, Mat *dst, size_t ndsts, const int *fromTo, size_t npairs)
| Copies specified channels from input arrays to the specified channels of output arrays. More...
void | cv::mixChannels (InputArrayOfArrays src, InputOutputArrayOfArrays dst, const int *fromTo, size_t npairs)
void | cv::mixChannels (InputArrayOfArrays src, InputOutputArrayOfArrays dst, const std::vector< int > &fromTo)
void | cv::mulSpectrums (InputArray a, InputArray b, OutputArray c, int flags, bool conjB=false)
| Performs the per-element multiplication of two Fourier spectrums. More...
void | cv::multiply (InputArray src1, InputArray src2, OutputArray dst, double scale=1, int dtype=-1)
| Calculates the per-element scaled product of two arrays. More...
void | cv::mulTransposed (InputArray src, OutputArray dst, bool aTa, InputArray delta=noArray(), double scale=1, int dtype=-1)
| Calculates the product of a matrix and its transposition. More...
double | cv::norm (InputArray src1, int normType=NORM_L2, InputArray mask=noArray())
| Calculates the absolute norm of an array. More...
double | cv::norm (InputArray src1, InputArray src2, int normType=NORM_L2, InputArray mask=noArray())
| Calculates an absolute difference norm or a relative difference norm. More...
double | cv::norm (const SparseMat &src, int normType)
void | cv::normalize (InputArray src, InputOutputArray dst, double alpha=1, double beta=0, int norm_type=NORM_L2, int dtype=-1, InputArray mask=noArray())
| Normalizes the norm or value range of an array. More...
void | cv::normalize (const SparseMat &src, SparseMat &dst, double alpha, int normType)
void | cv::patchNaNs (InputOutputArray a, double val=0)
| converts NaN's to the given number More...
void | cv::PCABackProject (InputArray data, InputArray mean, InputArray eigenvectors, OutputArray result)
void | cv::PCACompute (InputArray data, InputOutputArray mean, OutputArray eigenvectors, int maxComponents=0)
void | cv::PCACompute (InputArray data, InputOutputArray mean, OutputArray eigenvectors, double retainedVariance)
void | cv::PCAProject (InputArray data, InputArray mean, InputArray eigenvectors, OutputArray result)
void | cv::perspectiveTransform (InputArray src, OutputArray dst, InputArray m)
| Performs the perspective matrix transformation of vectors. More...
void | cv::phase (InputArray x, InputArray y, OutputArray angle, bool angleInDegrees=false)
| Calculates the rotation angle of 2D vectors. More...
void | cv::polarToCart (InputArray magnitude, InputArray angle, OutputArray x, OutputArray y, bool angleInDegrees=false)
| Calculates x and y coordinates of 2D vectors from their magnitude and angle. More...
void | cv::pow (InputArray src, double power, OutputArray dst)
| Raises every array element to a power. More...
double | cv::PSNR (InputArray src1, InputArray src2)
| Computes the Peak Signal-to-Noise Ratio (PSNR) image quality metric. More...
void | cv::randn (InputOutputArray dst, InputArray mean, InputArray stddev)
| Fills the array with normally distributed random numbers. More...
void | cv::randShuffle (InputOutputArray dst, double iterFactor=1., RNG *rng=0)
| Shuffles the array elements randomly. More...
void | cv::randu (InputOutputArray dst, InputArray low, InputArray high)
| Generates a single uniformly-distributed random number or an array of random numbers. More...
void | cv::reduce (InputArray src, OutputArray dst, int dim, int rtype, int dtype=-1)
| Reduces a matrix to a vector. More...
void | cv::repeat (InputArray src, int ny, int nx, OutputArray dst)
| Fills the output array with repeated copies of the input array. More...
Mat | cv::repeat (const Mat &src, int ny, int nx)
void | cv::rotate (InputArray src, OutputArray dst, int rotateCode)
| Rotates a 2D array in multiples of 90 degrees. The function cv::rotate rotates the array in one of three different ways: Rotate by 90 degrees clockwise (rotateCode = ROTATE_90_CLOCKWISE). Rotate by 180 degrees clockwise (rotateCode = ROTATE_180). Rotate by 270 degrees clockwise (rotateCode = ROTATE_90_COUNTERCLOCKWISE). More...
void | cv::scaleAdd (InputArray src1, double alpha, InputArray src2, OutputArray dst)
| Calculates the sum of a scaled array and another array. More...
void | cv::setIdentity (InputOutputArray mtx, const Scalar &s=Scalar(1))
| Initializes a scaled identity matrix. More...
void | cv::setRNGSeed (int seed)
| Sets state of default random number generator. More...
bool | cv::solve (InputArray src1, InputArray src2, OutputArray dst, int flags=DECOMP_LU)
| Solves one or more linear systems or least-squares problems. More...
int | cv::solveCubic (InputArray coeffs, OutputArray roots)
| Finds the real roots of a cubic equation. More...
double | cv::solvePoly (InputArray coeffs, OutputArray roots, int maxIters=300)
| Finds the real or complex roots of a polynomial equation. More...
void | cv::sort (InputArray src, OutputArray dst, int flags)
| Sorts each row or each column of a matrix. More...
void | cv::sortIdx (InputArray src, OutputArray dst, int flags)
| Sorts each row or each column of a matrix. More...
void | cv::split (const Mat &src, Mat *mvbegin)
| Divides a multi-channel array into several single-channel arrays. More...
void | cv::split (InputArray m, OutputArrayOfArrays mv)
void | cv::sqrt (InputArray src, OutputArray dst)
| Calculates a square root of array elements. More...
void | cv::subtract (InputArray src1, InputArray src2, OutputArray dst, InputArray mask=noArray(), int dtype=-1)
| Calculates the per-element difference between two arrays or array and a scalar. More...
Scalar | cv::sum (InputArray src)
| Calculates the sum of array elements. More...
void | cv::SVBackSubst (InputArray w, InputArray u, InputArray vt, InputArray rhs, OutputArray dst)
void | cv::SVDecomp (InputArray src, OutputArray w, OutputArray u, OutputArray vt, int flags=0)
RNG & | cv::theRNG ()
| Returns the default random number generator. More...
Scalar | cv::trace (InputArray mtx)
| Returns the trace of a matrix. More...
void | cv::transform (InputArray src, OutputArray dst, InputArray m)
| Performs the matrix transformation of every array element. More...
void | cv::transpose (InputArray src, OutputArray dst)
| Transposes a matrix. More...
void | cv::vconcat (const Mat *src, size_t nsrc, OutputArray dst)
| Applies vertical concatenation to given matrices. More...
void | cv::vconcat (InputArray src1, InputArray src2, OutputArray dst)
void | cv::vconcat (InputArrayOfArrays src, OutputArray dst)

## Detailed Description

## Enumeration Type Documentation

## ◆ BorderTypes

enum cv::BorderTypes

Various border types, image boundaries are denoted with `|`

See also
  borderInterpolate, copyMakeBorder

Enumerator
BORDER_CONSTANT | `iiiiii|abcdefgh|iiiiiii` with some specified `i`
BORDER_REPLICATE | `aaaaaa|abcdefgh|hhhhhhh`
BORDER_REFLECT | `fedcba|abcdefgh|hgfedcb`
BORDER_WRAP | `cdefgh|abcdefgh|abcdefg`
BORDER_REFLECT_101 | `gfedcb|abcdefgh|gfedcba`
BORDER_TRANSPARENT | `uvwxyz|abcdefgh|ijklmno`
BORDER_REFLECT101 | same as BORDER_REFLECT_101
BORDER_DEFAULT | same as BORDER_REFLECT_101
BORDER_ISOLATED | do not look outside of ROI

## ◆ CmpTypes

enum cv::CmpTypes

comparison types

Enumerator
CMP_EQ | src1 is equal to src2.
CMP_GT | src1 is greater than src2.
CMP_GE | src1 is greater than or equal to src2.
CMP_LT | src1 is less than src2.
CMP_LE | src1 is less than or equal to src2.
CMP_NE | src1 is unequal to src2.

## ◆ DecompTypes

enum cv::DecompTypes

matrix decomposition types

Enumerator
DECOMP_LU | Gaussian elimination with the optimal pivot element chosen.
DECOMP_SVD | singular value decomposition (SVD) method; the system can be over-defined and/or the matrix src1 can be singular
DECOMP_EIG | eigenvalue decomposition; the matrix src1 must be symmetrical
DECOMP_CHOLESKY | Cholesky \(LL^T\) factorization; the matrix src1 must be symmetrical and positively defined
DECOMP_QR | QR factorization; the system can be over-defined and/or the matrix src1 can be singular
DECOMP_NORMAL | while all the previous flags are mutually exclusive, this flag can be used together with any of the previous; it means that the normal equations \(\texttt{src1}^T\cdot\texttt{src1}\cdot\texttt{dst}=\texttt{src1}^T\texttt{src2}\) are solved instead of the original system \(\texttt{src1}\cdot\texttt{dst}=\texttt{src2}\)

## ◆ DftFlags

enum cv::DftFlags

Enumerator
DFT_INVERSE | performs an inverse 1D or 2D transform instead of the default forward transform.
DFT_SCALE | scales the result: divide it by the number of array elements. Normally, it is combined with DFT_INVERSE.
DFT_ROWS | performs a forward or inverse transform of every individual row of the input matrix; this flag enables you to transform multiple vectors simultaneously and can be used to decrease the overhead (which is sometimes several times larger than the processing itself) to perform 3D and higher-dimensional transformations and so forth.
DFT_COMPLEX_OUTPUT | performs a forward transformation of 1D or 2D real array; the result, though being a complex array, has complex-conjugate symmetry (CCS, see the function description below for details), and such an array can be packed into a real array of the same size as input, which is the fastest option and which is what the function does by default; however, you may wish to get a full complex array (for simpler spectrum analysis, and so on) - pass the flag to enable the function to produce a full-size complex output array.
DFT_REAL_OUTPUT | performs an inverse transformation of a 1D or 2D complex array; the result is normally a complex array of the same size, however, if the input array has conjugate-complex symmetry (for example, it is a result of forward transformation with DFT_COMPLEX_OUTPUT flag), the output is a real array; while the function itself does not check whether the input is symmetrical or not, you can pass the flag and then the function will assume the symmetry and produce the real output array (note that when the input is packed into a real array and inverse transformation is executed, the function treats the input as a packed complex-conjugate symmetrical array, and the output will also be a real array).
DFT_COMPLEX_INPUT | specifies that input is complex input. If this flag is set, the input must have 2 channels. On the other hand, for backwards compatibility reason, if input has 2 channels, input is already considered complex.
DCT_INVERSE | performs an inverse 1D or 2D transform instead of the default forward transform.
DCT_ROWS | performs a forward or inverse transform of every individual row of the input matrix. This flag enables you to transform multiple vectors simultaneously and can be used to decrease the overhead (which is sometimes several times larger than the processing itself) to perform 3D and higher-dimensional transforms and so forth.

## ◆ GemmFlags

enum cv::GemmFlags

generalized matrix multiplication flags

Enumerator
GEMM_1_T | transposes src1
GEMM_2_T | transposes src2
GEMM_3_T | transposes src3

## ◆ NormTypes

enum cv::NormTypes

norm types

src1 and src2 denote input arrays.

Enumerator
NORM_INF | \[ norm = \forkthree {\|\texttt{src1}\|_{L_{\infty}} = \max _I | \texttt{src1} (I)|}{if \(\texttt{normType} = \texttt{NORM_INF}\) } {\|\texttt{src1}-\texttt{src2}\|_{L_{\infty}} = \max _I | \texttt{src1} (I) - \texttt{src2} (I)|}{if \(\texttt{normType} = \texttt{NORM_INF}\) } {\frac{\|\texttt{src1}-\texttt{src2}\|_{L_{\infty}} }{\|\texttt{src2}\|_{L_{\infty}} }}{if \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_INF}\) } \]
NORM_L1 | \[ norm = \forkthree {\| \texttt{src1} \| _{L_1} = \sum _I | \texttt{src1} (I)|}{if \(\texttt{normType} = \texttt{NORM_L1}\)} { \| \texttt{src1} - \texttt{src2} \| _{L_1} = \sum _I | \texttt{src1} (I) - \texttt{src2} (I)|}{if \(\texttt{normType} = \texttt{NORM_L1}\) } { \frac{\|\texttt{src1}-\texttt{src2}\|_{L_1} }{\|\texttt{src2}\|_{L_1}} }{if \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_L1}\) } \]
NORM_L2 | \[ norm = \forkthree { \| \texttt{src1} \| _{L_2} = \sqrt{\sum_I \texttt{src1}(I)^2} }{if \(\texttt{normType} = \texttt{NORM_L2}\) } { \| \texttt{src1} - \texttt{src2} \| _{L_2} = \sqrt{\sum_I (\texttt{src1}(I) - \texttt{src2}(I))^2} }{if \(\texttt{normType} = \texttt{NORM_L2}\) } { \frac{\|\texttt{src1}-\texttt{src2}\|_{L_2} }{\|\texttt{src2}\|_{L_2}} }{if \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_L2}\) } \]
NORM_L2SQR | \[ norm = \forkthree { \| \texttt{src1} \| _{L_2} ^{2} = \sum_I \texttt{src1}(I)^2} {if \(\texttt{normType} = \texttt{NORM_L2SQR}\)} { \| \texttt{src1} - \texttt{src2} \| _{L_2} ^{2} = \sum_I (\texttt{src1}(I) - \texttt{src2}(I))^2 }{if \(\texttt{normType} = \texttt{NORM_L2SQR}\) } { \left(\frac{\|\texttt{src1}-\texttt{src2}\|_{L_2} }{\|\texttt{src2}\|_{L_2}}\right)^2 }{if \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_L2}\) } \]
NORM_HAMMING | In the case of one input array, calculates the Hamming distance of the array from zero, In the case of two input arrays, calculates the Hamming distance between the arrays.
NORM_HAMMING2 | Similar to NORM_HAMMING, but in the calculation, each two bits of the input sequence will be added and treated as a single bit to be used in the same calculation as NORM_HAMMING.
NORM_TYPE_MASK | bit-mask which can be used to separate norm type from norm flags
NORM_RELATIVE | flag
NORM_MINMAX | flag

## ◆ RotateFlags

enum cv::RotateFlags

Enumerator
ROTATE_90_CLOCKWISE | Rotate 90 degrees clockwise.
ROTATE_180 | Rotate 180 degrees clockwise.
ROTATE_90_COUNTERCLOCKWISE | Rotate 270 degrees clockwise.

## Function Documentation

## ◆ absdiff()

void cv::absdiff | ( | InputArray | src1,
|  | InputArray | src2,
|  | OutputArray | dst
| ) |  |

Calculates the per-element absolute difference between two arrays or between an array and a scalar.

The function cv::absdiff calculates: Absolute difference between two arrays when they have the same size and type:

\[\texttt{dst}(I) = \texttt{saturate} (| \texttt{src1}(I) - \texttt{src2}(I)|)\]

Absolute difference between an array and a scalar when the second array is constructed from Scalar or has as many elements as the number of channels in `src1`:

\[\texttt{dst}(I) = \texttt{saturate} (| \texttt{src1}(I) - \texttt{src2} |)\]

Absolute difference between a scalar and an array when the first array is constructed from Scalar or has as many elements as the number of channels in `src2`:

\[\texttt{dst}(I) = \texttt{saturate} (| \texttt{src1} - \texttt{src2}(I) |)\]

where I is a multi-dimensional index of array elements. In case of multi-channel arrays, each channel is processed independently.

Note
  Saturation is not applied when the arrays have the depth CV_32S. You may even get a negative value in the case of overflow.

Parameters

  src1 | first input array or a scalar.
  src2 | second input array or a scalar.
  dst | output array that has the same size and type as input arrays.

See also
  cv::abs(const Mat&)

## ◆ add()

void cv::add | ( | InputArray | src1,
|  | InputArray | src2,
|  | OutputArray | dst,
|  | InputArray | mask = `noArray()`,
|  | int | dtype = `-1`
| ) |  |

Calculates the per-element sum of two arrays or an array and a scalar.

The function add calculates:

- Sum of two arrays when both input arrays have the same size and the same number of channels:

  \[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1}(I) + \texttt{src2}(I)) \quad \texttt{if mask}(I) \ne0\]

- Sum of an array and a scalar when src2 is constructed from Scalar or has the same number of elements as `src1.channels()`:

  \[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1}(I) + \texttt{src2} ) \quad \texttt{if mask}(I) \ne0\]

- Sum of a scalar and an array when src1 is constructed from Scalar or has the same number of elements as `src2.channels()`:

  \[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1} + \texttt{src2}(I) ) \quad \texttt{if mask}(I) \ne0\]

  where `I` is a multi-dimensional index of array elements. In case of multi-channel arrays, each channel is processed independently.

The first function in the list above can be replaced with matrix expressions:

dst = src1 + src2;
dst += src1; // equivalent to add(dst, src1, dst);

The input arrays and the output array can all have the same or different depths. For example, you can add a 16-bit unsigned array to a 8-bit signed array and store the sum as a 32-bit floating-point array. Depth of the output array is determined by the dtype parameter. In the second and third cases above, as well as in the first case, when src1.depth() == src2.depth(), dtype can be set to the default -1. In this case, the output array will have the same depth as the input array, be it src1, src2 or both.

Note
  Saturation is not applied when the output array has the depth CV_32S. You may even get result of an incorrect sign in the case of overflow.

Parameters

  src1 | first input array or a scalar.
  src2 | second input array or a scalar.
  dst | output array that has the same size and number of channels as the input array(s); the depth is defined by dtype or src1/src2.
  mask | optional operation mask - 8-bit single channel array, that specifies elements of the output array to be changed.
  dtype | optional depth of the output array (see the discussion below).

See also
  subtract, addWeighted, scaleAdd, Mat::convertTo

Examples:
  shape_example.cpp.

## ◆ addWeighted()

void cv::addWeighted | ( | InputArray | src1,
|  | double | alpha,
|  | InputArray | src2,
|  | double | beta,
|  | double | gamma,
|  | OutputArray | dst,
|  | int | dtype = `-1`
| ) |  |

Calculates the weighted sum of two arrays.

The function addWeighted calculates the weighted sum of two arrays as follows:

\[\texttt{dst} (I)= \texttt{saturate} ( \texttt{src1} (I)* \texttt{alpha} + \texttt{src2} (I)* \texttt{beta} + \texttt{gamma} )\]

where I is a multi-dimensional index of array elements. In case of multi-channel arrays, each channel is processed independently. The function can be replaced with a matrix expression:

dst = src1*alpha + src2*beta + gamma;

Note
  Saturation is not applied when the output array has the depth CV_32S. You may even get result of an incorrect sign in the case of overflow.

Parameters

  src1 | first input array.
  alpha | weight of the first array elements.
  src2 | second input array of the same size and channel number as src1.
  beta | weight of the second array elements.
  gamma | scalar added to each sum.
  dst | output array that has the same size and number of channels as the input arrays.
  dtype | optional depth of the output array; when both input arrays have the same depth, dtype can be set to -1, which will be equivalent to src1.depth().

See also
  add, subtract, scaleAdd, Mat::convertTo

Examples:
  AddingImagesTrackbar.cpp, and Sobel_Demo.cpp.

## ◆ batchDistance()

void cv::batchDistance | ( | InputArray | src1,
|  | InputArray | src2,
|  | OutputArray | dist,
|  | int | dtype,
|  | OutputArray | nidx,
|  | int | normType = `NORM_L2`,
|  | int | K = `0`,
|  | InputArray | mask = `noArray()`,
|  | int | update = `0`,
|  | bool | crosscheck = `false`
| ) |  |

naive nearest neighbor finder

see http://en.wikipedia.org/wiki/Nearest_neighbor_search

Todo:
  document

## ◆ bitwise_and()

void cv::bitwise_and | ( | InputArray | src1,
|  | InputArray | src2,
|  | OutputArray | dst,
|  | InputArray | mask = `noArray()`
| ) |  |

computes bitwise conjunction of the two arrays (dst = src1 & src2) Calculates the per-element bit-wise conjunction of two arrays or an array and a scalar.

The function cv::bitwise_and calculates the per-element bit-wise logical conjunction for: Two arrays when src1 and src2 have the same size:

\[\texttt{dst} (I) = \texttt{src1} (I) \wedge \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\]

An array and a scalar when src2 is constructed from Scalar or has the same number of elements as `src1.channels()`:

\[\texttt{dst} (I) = \texttt{src1} (I) \wedge \texttt{src2} \quad \texttt{if mask} (I) \ne0\]

A scalar and an array when src1 is constructed from Scalar or has the same number of elements as `src2.channels()`:

\[\texttt{dst} (I) = \texttt{src1} \wedge \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\]

In case of floating-point arrays, their machine-specific bit representations (usually IEEE754-compliant) are used for the operation. In case of multi-channel arrays, each channel is processed independently. In the second and third cases above, the scalar is first converted to the array type.

Parameters

  src1 | first input array or a scalar.
  src2 | second input array or a scalar.
  dst | output array that has the same size and type as the input arrays.
  mask | optional operation mask, 8-bit single channel array, that specifies elements of the output array to be changed.

## ◆ bitwise_not()

void cv::bitwise_not | ( | InputArray | src,
|  | OutputArray | dst,
|  | InputArray | mask = `noArray()`
| ) |  |

Inverts every bit of an array.

The function cv::bitwise_not calculates per-element bit-wise inversion of the input array:

\[\texttt{dst} (I) = \neg \texttt{src} (I)\]

In case of a floating-point input array, its machine-specific bit representation (usually IEEE754-compliant) is used for the operation. In case of multi-channel arrays, each channel is processed independently.

Parameters

  src | input array.
  dst | output array that has the same size and type as the input array.
  mask | optional operation mask, 8-bit single channel array, that specifies elements of the output array to be changed.

Examples:
  camshiftdemo.cpp.

## ◆ bitwise_or()

void cv::bitwise_or | ( | InputArray | src1,
|  | InputArray | src2,
|  | OutputArray | dst,
|  | InputArray | mask = `noArray()`
| ) |  |

Calculates the per-element bit-wise disjunction of two arrays or an array and a scalar.

The function cv::bitwise_or calculates the per-element bit-wise logical disjunction for: Two arrays when src1 and src2 have the same size:

\[\texttt{dst} (I) = \texttt{src1} (I) \vee \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\]

An array and a scalar when src2 is constructed from Scalar or has the same number of elements as `src1.channels()`:

\[\texttt{dst} (I) = \texttt{src1} (I) \vee \texttt{src2} \quad \texttt{if mask} (I) \ne0\]

A scalar and an array when src1 is constructed from Scalar or has the same number of elements as `src2.channels()`:

\[\texttt{dst} (I) = \texttt{src1} \vee \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\]

In case of floating-point arrays, their machine-specific bit representations (usually IEEE754-compliant) are used for the operation. In case of multi-channel arrays, each channel is processed independently. In the second and third cases above, the scalar is first converted to the array type.

Parameters

  src1 | first input array or a scalar.
  src2 | second input array or a scalar.
  dst | output array that has the same size and type as the input arrays.
  mask | optional operation mask, 8-bit single channel array, that specifies elements of the output array to be changed.

## ◆ bitwise_xor()

void cv::bitwise_xor | ( | InputArray | src1,
|  | InputArray | src2,
|  | OutputArray | dst,
|  | InputArray | mask = `noArray()`
| ) |  |

Calculates the per-element bit-wise "exclusive or" operation on two arrays or an array and a scalar.

The function cv::bitwise_xor calculates the per-element bit-wise logical "exclusive-or" operation for: Two arrays when src1 and src2 have the same size:

\[\texttt{dst} (I) = \texttt{src1} (I) \oplus \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\]

An array and a scalar when src2 is constructed from Scalar or has the same number of elements as `src1.channels()`:

\[\texttt{dst} (I) = \texttt{src1} (I) \oplus \texttt{src2} \quad \texttt{if mask} (I) \ne0\]

A scalar and an array when src1 is constructed from Scalar or has the same number of elements as `src2.channels()`:

\[\texttt{dst} (I) = \texttt{src1} \oplus \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\]

In case of floating-point arrays, their machine-specific bit representations (usually IEEE754-compliant) are used for the operation. In case of multi-channel arrays, each channel is processed independently. In the 2nd and 3rd cases above, the scalar is first converted to the array type.

Parameters

  src1 | first input array or a scalar.
  src2 | second input array or a scalar.
  dst | output array that has the same size and type as the input arrays.
  mask | optional operation mask, 8-bit single channel array, that specifies elements of the output array to be changed.

## ◆ borderInterpolate()

int cv::borderInterpolate | ( | int | p,
|  | int | len,
|  | int | borderType
| ) |  |

Computes the source location of an extrapolated pixel.

The function computes and returns the coordinate of a donor pixel corresponding to the specified extrapolated pixel when using the specified extrapolation border mode. For example, if you use cv::BORDER_WRAP mode in the horizontal direction, cv::BORDER_REFLECT_101 in the vertical direction and want to compute value of the "virtual" pixel Point(-5, 100) in a floating-point image img , it looks like:

float val = img.at<float>(borderInterpolate(100, img.rows, cv::BORDER_REFLECT_101),
borderInterpolate(-5, img.cols, cv::BORDER_WRAP));

Normally, the function is not called directly. It is used inside filtering functions and also in copyMakeBorder.

Parameters

  p | 0-based coordinate of the extrapolated pixel along one of the axes, likely <0 or >= len
  len | Length of the array along the corresponding axis.
  borderType | Border type, one of the BorderTypes, except for BORDER_TRANSPARENT and BORDER_ISOLATED . When borderType==BORDER_CONSTANT , the function always returns -1, regardless of p and len.

See also
  copyMakeBorder

## ◆ calcCovarMatrix() [1/2]

void cv::calcCovarMatrix | ( | const Mat * | samples,
|  | int | nsamples,
|  | Mat & | covar,
|  | Mat & | mean,
|  | int | flags,
|  | int | ctype = `CV_64F`
| ) |  |

Calculates the covariance matrix of a set of vectors.

The function cv::calcCovarMatrix calculates the covariance matrix and, optionally, the mean vector of the set of input vectors.

Parameters

  samples | samples stored as separate matrices
  nsamples | number of samples
  covar | output covariance matrix of the type ctype and square size.
  mean | input or output (depending on the flags) array as the average value of the input vectors.
  flags | operation flags as a combination of CovarFlags
  ctype | type of the matrixl; it equals 'CV_64F' by default.

See also
  PCA, mulTransposed, Mahalanobis

Todo:
  InputArrayOfArrays

## ◆ calcCovarMatrix() [2/2]

void cv::calcCovarMatrix | ( | InputArray | samples,
|  | OutputArray | covar,
|  | InputOutputArray | mean,
|  | int | flags,
|  | int | ctype = `CV_64F`
| ) |  |

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note
  use COVAR_ROWS or COVAR_COLS flag

Parameters

  samples | samples stored as rows/columns of a single matrix.
  covar | output covariance matrix of the type ctype and square size.
  mean | input or output (depending on the flags) array as the average value of the input vectors.
  flags | operation flags as a combination of CovarFlags
  ctype | type of the matrixl; it equals 'CV_64F' by default.

## ◆ cartToPolar()

void cv::cartToPolar | ( | InputArray | x,
|  | InputArray | y,
|  | OutputArray | magnitude,
|  | OutputArray | angle,
|  | bool | angleInDegrees = `false`
| ) |  |

Calculates the magnitude and angle of 2D vectors.

The function cv::cartToPolar calculates either the magnitude, angle, or both for every 2D vector (x(I),y(I)):

\[\begin{array}{l} \texttt{magnitude} (I)= \sqrt{\texttt{x}(I)^2+\texttt{y}(I)^2} , \\ \texttt{angle} (I)= \texttt{atan2} ( \texttt{y} (I), \texttt{x} (I))[ \cdot180 / \pi ] \end{array}\]

The angles are calculated with accuracy about 0.3 degrees. For the point (0,0), the angle is set to 0.

Parameters

  x | array of x-coordinates; this must be a single-precision or double-precision floating-point array.
  y | array of y-coordinates, that must have the same size and same type as x.
  magnitude | output array of magnitudes of the same size and type as x.
  angle | output array of angles that has the same size and type as x; the angles are measured in radians (from 0 to 2*Pi) or in degrees (0 to 360 degrees).
  angleInDegrees | a flag, indicating whether the angles are measured in radians (which is by default), or in degrees.

See also
  Sobel, Scharr

## ◆ checkRange()

bool cv::checkRange | ( | InputArray | a,
|  | bool | quiet = `true`,
|  | Point * | pos = `0`,
|  | double | minVal = `-DBL_MAX`,
|  | double | maxVal = `DBL_MAX`
| ) |  |

Checks every element of an input array for invalid values.

The function cv::checkRange checks that every array element is neither NaN nor infinite. When minVal > -DBL_MAX and maxVal < DBL_MAX, the function also checks that each value is between minVal and maxVal. In case of multi-channel arrays, each channel is processed independently. If some values are out of range, position of the first outlier is stored in pos (when pos != NULL). Then, the function either returns false (when quiet=true) or throws an exception.

Parameters

  a | input array.
  quiet | a flag, indicating whether the functions quietly return false when the array elements are out of range or they throw an exception.
  pos | optional output parameter, when not NULL, must be a pointer to array of src.dims elements.
  minVal | inclusive lower boundary of valid values range.
  maxVal | exclusive upper boundary of valid values range.

## ◆ compare()

void cv::compare | ( | InputArray | src1,
|  | InputArray | src2,
|  | OutputArray | dst,
|  | int | cmpop
| ) |  |

Performs the per-element comparison of two arrays or an array and scalar value.

The function compares: Elements of two arrays when src1 and src2 have the same size:

\[\texttt{dst} (I) = \texttt{src1} (I) \,\texttt{cmpop}\, \texttt{src2} (I)\]

Elements of src1 with a scalar src2 when src2 is constructed from Scalar or has a single element:

\[\texttt{dst} (I) = \texttt{src1}(I) \,\texttt{cmpop}\, \texttt{src2}\]

src1 with elements of src2 when src1 is constructed from Scalar or has a single element:

\[\texttt{dst} (I) = \texttt{src1} \,\texttt{cmpop}\, \texttt{src2} (I)\]

When the comparison result is true, the corresponding element of output array is set to 255. The comparison operations can be replaced with the equivalent matrix expressions:

Mat dst1 = src1 >= src2;
Mat dst2 = src1 < 8;
...

Parameters

  src1 | first input array or a scalar; when it is an array, it must have a single channel.
  src2 | second input array or a scalar; when it is an array, it must have a single channel.
  dst | output array of type ref CV_8U that has the same size and the same number of channels as the input arrays.
  cmpop | a flag, that specifies correspondence between the arrays (cv::CmpTypes)

See also
  checkRange, min, max, threshold

## ◆ completeSymm()

void cv::completeSymm | ( | InputOutputArray | m,
|  | bool | lowerToUpper = `false`
| ) |  |

Copies the lower or the upper half of a square matrix to its another half.

The function cv::completeSymm copies the lower or the upper half of a square matrix to its another half. The matrix diagonal remains unchanged:

- \(\texttt{m}_{ij}=\texttt{m}_{ji}\) for \(i > j\) if lowerToUpper=false
- \(\texttt{m}_{ij}=\texttt{m}_{ji}\) for \(i < j\) if lowerToUpper=true

Parameters

  m | input-output floating-point square matrix.
  lowerToUpper | operation flag; if true, the lower half is copied to the upper half. Otherwise, the upper half is copied to the lower half.

See also
  flip, transpose

## ◆ convertFp16()

void cv::convertFp16 | ( | InputArray | src,
|  | OutputArray | dst
| ) |  |

Converts an array to half precision floating number.

This function converts FP32 (single precision floating point) from/to FP16 (half precision floating point). CV_16S format is used to represent FP16 data. 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 CV_16S to represent the bit depth. If the input array is neither of them, the function will raise an error. The format of half precision floating point is defined in IEEE 754-2008.

Parameters

  src | input array.
  dst | output array.

## ◆ convertScaleAbs()

void cv::convertScaleAbs | ( | InputArray | src,
|  | OutputArray | dst,
|  | double | alpha = `1`,
|  | double | beta = `0`
| ) |  |

Scales, calculates absolute values, and converts the result to 8-bit.

On each element of the input array, the function convertScaleAbs performs three operations sequentially: scaling, taking an absolute value, conversion to an unsigned 8-bit type:

\[\texttt{dst} (I)= \texttt{saturate\_cast<uchar>} (| \texttt{src} (I)* \texttt{alpha} + \texttt{beta} |)\]

In case of multi-channel arrays, the function processes each channel independently. When the output is not 8-bit, the operation can be emulated by calling the Mat::convertTo method (or by using matrix expressions) and then by calculating an absolute value of the result. For example:

Mat_<float> A(30,30);
randu(A, Scalar(-100), Scalar(100));
Mat_<float> B = A*5 + 3;
B = abs(B);
// Mat_<float> B = abs(A*5+3) will also do the job,
// but it will allocate a temporary matrix

Parameters

  src | input array.
  dst | output array.
  alpha | optional scale factor.
  beta | optional delta added to the scaled values.

See also
  Mat::convertTo, cv::abs(const Mat&)

Examples:
  laplace.cpp, and Sobel_Demo.cpp.

## ◆ copyMakeBorder()

void cv::copyMakeBorder | ( | InputArray | src,
|  | OutputArray | dst,
|  | int | top,
|  | int | bottom,
|  | int | left,
|  | int | right,
|  | int | borderType,
|  | const Scalar & | value = `Scalar()`
| ) |  |

Forms a border around an image.

The function copies the source image into the middle of the destination image. The areas to the left, to the right, above and below the copied source image will be filled with extrapolated pixels. This is not what filtering functions based on it do (they extrapolate pixels on-fly), but what other more complex functions, including your own, may do to simplify image boundary handling.

The function supports the mode when src is already in the middle of dst . In this case, the function does not copy src itself but simply constructs the border, for example:

// let border be the same in all directions
int border=2;
// constructs a larger image to fit both the image and the border
Mat gray_buf(rgb.rows + border*2, rgb.cols + border*2, rgb.depth());
// select the middle part of it w/o copying data
Mat gray(gray_canvas, Rect(border, border, rgb.cols, rgb.rows));
// convert image from RGB to grayscale
cvtColor(rgb, gray, COLOR_RGB2GRAY);
// form a border in-place
copyMakeBorder(gray, gray_buf, border, border,
border, border, BORDER_REPLICATE);
// now do some custom filtering ...
...

Note
  When the source image is a part (ROI) of a bigger image, the function will try to use the pixels outside of the ROI to form a border. To disable this feature and always do extrapolation, as if src was not a ROI, use borderType | BORDER_ISOLATED.

Parameters

  src | Source image.
  dst | Destination image of the same type as src and the size Size(src.cols+left+right, src.rows+top+bottom) .
  top |
  bottom |
  left |
  right | Parameter specifying how many pixels in each direction from the source image rectangle to extrapolate. For example, top=1, bottom=1, left=1, right=1 mean that 1 pixel-wide border needs to be built.
  borderType | Border type. See borderInterpolate for details.
  value | Border value if borderType==BORDER_CONSTANT .

See also
  borderInterpolate

Examples:
  copyMakeBorder_demo.cpp.

## ◆ countNonZero()

int cv::countNonZero | ( | InputArray | src | ) |

Counts non-zero array elements.

The function returns the number of non-zero elements in src :

\[\sum _{I: \; \texttt{src} (I) \ne0 } 1\]

Parameters

  src | single-channel array.

See also
  mean, meanStdDev, norm, minMaxLoc, calcCovarMatrix

## ◆ dct()

void cv::dct | ( | InputArray | src,
|  | OutputArray | dst,
|  | int | flags = `0`
| ) |  |

Performs a forward or inverse discrete Cosine transform of 1D or 2D array.

The function cv::dct performs a forward or inverse discrete Cosine transform (DCT) of a 1D or 2D floating-point array:

- Forward Cosine transform of a 1D vector of N elements:

  \[Y = C^{(N)} \cdot X\]

  where

  \[C^{(N)}_{jk}= \sqrt{\alpha_j/N} \cos \left ( \frac{\pi(2k+1)j}{2N} \right )\]

  and \(\alpha_0=1\), \(\alpha_j=2\) for j > 0.
- Inverse Cosine transform of a 1D vector of N elements:

  \[X = \left (C^{(N)} \right )^{-1} \cdot Y = \left (C^{(N)} \right )^T \cdot Y\]

  (since \(C^{(N)}\) is an orthogonal matrix, \(C^{(N)} \cdot \left(C^{(N)}\right)^T = I\) )
- Forward 2D Cosine transform of M x N matrix:

  \[Y = C^{(N)} \cdot X \cdot \left (C^{(N)} \right )^T\]

- Inverse 2D Cosine transform of M x N matrix:

  \[X = \left (C^{(N)} \right )^T \cdot X \cdot C^{(N)}\]

The function chooses the mode of operation by looking at the flags and size of the input array:

- If (flags & DCT_INVERSE) == 0 , the function does a forward 1D or 2D transform. Otherwise, it is an inverse 1D or 2D transform.
- If (flags & DCT_ROWS) != 0 , the function performs a 1D transform of each row.
- If the array is a single column or a single row, the function performs a 1D transform.
- If none of the above is true, the function performs a 2D transform.

Note
  Currently dct supports even-size arrays (2, 4, 6 ...). For data analysis and approximation, you can pad the array when necessary. Also, the function performance depends very much, and not monotonically, on the array size (see getOptimalDFTSize ). In the current implementation DCT of a vector of size N is calculated via DFT of a vector of size N/2 . Thus, the optimal DCT size N1 >= N can be calculated as:
  size_t getOptimalDCTSize(size_t N) { return 2*getOptimalDFTSize((N+1)/2); }
  N1 = getOptimalDCTSize(N);

Parameters

  src | input floating-point array.
  dst | output array of the same size and type as src .
  flags | transformation flags as a combination of cv::DftFlags (DCT_*)

See also
  dft , getOptimalDFTSize , idct

## ◆ determinant()

double cv::determinant | ( | InputArray | mtx | ) |

Returns the determinant of a square floating-point matrix.

The function cv::determinant calculates and returns the determinant of the specified matrix. For small matrices ( mtx.cols=mtx.rows<=3 ), the direct method is used. For larger matrices, the function uses LU factorization with partial pivoting.

For symmetric positively-determined matrices, it is also possible to use eigen decomposition to calculate the determinant.

Parameters

  mtx | input matrix that must have CV_32FC1 or CV_64FC1 type and square size.

See also
  trace, invert, solve, eigen, MatrixExpressions

## ◆ dft()

void cv::dft | ( | InputArray | src,
|  | OutputArray | dst,
|  | int | flags = `0`,
|  | int | nonzeroRows = `0`
| ) |  |

Performs a forward or inverse Discrete Fourier transform of a 1D or 2D floating-point array.

The function cv::dft performs one of the following:

- Forward the Fourier transform of a 1D vector of N elements:

  \[Y = F^{(N)} \cdot X,\]

  where \(F^{(N)}_{jk}=\exp(-2\pi i j k/N)\) and \(i=\sqrt{-1}\)
- Inverse the Fourier transform of a 1D vector of N elements:

  \[\begin{array}{l} X'= \left (F^{(N)} \right )^{-1} \cdot Y = \left (F^{(N)} \right )^* \cdot y \\ X = (1/N) \cdot X, \end{array}\]

  where \(F^*=\left(\textrm{Re}(F^{(N)})-\textrm{Im}(F^{(N)})\right)^T\)
- Forward the 2D Fourier transform of a M x N matrix:

  \[Y = F^{(M)} \cdot X \cdot F^{(N)}\]

- Inverse the 2D Fourier transform of a M x N matrix:

  \[\begin{array}{l} X'= \left (F^{(M)} \right )^* \cdot Y \cdot \left (F^{(N)} \right )^* \\ X = \frac{1}{M \cdot N} \cdot X' \end{array}\]

In case of real (single-channel) data, the output spectrum of the forward Fourier transform or input spectrum of the inverse Fourier transform can be represented in a packed format called CCS (complex-conjugate-symmetrical). It was borrowed from IPL (Intel* Image Processing Library). Here is how 2D CCS spectrum looks:

\[\begin{bmatrix} Re Y_{0,0} & Re Y_{0,1} & Im Y_{0,1} & Re Y_{0,2} & Im Y_{0,2} & \cdots & Re Y_{0,N/2-1} & Im Y_{0,N/2-1} & Re Y_{0,N/2} \\ Re Y_{1,0} & Re Y_{1,1} & Im Y_{1,1} & Re Y_{1,2} & Im Y_{1,2} & \cdots & Re Y_{1,N/2-1} & Im Y_{1,N/2-1} & Re Y_{1,N/2} \\ Im Y_{1,0} & Re Y_{2,1} & Im Y_{2,1} & Re Y_{2,2} & Im Y_{2,2} & \cdots & Re Y_{2,N/2-1} & Im Y_{2,N/2-1} & Im Y_{1,N/2} \\ \hdotsfor{9} \\ Re Y_{M/2-1,0} & Re Y_{M-3,1} & Im Y_{M-3,1} & \hdotsfor{3} & Re Y_{M-3,N/2-1} & Im Y_{M-3,N/2-1}& Re Y_{M/2-1,N/2} \\ Im Y_{M/2-1,0} & Re Y_{M-2,1} & Im Y_{M-2,1} & \hdotsfor{3} & Re Y_{M-2,N/2-1} & Im Y_{M-2,N/2-1}& Im Y_{M/2-1,N/2} \\ Re Y_{M/2,0} & Re Y_{M-1,1} & Im Y_{M-1,1} & \hdotsfor{3} & Re Y_{M-1,N/2-1} & Im Y_{M-1,N/2-1}& Re Y_{M/2,N/2} \end{bmatrix}\]

In case of 1D transform of a real vector, the output looks like the first row of the matrix above.

So, the function chooses an operation mode depending on the flags and size of the input array:

- If DFT_ROWS is set or the input array has a single row or single column, the function performs a 1D forward or inverse transform of each row of a matrix when DFT_ROWS is set. Otherwise, it performs a 2D transform.
- If the input array is real and DFT_INVERSE is not set, the function performs a forward 1D or 2D transform:
  - When DFT_COMPLEX_OUTPUT is set, the output is a complex matrix of the same size as input.
  - When DFT_COMPLEX_OUTPUT is not set, the output is a real matrix of the same size as input. In case of 2D transform, it uses the packed format as shown above. In case of a single 1D transform, it looks like the first row of the matrix above. In case of multiple 1D transforms (when using the DFT_ROWS flag), each row of the output matrix looks like the first row of the matrix above.
- If the input array is complex and either DFT_INVERSE or DFT_REAL_OUTPUT are not set, the output is a complex array of the same size as input. The function performs a forward or inverse 1D or 2D transform of the whole input array or each row of the input array independently, depending on the flags DFT_INVERSE and DFT_ROWS.
- When DFT_INVERSE is set and the input array is real, or it is complex but DFT_REAL_OUTPUT is set, the output is a real array of the same size as input. The function performs a 1D or 2D inverse transformation of the whole input array or each individual row, depending on the flags DFT_INVERSE and DFT_ROWS.

If DFT_SCALE is set, the scaling is done after the transformation.

Unlike dct , the function supports arrays of arbitrary size. But only those arrays are processed efficiently, whose sizes can be factorized in a product of small prime numbers (2, 3, and 5 in the current implementation). Such an efficient DFT size can be calculated using the getOptimalDFTSize method.

The sample below illustrates how to calculate a DFT-based convolution of two 2D real arrays:

void convolveDFT(InputArray A, InputArray B, OutputArray C)
{
// reallocate the output array if needed
C.create(abs(A.rows - B.rows)+1, abs(A.cols - B.cols)+1, A.type());
Size dftSize;
// calculate the size of DFT transform
dftSize.width = getOptimalDFTSize(A.cols + B.cols - 1);
dftSize.height = getOptimalDFTSize(A.rows + B.rows - 1);
// allocate temporary buffers and initialize them with 0's
Mat tempA(dftSize, A.type(), Scalar::all(0));
Mat tempB(dftSize, B.type(), Scalar::all(0));
// copy A and B to the top-left corners of tempA and tempB, respectively
Mat roiA(tempA, Rect(0,0,A.cols,A.rows));
A.copyTo(roiA);
Mat roiB(tempB, Rect(0,0,B.cols,B.rows));
B.copyTo(roiB);
// now transform the padded A & B in-place;
// use "nonzeroRows" hint for faster processing
dft(tempA, tempA, 0, A.rows);
dft(tempB, tempB, 0, B.rows);
// multiply the spectrums;
// the function handles packed spectrum representations well
mulSpectrums(tempA, tempB, tempA);
// transform the product back from the frequency domain.
// Even though all the result rows will be non-zero,
// you need only the first C.rows of them, and thus you
// pass nonzeroRows == C.rows
dft(tempA, tempA, DFT_INVERSE + DFT_SCALE, C.rows);
// now copy the result back to C.
tempA(Rect(0, 0, C.cols, C.rows)).copyTo(C);
// all the temporary buffers will be deallocated automatically
}

To optimize this sample, consider the following approaches:

- Since nonzeroRows != 0 is passed to the forward transform calls and since A and B are copied to the top-left corners of tempA and tempB, respectively, it is not necessary to clear the whole tempA and tempB. It is only necessary to clear the tempA.cols - A.cols ( tempB.cols - B.cols) rightmost columns of the matrices.
- This DFT-based convolution does not have to be applied to the whole big arrays, especially if B is significantly smaller than A or vice versa. Instead, you can calculate convolution by parts. To do this, you need to split the output array C into multiple tiles. For each tile, estimate which parts of A and B are required to calculate convolution in this tile. If the tiles in C are too small, the speed will decrease a lot because of repeated work. In the ultimate case, when each tile in C is a single pixel, the algorithm becomes equivalent to the naive convolution algorithm. If the tiles are too big, the temporary arrays tempA and tempB become too big and there is also a slowdown because of bad cache locality. So, there is an optimal tile size somewhere in the middle.
- If different tiles in C can be calculated in parallel and, thus, the convolution is done by parts, the loop can be threaded.

All of the above improvements have been implemented in matchTemplate and filter2D . Therefore, by using them, you can get the performance even better than with the above theoretically optimal implementation. Though, those two functions actually calculate cross-correlation, not convolution, so you need to "flip" the second convolution operand B vertically and horizontally using flip .

Note
  - An example using the discrete fourier transform can be found at opencv_source_code/samples/cpp/dft.cpp
  - (Python) An example using the dft functionality to perform Wiener deconvolution can be found at opencv_source/samples/python/deconvolution.py
  - (Python) An example rearranging the quadrants of a Fourier image can be found at opencv_source/samples/python/dft.py

Parameters

  src | input array that could be real or complex.
  dst | output array whose size and type depends on the flags .
  flags | transformation flags, representing a combination of the DftFlags
  nonzeroRows | when the parameter is not zero, the function assumes that only the first nonzeroRows rows of the input array (DFT_INVERSE is not set) or only the first nonzeroRows of the output array (DFT_INVERSE is set) contain non-zeros, thus, the function can handle the rest of the rows more efficiently and save some time; this technique is very useful for calculating array cross-correlation or convolution using DFT.

See also
  dct , getOptimalDFTSize , mulSpectrums, filter2D , matchTemplate , flip , cartToPolar , magnitude , phase

## ◆ divide() [1/2]

void cv::divide | ( | InputArray | src1,
|  | InputArray | src2,
|  | OutputArray | dst,
|  | double | scale = `1`,
|  | int | dtype = `-1`
| ) |  |

Performs per-element division of two arrays or a scalar by an array.

The function cv::divide divides one array by another:

\[\texttt{dst(I) = saturate(src1(I)*scale/src2(I))}\]

or a scalar by an array when there is no src1 :

\[\texttt{dst(I) = saturate(scale/src2(I))}\]

When src2(I) is zero, dst(I) will also be zero. Different channels of multi-channel arrays are processed independently.

Note
  Saturation is not applied when the output array has the depth CV_32S. You may even get result of an incorrect sign in the case of overflow.

Parameters

  src1 | first input array.
  src2 | second input array of the same size and type as src1.
  scale | scalar factor.
  dst | output array of the same size and type as src2.
  dtype | optional depth of the output array; if -1, dst will have depth src2.depth(), but in case of an array-by-array division, you can only pass -1 when src1.depth()==src2.depth().

See also
  multiply, add, subtract

## ◆ divide() [2/2]

void cv::divide | ( | double | scale,
|  | InputArray | src2,
|  | OutputArray | dst,
|  | int | dtype = `-1`
| ) |  |

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

## ◆ eigen()

bool cv::eigen | ( | InputArray | src,
|  | OutputArray | eigenvalues,
|  | OutputArray | eigenvectors = `noArray()`
| ) |  |

Calculates eigenvalues and eigenvectors of a symmetric matrix.

The function cv::eigen calculates just eigenvalues, or eigenvalues and eigenvectors of the symmetric matrix src:

src*eigenvectors.row(i).t() = eigenvalues.at<srcType>(i)*eigenvectors.row(i).t()

Note
  Use cv::eigenNonSymmetric for calculation of real eigenvalues and eigenvectors of non-symmetric matrix.

Parameters

  src | input matrix that must have CV_32FC1 or CV_64FC1 type, square size and be symmetrical (src ^T^ == src).
  eigenvalues | output vector of eigenvalues of the same type as src; the eigenvalues are stored in the descending order.
  eigenvectors | output matrix of eigenvectors; it has the same size and type as src; the eigenvectors are stored as subsequent matrix rows, in the same order as the corresponding eigenvalues.

See also
  eigenNonSymmetric, completeSymm , PCA

## ◆ eigenNonSymmetric()

void cv::eigenNonSymmetric | ( | InputArray | src,
|  | OutputArray | eigenvalues,
|  | OutputArray | eigenvectors
| ) |  |

Calculates eigenvalues and eigenvectors of a non-symmetric matrix (real eigenvalues only).

Note
  Assumes real eigenvalues.

The function calculates eigenvalues and eigenvectors (optional) of the square matrix src:

src*eigenvectors.row(i).t() = eigenvalues.at<srcType>(i)*eigenvectors.row(i).t()

Parameters

  src | input matrix (CV_32FC1 or CV_64FC1 type).
  eigenvalues | output vector of eigenvalues (type is the same type as src).
  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.

See also
  eigen

## ◆ exp()

void cv::exp | ( | InputArray | src,
|  | OutputArray | dst
| ) |  |

Calculates the exponent of every array element.

The function cv::exp calculates the exponent of every element of the input array:

\[\texttt{dst} [I] = e^{ src(I) }\]

The maximum relative error is about 7e-6 for single-precision input and less than 1e-10 for double-precision input. Currently, the function converts denormalized values to zeros on output. Special values (NaN, Inf) are not handled.

Parameters

  src | input array.
  dst | output array of the same size and type as src.

See also
  log , cartToPolar , polarToCart , phase , pow , sqrt , magnitude

## ◆ extractChannel()

void cv::extractChannel | ( | InputArray | src,
|  | OutputArray | dst,
|  | int | coi
| ) |  |

Extracts a single channel from src (coi is 0-based index)

Parameters

  src | input array
  dst | output array
  coi | index of channel to extract

See also
  mixChannels, split

## ◆ findNonZero()

void cv::findNonZero | ( | InputArray | src,
|  | OutputArray | idx
| ) |  |

Returns the list of locations of non-zero pixels.

Given a binary matrix (likely returned from an operation such as threshold(), compare(), >, ==, etc, return all of the non-zero indices as a cv::Mat or std::vector<cv::Point> (x,y) For example:

cv::Mat binaryImage; // input, binary image
cv::Mat locations; // output, locations of non-zero pixels
cv::findNonZero(binaryImage, locations);
// access pixel coordinates
Point pnt = locations.at<Point>(i);

or

cv::Mat binaryImage; // input, binary image
vector<Point> locations; // output, locations of non-zero pixels
cv::findNonZero(binaryImage, locations);
// access pixel coordinates
Point pnt = locations[i];

Parameters

  src | single-channel array (type CV_8UC1)
  idx | the output array, type of cv::Mat or std::vector<Point>, corresponding to non-zero indices in the input

## ◆ flip()

void cv::flip | ( | InputArray | src,
|  | OutputArray | dst,
|  | int | flipCode
| ) |  |

Flips a 2D array around vertical, horizontal, or both axes.

The function cv::flip flips the array in one of three different ways (row and column indices are 0-based):

\[\texttt{dst} _{ij} = \left\{ \begin{array}{l l} \texttt{src} _{\texttt{src.rows}-i-1,j} & if\; \texttt{flipCode} = 0 \\ \texttt{src} _{i, \texttt{src.cols} -j-1} & if\; \texttt{flipCode} > 0 \\ \texttt{src} _{ \texttt{src.rows} -i-1, \texttt{src.cols} -j-1} & if\; \texttt{flipCode} < 0 \\ \end{array} \right.\]

The example scenarios of using the function are the following: Vertical flipping of the image (flipCode == 0) to switch between top-left and bottom-left image origin. This is a typical operation in video processing on Microsoft Windows* OS. Horizontal flipping of the image with the subsequent horizontal shift and absolute difference calculation to check for a vertical-axis symmetry (flipCode > 0). Simultaneous horizontal and vertical flipping of the image with the subsequent shift and absolute difference calculation to check for a central symmetry (flipCode < 0). Reversing the order of point arrays (flipCode > 0 or flipCode == 0).

Parameters

  src | input array.
  dst | output array of the same size and type as src.
  flipCode | a flag to specify how to flip the array; 0 means flipping around the x-axis and positive value (for example, 1) means flipping around y-axis. Negative value (for example, -1) means flipping around both axes.

See also
  transpose , repeat , completeSymm

Examples:
  facedetect.cpp, and train_HOG.cpp.

## ◆ gemm()

void cv::gemm | ( | InputArray | src1,
|  | InputArray | src2,
|  | double | alpha,
|  | InputArray | src3,
|  | double | beta,
|  | OutputArray | dst,
|  | int | flags = `0`
| ) |  |

Performs generalized matrix multiplication.

The function cv::gemm performs generalized matrix multiplication similar to the gemm functions in BLAS level 3. For example, `gemm(src1, src2, alpha, src3, beta, dst, GEMM_1_T + GEMM_3_T)` corresponds to

\[\texttt{dst} = \texttt{alpha} \cdot \texttt{src1} ^T \cdot \texttt{src2} + \texttt{beta} \cdot \texttt{src3} ^T\]

In case of complex (two-channel) data, performed a complex matrix multiplication.

The function can be replaced with a matrix expression. For example, the above call can be replaced with:

dst = alpha*src1.t()*src2 + beta*src3.t();

Parameters

  src1 | first multiplied input matrix that could be real(CV_32FC1, CV_64FC1) or complex(CV_32FC2, CV_64FC2).
  src2 | second multiplied input matrix of the same type as src1.
  alpha | weight of the matrix product.
  src3 | third optional delta matrix added to the matrix product; it should have the same type as src1 and src2.
  beta | weight of src3.
  dst | output matrix; it has the proper size and the same type as input matrices.
  flags | operation flags (cv::GemmFlags)

See also
  mulTransposed , transform

Examples:
  image_alignment.cpp.

## ◆ getOptimalDFTSize()

int cv::getOptimalDFTSize | ( | int | vecsize | ) |

Returns the optimal DFT size for a given vector size.

DFT performance is not a monotonic function of a vector size. Therefore, when you calculate convolution of two arrays or perform the spectral analysis of an array, it usually makes sense to pad the input data with zeros to get a bit larger array that can be transformed much faster than the original one. Arrays whose size is a power-of-two (2, 4, 8, 16, 32, ...) are the fastest to process. Though, the arrays whose size is a product of 2's, 3's, and 5's (for example, 300 = 5*5*3*2*2) are also processed quite efficiently.

The function cv::getOptimalDFTSize returns the minimum number N that is greater than or equal to vecsize so that the DFT of a vector of size N can be processed efficiently. In the current implementation N = 2 ^p^ * 3 ^q^ * 5 ^r^ for some integer p, q, r.

The function returns a negative number if vecsize is too large (very close to INT_MAX ).

While the function cannot be used directly to estimate the optimal vector size for DCT transform (since the current DCT implementation supports only even-size vectors), it can be easily processed as getOptimalDFTSize((vecsize+1)/2)*2.

Parameters

  vecsize | vector size.

See also
  dft , dct , idft , idct , mulSpectrums

## ◆ hconcat() [1/3]

void cv::hconcat | ( | const Mat * | src,
|  | size_t | nsrc,
|  | OutputArray | dst
| ) |  |

Applies horizontal concatenation to given matrices.

The function horizontally concatenates two or more cv::Mat matrices (with the same number of rows).

cv::Mat matArray[] = { cv::Mat(4, 1, CV_8UC1, cv::Scalar(1)),
cv::Mat(4, 1, CV_8UC1, cv::Scalar(2)),
cv::Mat(4, 1, CV_8UC1, cv::Scalar(3)),};
cv::Mat out;
cv::hconcat( matArray, 3, out );
//out:
//[1, 2, 3;
// 1, 2, 3;
// 1, 2, 3;
// 1, 2, 3]

Parameters

  src | input array or vector of matrices. all of the matrices must have the same number of rows and the same depth.
  nsrc | number of matrices in src.
  dst | output array. It has the same number of rows and depth as the src, and the sum of cols of the src.

See also
  cv::vconcat(const Mat*, size_t, OutputArray),
  cv::vconcat(InputArrayOfArrays, OutputArray) and
  cv::vconcat(InputArray, InputArray, OutputArray)

Examples:
  homography_from_camera_displacement.cpp.

## ◆ hconcat() [2/3]

void cv::hconcat | ( | InputArray | src1,
|  | InputArray | src2,
|  | OutputArray | dst
| ) |  |

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

cv::Mat_<float> A = (cv::Mat_<float>(3, 2) << 1, 4,
2, 5,
3, 6);
cv::Mat_<float> B = (cv::Mat_<float>(3, 2) << 7, 10,
8, 11,
9, 12);
cv::Mat C;
cv::hconcat(A, B, C);
//C:
//[1, 4, 7, 10;
// 2, 5, 8, 11;
// 3, 6, 9, 12]

Parameters

  src1 | first input array to be considered for horizontal concatenation.
  src2 | second input array to be considered for horizontal concatenation.
  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.

## ◆ hconcat() [3/3]

void cv::hconcat | ( | InputArrayOfArrays | src,
|  | OutputArray | dst
| ) |  |

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

std::vector<cv::Mat> matrices = { cv::Mat(4, 1, CV_8UC1, cv::Scalar(1)),
cv::Mat(4, 1, CV_8UC1, cv::Scalar(2)),
cv::Mat(4, 1, CV_8UC1, cv::Scalar(3)),};
cv::Mat out;
cv::hconcat( matrices, out );
//out:
//[1, 2, 3;
// 1, 2, 3;
// 1, 2, 3;
// 1, 2, 3]

Parameters

  src | input array or vector of matrices. all of the matrices must have the same number of rows and the same depth.
  dst | output array. It has the same number of rows and depth as the src, and the sum of cols of the src. same depth.

## ◆ idct()

void cv::idct | ( | InputArray | src,
|  | OutputArray | dst,
|  | int | flags = `0`
| ) |  |

Calculates the inverse Discrete Cosine Transform of a 1D or 2D array.

idct(src, dst, flags) is equivalent to dct(src, dst, flags | DCT_INVERSE).

Parameters

  src | input floating-point single-channel array.
  dst | output array of the same size and type as src.
  flags | operation flags.

See also
  dct, dft, idft, getOptimalDFTSize

## ◆ idft()

void cv::idft | ( | InputArray | src,
|  | OutputArray | dst,
|  | int | flags = `0`,
|  | int | nonzeroRows = `0`
| ) |  |

Calculates the inverse Discrete Fourier Transform of a 1D or 2D array.

idft(src, dst, flags) is equivalent to dft(src, dst, flags | DFT_INVERSE) .

Note
  None of dft and idft scales the result by default. So, you should pass DFT_SCALE to one of dft or idft explicitly to make these transforms mutually inverse.

See also
  dft, dct, idct, mulSpectrums, getOptimalDFTSize

Parameters

  src | input floating-point real or complex array.
  dst | output array whose size and type depend on the flags.
  flags | operation flags (see dft and DftFlags).
  nonzeroRows | number of dst rows to process; the rest of the rows have undefined content (see the convolution sample in dft description.

## ◆ inRange()

void cv::inRange | ( | InputArray | src,
|  | InputArray | lowerb,
|  | InputArray | upperb,
|  | OutputArray | dst
| ) |  |

Checks if array elements lie between the elements of two other arrays.

The function checks the range as follows:

- For every element of a single-channel input array:

  \[\texttt{dst} (I)= \texttt{lowerb} (I)_0 \leq \texttt{src} (I)_0 \leq \texttt{upperb} (I)_0\]

- For two-channel arrays:

  \[\texttt{dst} (I)= \texttt{lowerb} (I)_0 \leq \texttt{src} (I)_0 \leq \texttt{upperb} (I)_0 \land \texttt{lowerb} (I)_1 \leq \texttt{src} (I)_1 \leq \texttt{upperb} (I)_1\]

- and so forth.

That is, dst (I) is set to 255 (all 1 -bits) if src (I) is within the specified 1D, 2D, 3D, ... box and 0 otherwise.

When the lower and/or upper boundary parameters are scalars, the indexes (I) at lowerb and upperb in the above formulas should be omitted.

Parameters

  src | first input array.
  lowerb | inclusive lower boundary array or a scalar.
  upperb | inclusive upper boundary array or a scalar.
  dst | output array of the same size as src and CV_8U type.

Examples:
  camshiftdemo.cpp.

## ◆ insertChannel()

void cv::insertChannel | ( | InputArray | src,
|  | InputOutputArray | dst,
|  | int | coi
| ) |  |

Inserts a single channel to dst (coi is 0-based index)

Parameters

  src | input array
  dst | output array
  coi | index of channel for insertion

See also
  mixChannels, merge

## ◆ invert()

double cv::invert | ( | InputArray | src,
|  | OutputArray | dst,
|  | int | flags = `DECOMP_LU`
| ) |  |

Finds the inverse or pseudo-inverse of a matrix.

The function cv::invert inverts the matrix src and stores the result in dst . When the matrix src is singular or non-square, the function calculates the pseudo-inverse matrix (the dst matrix) so that norm(src*dst - I) is minimal, where I is an identity matrix.

In case of the DECOMP_LU method, the function returns non-zero value if the inverse has been successfully calculated and 0 if src is singular.

In case of the DECOMP_SVD method, the function returns the inverse condition number of src (the ratio of the smallest singular value to the largest singular value) and 0 if src is singular. The SVD method calculates a pseudo-inverse matrix if src is singular.

Similarly to DECOMP_LU, the method DECOMP_CHOLESKY works only with non-singular square matrices that should also be symmetrical and positively defined. In this case, the function stores the inverted matrix in dst and returns non-zero. Otherwise, it returns 0.

Parameters

  src | input floating-point M x N matrix.
  dst | output matrix of N x M size and the same type as src.
  flags | inversion method (cv::DecompTypes)

See also
  solve, SVD

## ◆ log()

void cv::log | ( | InputArray | src,
|  | OutputArray | dst
| ) |  |

Calculates the natural logarithm of every array element.

The function cv::log calculates the natural logarithm of every element of the input array:

\[\texttt{dst} (I) = \log (\texttt{src}(I)) \]

Output on zero, negative and special (NaN, Inf) values is undefined.

Parameters

  src | input array.
  dst | output array of the same size and type as src .

See also
  exp, cartToPolar, polarToCart, phase, pow, sqrt, magnitude

## ◆ LUT()

void cv::LUT | ( | InputArray | src,
|  | InputArray | lut,
|  | OutputArray | dst
| ) |  |

Performs a look-up table transform of an array.

The function LUT fills the output array with values from the look-up table. Indices of the entries are taken from the input array. That is, the function processes each element of src as follows:

\[\texttt{dst} (I) \leftarrow \texttt{lut(src(I) + d)}\]

where

\[d = \fork{0}{if \(\texttt{src}\) has depth \(\texttt{CV_8U}\)}{128}{if \(\texttt{src}\) has depth \(\texttt{CV_8S}\)}\]

Parameters

  src | input array of 8-bit elements.
  lut | look-up table of 256 elements; in case of multi-channel input array, the table should either have a single channel (in this case the same table is used for all channels) or the same number of channels as in the input array.
  dst | output array of the same size and number of channels as src, and the same depth as lut.

See also
  convertScaleAbs, Mat::convertTo

## ◆ magnitude()

void cv::magnitude | ( | InputArray | x,
|  | InputArray | y,
|  | OutputArray | magnitude
| ) |  |

Calculates the magnitude of 2D vectors.

The function cv::magnitude calculates the magnitude of 2D vectors formed from the corresponding elements of x and y arrays:

\[\texttt{dst} (I) = \sqrt{\texttt{x}(I)^2 + \texttt{y}(I)^2}\]

Parameters

  x | floating-point array of x-coordinates of the vectors.
  y | floating-point array of y-coordinates of the vectors; it must have the same size as x.
  magnitude | output array of the same size and type as x.

See also
  cartToPolar, polarToCart, phase, sqrt

Examples:
  polar_transforms.cpp.

## ◆ Mahalanobis()

double cv::Mahalanobis | ( | InputArray | v1,
|  | InputArray | v2,
|  | InputArray | icovar
| ) |  |

Calculates the Mahalanobis distance between two vectors.

The function cv::Mahalanobis calculates and returns the weighted distance between two vectors:

\[d( \texttt{vec1} , \texttt{vec2} )= \sqrt{\sum_{i,j}{\texttt{icovar(i,j)}\cdot(\texttt{vec1}(I)-\texttt{vec2}(I))\cdot(\texttt{vec1(j)}-\texttt{vec2(j)})} }\]

The covariance matrix may be calculated using the calcCovarMatrix function and then inverted using the invert function (preferably using the DECOMP_SVD method, as the most accurate).

Parameters

  v1 | first 1D input vector.
  v2 | second 1D input vector.
  icovar | inverse covariance matrix.

## ◆ max() [1/3]

void cv::max | ( | InputArray | src1,
|  | InputArray | src2,
|  | OutputArray | dst
| ) |  |

Calculates per-element maximum of two arrays or an array and a scalar.

The function cv::max calculates the per-element maximum of two arrays:

\[\texttt{dst} (I)= \max ( \texttt{src1} (I), \texttt{src2} (I))\]

or array and a scalar:

\[\texttt{dst} (I)= \max ( \texttt{src1} (I), \texttt{value} )\]

Parameters

  src1 | first input array.
  src2 | second input array of the same size and type as src1 .
  dst | output array of the same size and type as src1.

See also
  min, compare, inRange, minMaxLoc, MatrixExpressions

## ◆ max() [2/3]

void cv::max | ( | const Mat & | src1,
|  | const Mat & | src2,
|  | Mat & | dst
| ) |  |

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. needed to avoid conflicts with const _Tp& std::min(const _Tp&, const _Tp&, _Compare)

## ◆ max() [3/3]

void cv::max | ( | const UMat & | src1,
|  | const UMat & | src2,
|  | UMat & | dst
| ) |  |

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. needed to avoid conflicts with const _Tp& std::min(const _Tp&, const _Tp&, _Compare)

## ◆ mean()

Scalar cv::mean | ( | InputArray | src,
|  | InputArray | mask = `noArray()`
| ) |  |

Calculates an average (mean) of array elements.

The function cv::mean calculates the mean value M of array elements, independently for each channel, and return it:

\[\begin{array}{l} N = \sum _{I: \; \texttt{mask} (I) \ne 0} 1 \\ M_c = \left ( \sum _{I: \; \texttt{mask} (I) \ne 0}{ \texttt{mtx} (I)_c} \right )/N \end{array}\]

When all the mask elements are 0's, the function returns Scalar::all(0)

Parameters

  src | input array that should have from 1 to 4 channels so that the result can be stored in Scalar_ .
  mask | optional operation mask.

See also
  countNonZero, meanStdDev, norm, minMaxLoc

## ◆ meanStdDev()

void cv::meanStdDev | ( | InputArray | src,
|  | OutputArray | mean,
|  | OutputArray | stddev,
|  | InputArray | mask = `noArray()`
| ) |  |

Calculates a mean and standard deviation of array elements.

The function cv::meanStdDev calculates the mean and the standard deviation M of array elements independently for each channel and returns it via the output parameters:

\[\begin{array}{l} N = \sum _{I, \texttt{mask} (I) \ne 0} 1 \\ \texttt{mean} _c = \frac{\sum_{ I: \; \texttt{mask}(I) \ne 0} \texttt{src} (I)_c}{N} \\ \texttt{stddev} _c = \sqrt{\frac{\sum_{ I: \; \texttt{mask}(I) \ne 0} \left ( \texttt{src} (I)_c - \texttt{mean} _c \right )^2}{N}} \end{array}\]

When all the mask elements are 0's, the function returns mean=stddev=Scalar::all(0).

Note
  The calculated standard deviation is only the diagonal of the complete normalized covariance matrix. If the full matrix is needed, you can reshape the multi-channel array M x N to the single-channel array M*N x mtx.channels() (only possible when the matrix is continuous) and then pass the matrix to calcCovarMatrix .

Parameters

  src | input array that should have from 1 to 4 channels so that the results can be stored in Scalar_ 's.
  mean | output parameter: calculated mean value.
  stddev | output parameter: calculated standard deviation.
  mask | optional operation mask.

See also
  countNonZero, mean, norm, minMaxLoc, calcCovarMatrix

## ◆ merge() [1/2]

void cv::merge | ( | const Mat * | mv,
|  | size_t | count,
|  | OutputArray | dst
| ) |  |

Creates one multi-channel array out of several single-channel ones.

The function cv::merge merges several arrays to make a single multi-channel array. That is, each element of the output array will be a concatenation of the elements of the input arrays, where elements of i-th input array are treated as mv[i].channels()-element vectors.

The function cv::split does the reverse operation. If you need to shuffle channels in some other advanced way, use cv::mixChannels.

The following example shows how to merge 3 single channel matrices into a single 3-channel matrix.

Mat m1 = (Mat_<uchar>(2,2) << 1,4,7,10);
Mat m2 = (Mat_<uchar>(2,2) << 2,5,8,11);
Mat m3 = (Mat_<uchar>(2,2) << 3,6,9,12);
Mat channels[3] = {m1, m2, m3};
Mat m;
merge(channels, 3, m);
/*
m =
[ 1, 2, 3, 4, 5, 6;
7, 8, 9, 10, 11, 12]
m.channels() = 3
*/

Parameters

  mv | input array of matrices to be merged; all the matrices in mv must have the same size and the same depth.
  count | number of input matrices when mv is a plain C array; it must be greater than zero.
  dst | output array of the same size and the same depth as mv[0]; The number of channels will be equal to the parameter count.

See also
  mixChannels, split, Mat::reshape

Examples:
  distrans.cpp.

## ◆ merge() [2/2]

void cv::merge | ( | InputArrayOfArrays | mv,
|  | OutputArray | dst
| ) |  |

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Parameters

  mv | input vector of matrices to be merged; all the matrices in mv must have the same size and the same depth.
  dst | output array of the same size and the same depth as mv[0]; The number of channels will be the total number of channels in the matrix array.

## ◆ min() [1/3]

void cv::min | ( | InputArray | src1,
|  | InputArray | src2,
|  | OutputArray | dst
| ) |  |

Calculates per-element minimum of two arrays or an array and a scalar.

The function cv::min calculates the per-element minimum of two arrays:

\[\texttt{dst} (I)= \min ( \texttt{src1} (I), \texttt{src2} (I))\]

or array and a scalar:

\[\texttt{dst} (I)= \min ( \texttt{src1} (I), \texttt{value} )\]

Parameters

  src1 | first input array.
  src2 | second input array of the same size and type as src1.
  dst | output array of the same size and type as src1.

See also
  max, compare, inRange, minMaxLoc

## ◆ min() [2/3]

void cv::min | ( | const Mat & | src1,
|  | const Mat & | src2,
|  | Mat & | dst
| ) |  |

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. needed to avoid conflicts with const _Tp& std::min(const _Tp&, const _Tp&, _Compare)

## ◆ min() [3/3]

void cv::min | ( | const UMat & | src1,
|  | const UMat & | src2,
|  | UMat & | dst
| ) |  |

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. needed to avoid conflicts with const _Tp& std::min(const _Tp&, const _Tp&, _Compare)

## ◆ minMaxIdx()

void cv::minMaxIdx | ( | InputArray | src,
|  | double * | minVal,
|  | double * | maxVal = `0`,
|  | int * | minIdx = `0`,
|  | int * | maxIdx = `0`,
|  | InputArray | mask = `noArray()`
| ) |  |

Finds the global minimum and maximum in an array.

The function cv::minMaxIdx finds the minimum and maximum element values and their positions. The extremums are searched across the whole array or, if mask is not an empty array, in the specified array region. The function does not work with multi-channel arrays. If you need to find minimum or maximum elements across all the channels, use Mat::reshape first to reinterpret the array as single-channel. Or you may extract the particular channel using either extractImageCOI , or mixChannels , or split . In case of a sparse matrix, the minimum is found among non-zero elements only.

Note
  When minIdx is not NULL, it must have at least 2 elements (as well as maxIdx), even if src is a single-row or single-column matrix. In OpenCV (following MATLAB) each array has at least 2 dimensions, i.e. single-column matrix is Mx1 matrix (and therefore minIdx/maxIdx will be (i1,0)/(i2,0)) and single-row matrix is 1xN matrix (and therefore minIdx/maxIdx will be (0,j1)/(0,j2)).

Parameters

  src | input single-channel array.
  minVal | pointer to the returned minimum value; NULL is used if not required.
  maxVal | pointer to the returned maximum value; NULL is used if not required.
  minIdx | pointer to the returned minimum location (in nD case); NULL is used if not required; Otherwise, it must point to an array of src.dims elements, the coordinates of the minimum element in each dimension are stored there sequentially.
  maxIdx | pointer to the returned maximum location (in nD case). NULL is used if not required.
  mask | specified array region

## ◆ minMaxLoc() [1/2]

void cv::minMaxLoc | ( | InputArray | src,
|  | double * | minVal,
|  | double * | maxVal = `0`,
|  | Point * | minLoc = `0`,
|  | Point * | maxLoc = `0`,
|  | InputArray | mask = `noArray()`
| ) |  |

Finds the global minimum and maximum in an array.

The function cv::minMaxLoc finds the minimum and maximum element values and their positions. The extremums are searched across the whole array or, if mask is not an empty array, in the specified array region.

The function do not work with multi-channel arrays. If you need to find minimum or maximum elements across all the channels, use Mat::reshape first to reinterpret the array as single-channel. Or you may extract the particular channel using either extractImageCOI , or mixChannels , or split .

Parameters

  src | input single-channel array.
  minVal | pointer to the returned minimum value; NULL is used if not required.
  maxVal | pointer to the returned maximum value; NULL is used if not required.
  minLoc | pointer to the returned minimum location (in 2D case); NULL is used if not required.
  maxLoc | pointer to the returned maximum location (in 2D case); NULL is used if not required.
  mask | optional mask used to select a sub-array.

See also
  max, min, compare, inRange, extractImageCOI, mixChannels, split, Mat::reshape

Examples:
  image_alignment.cpp, and MatchTemplate_Demo.cpp.

## ◆ minMaxLoc() [2/2]

void cv::minMaxLoc | ( | const SparseMat & | a,
|  | double * | minVal,
|  | double * | maxVal,
|  | int * | minIdx = `0`,
|  | int * | maxIdx = `0`
| ) |  |

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Parameters

  a | input single-channel array.
  minVal | pointer to the returned minimum value; NULL is used if not required.
  maxVal | pointer to the returned maximum value; NULL is used if not required.
  minIdx | pointer to the returned minimum location (in nD case); NULL is used if not required; Otherwise, it must point to an array of src.dims elements, the coordinates of the minimum element in each dimension are stored there sequentially.
  maxIdx | pointer to the returned maximum location (in nD case). NULL is used if not required.

## ◆ mixChannels() [1/3]

void cv::mixChannels | ( | const Mat * | src,
|  | size_t | nsrcs,
|  | Mat * | dst,
|  | size_t | ndsts,
|  | const int * | fromTo,
|  | size_t | npairs
| ) |  |

Copies specified channels from input arrays to the specified channels of output arrays.

The function cv::mixChannels provides an advanced mechanism for shuffling image channels.

cv::split,cv::merge,cv::extractChannel,cv::insertChannel and some forms of cv::cvtColor are partial cases of cv::mixChannels.

In the example below, the code splits a 4-channel BGRA image into a 3-channel BGR (with B and R channels swapped) and a separate alpha-channel image:

Mat bgra( 100, 100, CV_8UC4, Scalar(255,0,0,255) );
Mat bgr( bgra.rows, bgra.cols, CV_8UC3 );
Mat alpha( bgra.rows, bgra.cols, CV_8UC1 );
// forming an array of matrices is a quite efficient operation,
// because the matrix data is not copied, only the headers
Mat out[] = { bgr, alpha };
// bgra[0] -> bgr[2], bgra[1] -> bgr[1],
// bgra[2] -> bgr[0], bgra[3] -> alpha[0]
int from_to[] = { 0,2, 1,1, 2,0, 3,3 };
mixChannels( &bgra, 1, out, 2, from_to, 4 );

Note
  Unlike many other new-style C++ functions in OpenCV (see the introduction section and Mat::create ), cv::mixChannels requires the output arrays to be pre-allocated before calling the function.

Parameters

  src | input array or vector of matrices; all of the matrices must have the same size and the same depth.
  nsrcs | number of matrices in `src`.
  dst | output array or vector of matrices; all the matrices must be allocated; their size and depth must be the same as in `src[0]`.
  ndsts | number of matrices in `dst`.
  fromTo | array of index pairs specifying which channels are copied and where; fromTo[k*2] is a 0-based index of the input channel in src, fromTo[k*2+1] is an index of the output channel in dst; the continuous channel numbering is used: the first input image channels are indexed from 0 to src[0].channels()-1, the second input image channels are indexed from src[0].channels() to src[0].channels() + src[1].channels()-1, and so on, the same scheme is used for the output image channels; as a special case, when fromTo[k*2] is negative, the corresponding output channel is filled with zero .
  npairs | number of index pairs in `fromTo`.

See also
  split, merge, extractChannel, insertChannel, cvtColor

Examples:
  camshiftdemo.cpp.

## ◆ mixChannels() [2/3]

void cv::mixChannels | ( | InputArrayOfArrays | src,
|  | InputOutputArrayOfArrays | dst,
|  | const int * | fromTo,
|  | size_t | npairs
| ) |  |

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Parameters

  src | input array or vector of matrices; all of the matrices must have the same size and the same depth.
  dst | output array or vector of matrices; all the matrices must be allocated; their size and depth must be the same as in src[0].
  fromTo | array of index pairs specifying which channels are copied and where; fromTo[k*2] is a 0-based index of the input channel in src, fromTo[k*2+1] is an index of the output channel in dst; the continuous channel numbering is used: the first input image channels are indexed from 0 to src[0].channels()-1, the second input image channels are indexed from src[0].channels() to src[0].channels() + src[1].channels()-1, and so on, the same scheme is used for the output image channels; as a special case, when fromTo[k*2] is negative, the corresponding output channel is filled with zero .
  npairs | number of index pairs in fromTo.

## ◆ mixChannels() [3/3]

void cv::mixChannels | ( | InputArrayOfArrays | src,
|  | InputOutputArrayOfArrays | dst,
|  | const std::vector< int > & | fromTo
| ) |  |

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Parameters

  src | input array or vector of matrices; all of the matrices must have the same size and the same depth.
  dst | output array or vector of matrices; all the matrices must be allocated; their size and depth must be the same as in src[0].
  fromTo | array of index pairs specifying which channels are copied and where; fromTo[k*2] is a 0-based index of the input channel in src, fromTo[k*2+1] is an index of the output channel in dst; the continuous channel numbering is used: the first input image channels are indexed from 0 to src[0].channels()-1, the second input image channels are indexed from src[0].channels() to src[0].channels() + src[1].channels()-1, and so on, the same scheme is used for the output image channels; as a special case, when fromTo[k*2] is negative, the corresponding output channel is filled with zero .

## ◆ mulSpectrums()

void cv::mulSpectrums | ( | InputArray | a,
|  | InputArray | b,
|  | OutputArray | c,
|  | int | flags,
|  | bool | conjB = `false`
| ) |  |

Performs the per-element multiplication of two Fourier spectrums.

The function cv::mulSpectrums performs the per-element multiplication of the two CCS-packed or complex matrices that are results of a real or complex Fourier transform.

The function, together with dft and idft , may be used to calculate convolution (pass conjB=false ) or correlation (pass conjB=true ) of two arrays rapidly. When the arrays are complex, they are simply multiplied (per element) with an optional conjugation of the second-array elements. When the arrays are real, they are assumed to be CCS-packed (see dft for details).

Parameters

  a | first input array.
  b | second input array of the same size and type as src1 .
  c | output array of the same size and type as src1 .
  flags | operation flags; currently, the only supported flag is cv::DFT_ROWS, which indicates that 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.
  conjB | optional flag that conjugates the second input array before the multiplication (true) or not (false).

## ◆ multiply()

void cv::multiply | ( | InputArray | src1,
|  | InputArray | src2,
|  | OutputArray | dst,
|  | double | scale = `1`,
|  | int | dtype = `-1`
| ) |  |

Calculates the per-element scaled product of two arrays.

The function multiply calculates the per-element product of two arrays:

\[\texttt{dst} (I)= \texttt{saturate} ( \texttt{scale} \cdot \texttt{src1} (I) \cdot \texttt{src2} (I))\]

There is also a MatrixExpressions -friendly variant of the first function. See Mat::mul .

For a not-per-element matrix product, see gemm .

Note
  Saturation is not applied when the output array has the depth CV_32S. You may even get result of an incorrect sign in the case of overflow.

Parameters

  src1 | first input array.
  src2 | second input array of the same size and the same type as src1.
  dst | output array of the same size and type as src1.
  scale | optional scale factor.
  dtype | optional depth of the output array

See also
  add, subtract, divide, scaleAdd, addWeighted, accumulate, accumulateProduct, accumulateSquare, Mat::convertTo

## ◆ mulTransposed()

void cv::mulTransposed | ( | InputArray | src,
|  | OutputArray | dst,
|  | bool | aTa,
|  | InputArray | delta = `noArray()`,
|  | double | scale = `1`,
|  | int | dtype = `-1`
| ) |  |

Calculates the product of a matrix and its transposition.

The function cv::mulTransposed calculates the product of src and its transposition:

\[\texttt{dst} = \texttt{scale} ( \texttt{src} - \texttt{delta} )^T ( \texttt{src} - \texttt{delta} )\]

if aTa=true , and

\[\texttt{dst} = \texttt{scale} ( \texttt{src} - \texttt{delta} ) ( \texttt{src} - \texttt{delta} )^T\]

otherwise. The function is used to calculate the covariance matrix. With zero delta, it can be used as a faster substitute for general matrix product A*B when B=A'

Parameters

  src | input single-channel matrix. Note that unlike gemm, the function can multiply not only floating-point matrices.
  dst | output square matrix.
  aTa | Flag specifying the multiplication ordering. See the description below.
  delta | Optional delta matrix subtracted from src before the multiplication. When the matrix is empty ( delta=noArray() ), it is assumed to be zero, that is, nothing is subtracted. If it has the same size as src , it is simply subtracted. Otherwise, it is "repeated" (see repeat ) to cover the full src and then subtracted. Type of the delta matrix, when it is not empty, must be the same as the type of created output matrix. See the dtype parameter description below.
  scale | Optional scale factor for the matrix product.
  dtype | Optional type of the output matrix. When it is negative, the output matrix will have the same type as src . Otherwise, it will be type=CV_MAT_DEPTH(dtype) that should be either CV_32F or CV_64F .

See also
  calcCovarMatrix, gemm, repeat, reduce

## ◆ norm() [1/3]

double cv::norm | ( | InputArray | src1,
|  | int | normType = `NORM_L2`,
|  | InputArray | mask = `noArray()`
| ) |  |

Calculates the absolute norm of an array.

This version of norm calculates the absolute norm of src1. The type of norm to calculate is specified using NormTypes.

As example for one array consider the function \(r(x)= \begin{pmatrix} x \\ 1-x \end{pmatrix}, x \in [-1;1]\). The \( L_{1}, L_{2} \) and \( L_{\infty} \) norm for the sample value \(r(-1) = \begin{pmatrix} -1 \\ 2 \end{pmatrix}\) is calculated as follows

\begin{align*} \| r(-1) \|_{L_1} &= |-1| + |2| = 3 \\ \| r(-1) \|_{L_2} &= \sqrt{(-1)^{2} + (2)^{2}} = \sqrt{5} \\ \| r(-1) \|_{L_\infty} &= \max(|-1|,|2|) = 2 \end{align*}

and for \(r(0.5) = \begin{pmatrix} 0.5 \\ 0.5 \end{pmatrix}\) the calculation is

\begin{align*} \| r(0.5) \|_{L_1} &= |0.5| + |0.5| = 1 \\ \| r(0.5) \|_{L_2} &= \sqrt{(0.5)^{2} + (0.5)^{2}} = \sqrt{0.5} \\ \| r(0.5) \|_{L_\infty} &= \max(|0.5|,|0.5|) = 0.5. \end{align*}

The following graphic shows all values for the three norm functions \(\| r(x) \|_{L_1}, \| r(x) \|_{L_2}\) and \(\| r(x) \|_{L_\infty}\). It is notable that the \( L_{1} \) norm forms the upper and the \( L_{\infty} \) norm forms the lower border for the example function \( r(x) \).

Graphs for the different norm functions from the above example

When the mask parameter is specified and it is not empty, the norm is

If normType is not specified, NORM_L2 is used. calculated only over the region specified by the mask.

Multi-channel input arrays are treated as single-channel arrays, that is, the results for all channels are combined.

Hamming norms can only be calculated with CV_8U depth arrays.

Parameters

  src1 | first input array.
  normType | type of the norm (see NormTypes).
  mask | optional operation mask; it must have the same size as src1 and CV_8UC1 type.

## ◆ norm() [2/3]

double cv::norm | ( | InputArray | src1,
|  | InputArray | src2,
|  | int | normType = `NORM_L2`,
|  | InputArray | mask = `noArray()`
| ) |  |

Calculates an absolute difference norm or a relative difference norm.

This version of cv::norm calculates the absolute difference norm or the relative difference norm of arrays src1 and src2. The type of norm to calculate is specified using NormTypes.

Parameters

  src1 | first input array.
  src2 | second input array of the same size and the same type as src1.
  normType | type of the norm (see NormTypes).
  mask | optional operation mask; it must have the same size as src1 and CV_8UC1 type.

## ◆ norm() [3/3]

double cv::norm | ( | const SparseMat & | src,
|  | int | normType
| ) |  |

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Parameters

  src | first input array.
  normType | type of the norm (see NormTypes).

## ◆ normalize() [1/2]

void cv::normalize | ( | InputArray | src,
|  | InputOutputArray | dst,
|  | double | alpha = `1`,
|  | double | beta = `0`,
|  | int | norm_type = `NORM_L2`,
|  | int | dtype = `-1`,
|  | InputArray | mask = `noArray()`
| ) |  |

Normalizes the norm or value range of an array.

The function cv::normalize normalizes scale and shift the input array elements so that

\[\| \texttt{dst} \| _{L_p}= \texttt{alpha}\]

(where p=Inf, 1 or 2) when normType=NORM_INF, NORM_L1, or NORM_L2, respectively; or so that

\[\min _I \texttt{dst} (I)= \texttt{alpha} , \, \, \max _I \texttt{dst} (I)= \texttt{beta}\]

when normType=NORM_MINMAX (for dense arrays only). The optional mask specifies a sub-array to be normalized. This means that the norm or min-n-max are calculated over the sub-array, and then this sub-array is modified to be normalized. If you want to only use the mask to calculate the norm or min-max but modify the whole array, you can use norm and Mat::convertTo.

In case of sparse matrices, only the non-zero values are analyzed and transformed. Because of this, the range transformation for sparse matrices is not allowed since it can shift the zero level.

Possible usage with some positive example data:

vector<double> positiveData = { 2.0, 8.0, 10.0 };
vector<double> normalizedData_l1, normalizedData_l2, normalizedData_inf, normalizedData_minmax;
// Norm to probability (total count)
// sum(numbers) = 20.0
// 2.0 0.1 (2.0/20.0)
// 8.0 0.4 (8.0/20.0)
// 10.0 0.5 (10.0/20.0)
normalize(positiveData, normalizedData_l1, 1.0, 0.0, NORM_L1);
// Norm to unit vector: ||positiveData|| = 1.0
// 2.0 0.15
// 8.0 0.62
// 10.0 0.77
normalize(positiveData, normalizedData_l2, 1.0, 0.0, NORM_L2);
// Norm to max element
// 2.0 0.2 (2.0/10.0)
// 8.0 0.8 (8.0/10.0)
// 10.0 1.0 (10.0/10.0)
normalize(positiveData, normalizedData_inf, 1.0, 0.0, NORM_INF);
// Norm to range [0.0;1.0]
// 2.0 0.0 (shift to left border)
// 8.0 0.75 (6.0/8.0)
// 10.0 1.0 (shift to right border)
normalize(positiveData, normalizedData_minmax, 1.0, 0.0, NORM_MINMAX);

Parameters

  src | input array.
  dst | output array of the same size as src .
  alpha | norm value to normalize to or the lower range boundary in case of the range normalization.
  beta | upper range boundary in case of the range normalization; it is not used for the norm normalization.
  norm_type | normalization type (see cv::NormTypes).
  dtype | when negative, the output array has the same type as src; otherwise, it has the same number of channels as src and the depth =CV_MAT_DEPTH(dtype).
  mask | optional operation mask.

See also
  norm, Mat::convertTo, SparseMat::convertTo

## ◆ normalize() [2/2]

void cv::normalize | ( | const SparseMat & | src,
|  | SparseMat & | dst,
|  | double | alpha,
|  | int | normType
| ) |  |

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Parameters

  src | input array.
  dst | output array of the same size as src .
  alpha | norm value to normalize to or the lower range boundary in case of the range normalization.
  normType | normalization type (see cv::NormTypes).

## ◆ patchNaNs()

void cv::patchNaNs | ( | InputOutputArray | a,
|  | double | val = `0`
| ) |  |

converts NaN's to the given number

## ◆ PCABackProject()

void cv::PCABackProject | ( | InputArray | data,
|  | InputArray | mean,
|  | InputArray | eigenvectors,
|  | OutputArray | result
| ) |  |

wrap PCA::backProject

## ◆ PCACompute() [1/2]

void cv::PCACompute | ( | InputArray | data,
|  | InputOutputArray | mean,
|  | OutputArray | eigenvectors,
|  | int | maxComponents = `0`
| ) |  |

wrap PCA::operator()

## ◆ PCACompute() [2/2]

void cv::PCACompute | ( | InputArray | data,
|  | InputOutputArray | mean,
|  | OutputArray | eigenvectors,
|  | double | retainedVariance
| ) |  |

wrap PCA::operator()

## ◆ PCAProject()

void cv::PCAProject | ( | InputArray | data,
|  | InputArray | mean,
|  | InputArray | eigenvectors,
|  | OutputArray | result
| ) |  |

wrap PCA::project

## ◆ perspectiveTransform()

void cv::perspectiveTransform | ( | InputArray | src,
|  | OutputArray | dst,
|  | InputArray | m
| ) |  |

Performs the perspective matrix transformation of vectors.

The function cv::perspectiveTransform transforms every element of src by treating it as a 2D or 3D vector, in the following way:

\[(x, y, z) \rightarrow (x'/w, y'/w, z'/w)\]

where

\[(x', y', z', w') = \texttt{mat} \cdot \begin{bmatrix} x & y & z & 1 \end{bmatrix}\]

and

\[w = \fork{w'}{if \(w' \ne 0\)}{\infty}{otherwise}\]

Here a 3D vector transformation is shown. In case of a 2D vector transformation, the z component is omitted.

Note
  The function transforms a sparse set of 2D or 3D vectors. If you want to transform an image using perspective transformation, use warpPerspective . If you have an inverse problem, that is, you want to compute the most probable perspective transformation out of several pairs of corresponding points, you can use getPerspectiveTransform or findHomography .

Parameters

  src | input two-channel or three-channel floating-point array; each element is a 2D/3D vector to be transformed.
  dst | output array of the same size and type as src.
  m | 3x3 or 4x4 floating-point transformation matrix.

See also
  transform, warpPerspective, getPerspectiveTransform, findHomography

## ◆ phase()

void cv::phase | ( | InputArray | x,
|  | InputArray | y,
|  | OutputArray | angle,
|  | bool | angleInDegrees = `false`
| ) |  |

Calculates the rotation angle of 2D vectors.

The function cv::phase calculates the rotation angle of each 2D vector that is formed from the corresponding elements of x and y :

\[\texttt{angle} (I) = \texttt{atan2} ( \texttt{y} (I), \texttt{x} (I))\]

The angle estimation accuracy is about 0.3 degrees. When x(I)=y(I)=0 , the corresponding angle(I) is set to 0.

Parameters

  x | input floating-point array of x-coordinates of 2D vectors.
  y | input array of y-coordinates of 2D vectors; it must have the same size and the same type as x.
  angle | output array of vector angles; it has the same size and same type as x .
  angleInDegrees | when true, the function calculates the angle in degrees, otherwise, they are measured in radians.

## ◆ polarToCart()

void cv::polarToCart | ( | InputArray | magnitude,
|  | InputArray | angle,
|  | OutputArray | x,
|  | OutputArray | y,
|  | bool | angleInDegrees = `false`
| ) |  |

Calculates x and y coordinates of 2D vectors from their magnitude and angle.

The function cv::polarToCart calculates the Cartesian coordinates of each 2D vector represented by the corresponding elements of magnitude and angle:

\[\begin{array}{l} \texttt{x} (I) = \texttt{magnitude} (I) \cos ( \texttt{angle} (I)) \\ \texttt{y} (I) = \texttt{magnitude} (I) \sin ( \texttt{angle} (I)) \\ \end{array}\]

The relative accuracy of the estimated coordinates is about 1e-6.

Parameters

  magnitude | input floating-point array of magnitudes of 2D vectors; it can be an empty matrix (=Mat()), in this case, the function assumes that all the magnitudes are =1; if it is not empty, it must have the same size and type as angle.
  angle | input floating-point array of angles of 2D vectors.
  x | output array of x-coordinates of 2D vectors; it has the same size and type as angle.
  y | output array of y-coordinates of 2D vectors; it has the same size and type as angle.
  angleInDegrees | when true, the input angles are measured in degrees, otherwise, they are measured in radians.

See also
  cartToPolar, magnitude, phase, exp, log, pow, sqrt

## ◆ pow()

void cv::pow | ( | InputArray | src,
|  | double | power,
|  | OutputArray | dst
| ) |  |

Raises every array element to a power.

The function cv::pow raises every element of the input array to power :

\[\texttt{dst} (I) = \fork{\texttt{src}(I)^{power}}{if \(\texttt{power}\) is integer}{|\texttt{src}(I)|^{power}}{otherwise}\]

So, for a non-integer power exponent, the absolute values of input array elements are used. However, it is possible to get true values for negative values using some extra operations. In the example below, computing the 5th root of array src shows:

Mat mask = src < 0;
pow(src, 1./5, dst);
subtract(Scalar::all(0), dst, dst, mask);

For some values of power, such as integer values, 0.5 and -0.5, specialized faster algorithms are used.

Special values (NaN, Inf) are not handled.

Parameters

  src | input array.
  power | exponent of power.
  dst | output array of the same size and type as src.

See also
  sqrt, exp, log, cartToPolar, polarToCart

## ◆ PSNR()

double cv::PSNR | ( | InputArray | src1,
|  | InputArray | src2
| ) |  |

Computes the Peak Signal-to-Noise Ratio (PSNR) image quality metric.

This function calculates the Peak Signal-to-Noise Ratio (PSNR) image quality metric in decibels (dB), between two input arrays src1 and src2. Arrays must have depth CV_8U.

The PSNR is calculated as follows:

\[ \texttt{PSNR} = 10 \cdot \log_{10}{\left( \frac{R^2}{MSE} \right) } \]

where R is the maximum integer value of depth CV_8U (255) and MSE is the mean squared error between the two arrays.

Parameters

  src1 | first input array.
  src2 | second input array of the same size as src1.

## ◆ randn()

void cv::randn | ( | InputOutputArray | dst,
|  | InputArray | mean,
|  | InputArray | stddev
| ) |  |

Fills the array with normally distributed random numbers.

The function cv::randn fills the matrix dst with normally distributed random numbers with the specified mean vector and the standard deviation matrix. The generated random numbers are clipped to fit the value range of the output array data type.

Parameters

  dst | output array of random numbers; the array must be pre-allocated and have 1 to 4 channels.
  mean | mean value (expectation) of the generated random numbers.
  stddev | standard deviation of the generated random numbers; it can be either a vector (in which case a diagonal standard deviation matrix is assumed) or a square matrix.

See also
  RNG, randu

Examples:
  kalman.cpp.

## ◆ randShuffle()

void cv::randShuffle | ( | InputOutputArray | dst,
|  | double | iterFactor = `1.`,
|  | RNG * | rng = `0`
| ) |  |

Shuffles the array elements randomly.

The function cv::randShuffle shuffles the specified 1D array by randomly choosing pairs of elements and swapping them. The number of such swap operations will be dst.rows*dst.cols*iterFactor .

Parameters

  dst | input/output numerical 1D array.
  iterFactor | scale factor that determines the number of random swap operations (see the details below).
  rng | optional random number generator used for shuffling; if it is zero, theRNG () is used instead.

See also
  RNG, sort

Examples:
  kmeans.cpp, and shape_example.cpp.

## ◆ randu()

void cv::randu | ( | InputOutputArray | dst,
|  | InputArray | low,
|  | InputArray | high
| ) |  |

Generates a single uniformly-distributed random number or an array of random numbers.

Non-template variant of the function fills the matrix dst with uniformly-distributed random numbers from the specified range:

\[\texttt{low} _c \leq \texttt{dst} (I)_c < \texttt{high} _c\]

Parameters

  dst | output array of random numbers; the array must be pre-allocated.
  low | inclusive lower boundary of the generated random numbers.
  high | exclusive upper boundary of the generated random numbers.

See also
  RNG, randn, theRNG

Examples:
  cout_mat.cpp, and falsecolor.cpp.

## ◆ reduce()

void cv::reduce | ( | InputArray | src,
|  | OutputArray | dst,
|  | int | dim,
|  | int | rtype,
|  | int | dtype = `-1`
| ) |  |

Reduces a matrix to a vector.

The function reduce reduces the matrix to a vector by treating the matrix rows/columns as a set of 1D vectors and performing the specified operation on the vectors until a single row/column is obtained. For example, the function can be used to compute horizontal and vertical projections of a raster image. In case of REDUCE_MAX and REDUCE_MIN , the output image should have the same type as the source one. In case of REDUCE_SUM and REDUCE_AVG , the output may have a larger element bit-depth to preserve accuracy. And multi-channel arrays are also supported in these two reduction modes.

The following code demonstrates its usage for a single channel matrix.

Mat m = (Mat_<uchar>(3,2) << 1,2,3,4,5,6);
Mat col_sum, row_sum;
reduce(m, col_sum, 0, REDUCE_SUM, CV_32F);
reduce(m, row_sum, 1, REDUCE_SUM, CV_32F);
/*
m =
[ 1, 2;
3, 4;
5, 6]
col_sum =
[9, 12]
row_sum =
[3;
7;
11]
*/

And the following code demonstrates its usage for a two-channel matrix.

// two channels
char d[] = {1,2,3,4,5,6};
Mat m(3, 1, CV_8UC2, d);
Mat col_sum_per_channel;
reduce(m, col_sum_per_channel, 0, REDUCE_SUM, CV_32F);
/*
col_sum_per_channel =
[9, 12]
*/

Parameters

  src | input 2D matrix.
  dst | output vector. Its size and type is defined by dim and dtype parameters.
  dim | dimension index along which the matrix is reduced. 0 means that the matrix is reduced to a single row. 1 means that the matrix is reduced to a single column.
  rtype | reduction operation that could be one of ReduceTypes
  dtype | when negative, the output vector will have the same type as the input matrix, otherwise, its type will be CV_MAKE_TYPE(CV_MAT_DEPTH(dtype), src.channels()).

See also
  repeat

## ◆ repeat() [1/2]

void cv::repeat | ( | InputArray | src,
|  | int | ny,
|  | int | nx,
|  | OutputArray | dst
| ) |  |

Fills the output array with repeated copies of the input array.

The function cv::repeat duplicates the input array one or more times along each of the two axes:

\[\texttt{dst} _{ij}= \texttt{src} _{i\mod src.rows, \; j\mod src.cols }\]

The second variant of the function is more convenient to use with MatrixExpressions.

Parameters

  src | input array to replicate.
  ny | Flag to specify how many times the `src` is repeated along the vertical axis.
  nx | Flag to specify how many times the `src` is repeated along the horizontal axis.
  dst | output array of the same type as `src`.

See also
  cv::reduce

## ◆ repeat() [2/2]

Mat cv::repeat | ( | const Mat & | src,
|  | int | ny,
|  | int | nx
| ) |  |

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Parameters

  src | input array to replicate.
  ny | Flag to specify how many times the `src` is repeated along the vertical axis.
  nx | Flag to specify how many times the `src` is repeated along the horizontal axis.

## ◆ rotate()

void cv::rotate | ( | InputArray | src,
|  | OutputArray | dst,
|  | int | rotateCode
| ) |  |

Rotates a 2D array in multiples of 90 degrees. The function cv::rotate rotates the array in one of three different ways: Rotate by 90 degrees clockwise (rotateCode = ROTATE_90_CLOCKWISE). Rotate by 180 degrees clockwise (rotateCode = ROTATE_180). Rotate by 270 degrees clockwise (rotateCode = ROTATE_90_COUNTERCLOCKWISE).

Parameters

  src | input array.
  dst | output array of the same type as src. The size is the same with ROTATE_180, and the rows and cols are switched for ROTATE_90_CLOCKWISE and ROTATE_90_COUNTERCLOCKWISE.
  rotateCode | an enum to specify how to rotate the array; see the enum RotateFlags

See also
  transpose , repeat , completeSymm, flip, RotateFlags

## ◆ scaleAdd()

void cv::scaleAdd | ( | InputArray | src1,
|  | double | alpha,
|  | InputArray | src2,
|  | OutputArray | dst
| ) |  |

Calculates the sum of a scaled array and another array.

The function scaleAdd is one of the classical primitive linear algebra operations, known as DAXPY or SAXPY in BLAS. It calculates the sum of a scaled array and another array:

\[\texttt{dst} (I)= \texttt{scale} \cdot \texttt{src1} (I) + \texttt{src2} (I)\]

The function can also be emulated with a matrix expression, for example:

Mat A(3, 3, CV_64F);
...
A.row(0) = A.row(1)*2 + A.row(2);

Parameters

  src1 | first input array.
  alpha | scale factor for the first array.
  src2 | second input array of the same size and type as src1.
  dst | output array of the same size and type as src1.

See also
  add, addWeighted, subtract, Mat::dot, Mat::convertTo

## ◆ setIdentity()

void cv::setIdentity | ( | InputOutputArray | mtx,
|  | const Scalar & | s = `Scalar(1)`
| ) |  |

Initializes a scaled identity matrix.

The function cv::setIdentity initializes a scaled identity matrix:

\[\texttt{mtx} (i,j)= \fork{\texttt{value}}{ if \(i=j\)}{0}{otherwise}\]

The function can also be emulated using the matrix initializers and the matrix expressions:

Mat A = Mat::eye(4, 3, CV_32F)*5;
// A will be set to [[5, 0, 0], [0, 5, 0], [0, 0, 5], [0, 0, 0]]

Parameters

  mtx | matrix to initialize (not necessarily square).
  s | value to assign to diagonal elements.

See also
  Mat::zeros, Mat::ones, Mat::setTo, Mat::operator=

Examples:
  kalman.cpp.

## ◆ setRNGSeed()

void cv::setRNGSeed | ( | int | seed | ) |

Sets state of default random number generator.

The function cv::setRNGSeed sets state of default random number generator to custom value.

Parameters

  seed | new state for default random number generator

See also
  RNG, randu, randn

## ◆ solve()

bool cv::solve | ( | InputArray | src1,
|  | InputArray | src2,
|  | OutputArray | dst,
|  | int | flags = `DECOMP_LU`
| ) |  |

Solves one or more linear systems or least-squares problems.

The function cv::solve solves a linear system or least-squares problem (the latter is possible with SVD or QR methods, or by specifying the flag DECOMP_NORMAL ):

\[\texttt{dst} = \arg \min _X \| \texttt{src1} \cdot \texttt{X} - \texttt{src2} \|\]

If DECOMP_LU or DECOMP_CHOLESKY method is used, the function returns 1 if src1 (or \(\texttt{src1}^T\texttt{src1}\) ) is non-singular. Otherwise, it returns 0. In the latter case, dst is not valid. Other methods find a pseudo-solution in case of a singular left-hand side part.

Note
  If you want to find a unity-norm solution of an under-defined singular system \(\texttt{src1}\cdot\texttt{dst}=0\) , the function solve will not do the work. Use SVD::solveZ instead.

Parameters

  src1 | input matrix on the left-hand side of the system.
  src2 | input matrix on the right-hand side of the system.
  dst | output solution.
  flags | solution (matrix inversion) method (DecompTypes)

See also
  invert, SVD, eigen

## ◆ solveCubic()

int cv::solveCubic | ( | InputArray | coeffs,
|  | OutputArray | roots
| ) |  |

Finds the real roots of a cubic equation.

The function solveCubic finds the real roots of a cubic equation:

- if coeffs is a 4-element vector:

  \[\texttt{coeffs} [0] x^3 + \texttt{coeffs} [1] x^2 + \texttt{coeffs} [2] x + \texttt{coeffs} [3] = 0\]

- if coeffs is a 3-element vector:

  \[x^3 + \texttt{coeffs} [0] x^2 + \texttt{coeffs} [1] x + \texttt{coeffs} [2] = 0\]

The roots are stored in the roots array.

Parameters

  coeffs | equation coefficients, an array of 3 or 4 elements.
  roots | output array of real roots that has 1 or 3 elements.

Returns
  number of real roots. It can be 0, 1 or 2.

## ◆ solvePoly()

double cv::solvePoly | ( | InputArray | coeffs,
|  | OutputArray | roots,
|  | int | maxIters = `300`
| ) |  |

Finds the real or complex roots of a polynomial equation.

The function cv::solvePoly finds real and complex roots of a polynomial equation:

\[\texttt{coeffs} [n] x^{n} + \texttt{coeffs} [n-1] x^{n-1} + ... + \texttt{coeffs} [1] x + \texttt{coeffs} [0] = 0\]

Parameters

  coeffs | array of polynomial coefficients.
  roots | output (complex) array of roots.
  maxIters | maximum number of iterations the algorithm does.

## ◆ sort()

void cv::sort | ( | InputArray | src,
|  | OutputArray | dst,
|  | int | flags
| ) |  |

Sorts each row or each column of a matrix.

The function cv::sort sorts each matrix row or each matrix column in ascending or descending order. So you should pass two operation flags to get desired behaviour. If you want to sort matrix rows or columns lexicographically, you can use STL std::sort generic function with the proper comparison predicate.

Parameters

  src | input single-channel array.
  dst | output array of the same size and type as src.
  flags | operation flags, a combination of SortFlags

See also
  sortIdx, randShuffle

## ◆ sortIdx()

void cv::sortIdx | ( | InputArray | src,
|  | OutputArray | dst,
|  | int | flags
| ) |  |

Sorts each row or each column of a matrix.

The function cv::sortIdx sorts each matrix row or each matrix column in the ascending or descending order. So you should pass two operation flags to get desired behaviour. Instead of reordering the elements themselves, it stores the indices of sorted elements in the output array. For example:

Mat A = Mat::eye(3,3,CV_32F), B;
sortIdx(A, B, SORT_EVERY_ROW + SORT_ASCENDING);
// B will probably contain
// (because of equal elements in A some permutations are possible):
// [[1, 2, 0], [0, 2, 1], [0, 1, 2]]

Parameters

  src | input single-channel array.
  dst | output integer array of the same size as src.
  flags | operation flags that could be a combination of cv::SortFlags

See also
  sort, randShuffle

## ◆ split() [1/2]

void cv::split | ( | const Mat & | src,
|  | Mat * | mvbegin
| ) |  |

Divides a multi-channel array into several single-channel arrays.

The function cv::split splits a multi-channel array into separate single-channel arrays:

\[\texttt{mv} [c](I) = \texttt{src} (I)_c\]

If you need to extract a single channel or do some other sophisticated channel permutation, use mixChannels .

The following example demonstrates how to split a 3-channel matrix into 3 single channel matrices.

char d[] = {1,2,3,4,5,6,7,8,9,10,11,12};
Mat m(2, 2, CV_8UC3, d);
Mat channels[3];
split(m, channels);
/*
channels[0] =
[ 1, 4;
7, 10]
channels[1] =
[ 2, 5;
8, 11]
channels[2] =
[ 3, 6;
9, 12]
*/

Parameters

  src | input multi-channel array.
  mvbegin | output array; the number of arrays must match src.channels(); the arrays themselves are reallocated, if needed.

See also
  merge, mixChannels, cvtColor

## ◆ split() [2/2]

void cv::split | ( | InputArray | m,
|  | OutputArrayOfArrays | mv
| ) |  |

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Parameters

  m | input multi-channel array.
  mv | output vector of arrays; the arrays themselves are reallocated, if needed.

## ◆ sqrt()

void cv::sqrt | ( | InputArray | src,
|  | OutputArray | dst
| ) |  |

Calculates a square root of array elements.

The function cv::sqrt calculates a square root of each input array element. In case of multi-channel arrays, each channel is processed independently. The accuracy is approximately the same as of the built-in std::sqrt .

Parameters

  src | input floating-point array.
  dst | output array of the same size and type as src.

## ◆ subtract()

void cv::subtract | ( | InputArray | src1,
|  | InputArray | src2,
|  | OutputArray | dst,
|  | InputArray | mask = `noArray()`,
|  | int | dtype = `-1`
| ) |  |

Calculates the per-element difference between two arrays or array and a scalar.

The function subtract calculates:

- Difference between two arrays, when both input arrays have the same size and the same number of channels:

  \[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1}(I) - \texttt{src2}(I)) \quad \texttt{if mask}(I) \ne0\]

- Difference between an array and a scalar, when src2 is constructed from Scalar or has the same number of elements as `src1.channels()`:

  \[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1}(I) - \texttt{src2} ) \quad \texttt{if mask}(I) \ne0\]

- Difference between a scalar and an array, when src1 is constructed from Scalar or has the same number of elements as `src2.channels()`:

  \[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1} - \texttt{src2}(I) ) \quad \texttt{if mask}(I) \ne0\]

- The reverse difference between a scalar and an array in the case of `SubRS`:

  \[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src2} - \texttt{src1}(I) ) \quad \texttt{if mask}(I) \ne0\]

  where I is a multi-dimensional index of array elements. In case of multi-channel arrays, each channel is processed independently.

The first function in the list above can be replaced with matrix expressions:

dst = src1 - src2;
dst -= src1; // equivalent to subtract(dst, src1, dst);

The input arrays and the output array can all have the same or different depths. For example, you can subtract to 8-bit unsigned arrays and store the difference in a 16-bit signed array. Depth of the output array is determined by dtype parameter. In the second and third cases above, as well as in the first case, when src1.depth() == src2.depth(), dtype can be set to the default -1. In this case the output array will have the same depth as the input array, be it src1, src2 or both.

Note
  Saturation is not applied when the output array has the depth CV_32S. You may even get result of an incorrect sign in the case of overflow.

Parameters

  src1 | first input array or a scalar.
  src2 | second input array or a scalar.
  dst | output array of the same size and the same number of channels as the input array.
  mask | optional operation mask; this is an 8-bit single channel array that specifies elements of the output array to be changed.
  dtype | optional depth of the output array

See also
  add, addWeighted, scaleAdd, Mat::convertTo

Examples:
  image_alignment.cpp.

## ◆ sum()

Scalar cv::sum | ( | InputArray | src | ) |

Calculates the sum of array elements.

The function cv::sum calculates and returns the sum of array elements, independently for each channel.

Parameters

  src | input array that must have from 1 to 4 channels.

See also
  countNonZero, mean, meanStdDev, norm, minMaxLoc, reduce

## ◆ SVBackSubst()

void cv::SVBackSubst | ( | InputArray | w,
|  | InputArray | u,
|  | InputArray | vt,
|  | InputArray | rhs,
|  | OutputArray | dst
| ) |  |

wrap SVD::backSubst

## ◆ SVDecomp()

void cv::SVDecomp | ( | InputArray | src,
|  | OutputArray | w,
|  | OutputArray | u,
|  | OutputArray | vt,
|  | int | flags = `0`
| ) |  |

wrap SVD::compute

Examples:
  pose_from_homography.cpp.

## ◆ theRNG()

RNG& cv::theRNG | ( |  | ) |

Returns the default random number generator.

The function cv::theRNG returns the default random number generator. For each thread, there is a separate random number generator, so you can use the function safely in multi-thread environments. If you just need to get a single random number using this generator or initialize an array, you can use randu or randn instead. But if you are going to generate many random numbers inside a loop, it is much faster to use this function to retrieve the generator and then use RNG::operator _Tp() .

See also
  RNG, randu, randn

Examples:
  convexhull.cpp, ffilldemo.cpp, kalman.cpp, minarea.cpp, and watershed.cpp.

## ◆ trace()

Scalar cv::trace | ( | InputArray | mtx | ) |

Returns the trace of a matrix.

The function cv::trace returns the sum of the diagonal elements of the matrix mtx .

\[\mathrm{tr} ( \texttt{mtx} ) = \sum _i \texttt{mtx} (i,i)\]

Parameters

  mtx | input matrix.

## ◆ transform()

void cv::transform | ( | InputArray | src,
|  | OutputArray | dst,
|  | InputArray | m
| ) |  |

Performs the matrix transformation of every array element.

The function cv::transform performs the matrix transformation of every element of the array src and stores the results in dst :

\[\texttt{dst} (I) = \texttt{m} \cdot \texttt{src} (I)\]

(when m.cols=src.channels() ), or

\[\texttt{dst} (I) = \texttt{m} \cdot [ \texttt{src} (I); 1]\]

(when m.cols=src.channels()+1 )

Every element of the N -channel array src is interpreted as N -element vector that is transformed using the M x N or M x (N+1) matrix m to M-element vector - the corresponding element of the output array dst .

The function may be used for geometrical transformation of N -dimensional points, arbitrary linear color space transformation (such as various kinds of RGB to YUV transforms), shuffling the image channels, and so forth.

Parameters

  src | input array that must have as many channels (1 to 4) as m.cols or m.cols-1.
  dst | output array of the same size and depth as src; it has as many channels as m.rows.
  m | transformation 2x2 or 2x3 floating-point matrix.

See also
  perspectiveTransform, getAffineTransform, estimateAffine2D, warpAffine, warpPerspective

## ◆ transpose()

void cv::transpose | ( | InputArray | src,
|  | OutputArray | dst
| ) |  |

Transposes a matrix.

The function cv::transpose transposes the matrix src :

\[\texttt{dst} (i,j) = \texttt{src} (j,i)\]

Note
  No complex conjugation is done in case of a complex matrix. It should be done separately if needed.

Parameters

  src | input array.
  dst | output array of the same type as src.

Examples:
  train_HOG.cpp.

## ◆ vconcat() [1/3]

void cv::vconcat | ( | const Mat * | src,
|  | size_t | nsrc,
|  | OutputArray | dst
| ) |  |

Applies vertical concatenation to given matrices.

The function vertically concatenates two or more cv::Mat matrices (with the same number of cols).

cv::Mat matArray[] = { cv::Mat(1, 4, CV_8UC1, cv::Scalar(1)),
cv::Mat(1, 4, CV_8UC1, cv::Scalar(2)),
cv::Mat(1, 4, CV_8UC1, cv::Scalar(3)),};
cv::Mat out;
cv::vconcat( matArray, 3, out );
//out:
//[1, 1, 1, 1;
// 2, 2, 2, 2;
// 3, 3, 3, 3]

Parameters

  src | input array or vector of matrices. all of the matrices must have the same number of cols and the same depth.
  nsrc | number of matrices in src.
  dst | output array. It has the same number of cols and depth as the src, and the sum of rows of the src.

See also
  cv::hconcat(const Mat*, size_t, OutputArray),
  cv::hconcat(InputArrayOfArrays, OutputArray) and
  cv::hconcat(InputArray, InputArray, OutputArray)

## ◆ vconcat() [2/3]

void cv::vconcat | ( | InputArray | src1,
|  | InputArray | src2,
|  | OutputArray | dst
| ) |  |

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

cv::Mat_<float> A = (cv::Mat_<float>(3, 2) << 1, 7,
2, 8,
3, 9);
cv::Mat_<float> B = (cv::Mat_<float>(3, 2) << 4, 10,
5, 11,
6, 12);
cv::Mat C;
cv::vconcat(A, B, C);
//C:
//[1, 7;
// 2, 8;
// 3, 9;
// 4, 10;
// 5, 11;
// 6, 12]

Parameters

  src1 | first input array to be considered for vertical concatenation.
  src2 | second input array to be considered for vertical concatenation.
  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.

## ◆ vconcat() [3/3]

void cv::vconcat | ( | InputArrayOfArrays | src,
|  | OutputArray | dst
| ) |  |

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

std::vector<cv::Mat> matrices = { cv::Mat(1, 4, CV_8UC1, cv::Scalar(1)),
cv::Mat(1, 4, CV_8UC1, cv::Scalar(2)),
cv::Mat(1, 4, CV_8UC1, cv::Scalar(3)),};
cv::Mat out;
cv::vconcat( matrices, out );
//out:
//[1, 1, 1, 1;
// 2, 2, 2, 2;
// 3, 3, 3, 3]

Parameters

  src | input array or vector of matrices. all of the matrices must have the same number of cols and the same depth
  dst | output array. It has the same number of cols and depth as the src, and the sum of rows of the src. same depth.