Computes absolute value of each matrix element
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abs is a meta-function that is expanded to one of absdiff() forms:
The output matrix will have the same size and the same type as the input one (except for the last case, where C will be depth=CV_8U ).
See also: Matrix Expressions , absdiff() ,
Computes per-element absolute difference between 2 arrays or between array and a scalar.
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The functions absdiff compute:
absolute difference between two arrays
or absolute difference between array and a scalar:
where I is multi-dimensional index of array elements. in the case of multi-channel arrays each channel is processed independently.
See also: abs() ,
Computes the per-element sum of two arrays or an array and a scalar.
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The functions add compute:
the sum of two arrays:
or the sum of array and a scalar:
where I is multi-dimensional index of array elements.
The first function in the above list can be replaced with matrix expressions:
dst = src1 + src2;
dst += src1; // equivalent to add(dst, src1, dst);
in the case of multi-channel arrays each channel is processed independently.
See also: subtract() , addWeighted() , scaleAdd() , convertScale() , Matrix Expressions , .
Computes the weighted sum of two arrays.
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The functions addWeighted calculate the weighted sum of two arrays as follows:
where I is multi-dimensional index of array elements.
The first function can be replaced with a matrix expression:
dst = src1*alpha + src2*beta + gamma;
In the case of multi-channel arrays each channel is processed independently.
See also: add() , subtract() , scaleAdd() , convertScale() , Matrix Expressions , .
Calculates per-element bit-wise conjunction of two arrays and an array and a scalar.
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The functions bitwise_and compute per-element bit-wise logical conjunction:
of two arrays
or array and a scalar:
In the case of floating-point arrays their machine-specific bit representations (usually IEEE754-compliant) are used for the operation, and in the case of multi-channel arrays each channel is processed independently.
See also: , ,
Inverts every bit of array
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The functions bitwise_not compute per-element bit-wise inversion of the source array:
In the case of floating-point source array its machine-specific bit representation (usually IEEE754-compliant) is used for the operation. in the case of multi-channel arrays each channel is processed independently.
See also: , ,
Calculates per-element bit-wise disjunction of two arrays and an array and a scalar.
Parameters: |
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The functions bitwise_or compute per-element bit-wise logical disjunction
of two arrays
or array and a scalar:
In the case of floating-point arrays their machine-specific bit representations (usually IEEE754-compliant) are used for the operation. in the case of multi-channel arrays each channel is processed independently.
See also: , ,
Calculates per-element bit-wise “exclusive or” operation on two arrays and an array and a scalar.
Parameters: |
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The functions bitwise_xor compute per-element bit-wise logical “exclusive or” operation
on two arrays
or array and a scalar:
In the case of floating-point arrays their machine-specific bit representations (usually IEEE754-compliant) are used for the operation. in the case of multi-channel arrays each channel is processed independently.
See also: , ,
Calculates covariation matrix of a set of vectors
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The functions calcCovarMatrix calculate the covariance matrix and, optionally, the mean vector of the set of input vectors.
See also: PCA() , mulTransposed() , Mahalanobis()
Calculates the magnitude and angle of 2d vectors.
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The function cartToPolar calculates either the magnitude, angle, or both of every 2d vector (x(I),y(I)):
The angles are calculated with accuracy. For the (0,0) point, the angle is set to 0.
Checks every element of an input array for invalid values.
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The functions checkRange check that every array element is neither NaN nor . When minVal < -DBL_MAX and maxVal < DBL_MAX , then the functions also check that each value is between minVal and maxVal . in the 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 ), and then the functions either return false (when quiet=true ) or throw an exception.
Performs per-element comparison of two arrays or an array and scalar value.
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The functions compare compare each element of src1 with the corresponding element of src2 or with real scalar value . When the comparison result is true, the corresponding element of destination array is set to 255, otherwise it is set to 0:
The comparison operations can be replaced with the equivalent matrix expressions:
Mat dst1 = src1 >= src2;
Mat dst2 = src1 < 8;
...
See also: checkRange() , min() , max() , threshold() , Matrix Expressions
Copies the lower or the upper half of a square matrix to another half.
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The function completeSymm copies the lower half of a square matrix to its another half; the matrix diagonal remains unchanged:
See also: flip() , transpose()
Scales, computes absolute values and converts the result to 8-bit.
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On each element of the input array the function convertScaleAbs performs 3 operations sequentially: scaling, taking absolute value, conversion to unsigned 8-bit type:
in the 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 Mat::convertTo method (or by using matrix expressions) and then by computing 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
See also: Mat::convertTo() , abs()
Counts non-zero array elements.
Parameters: |
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The function cvCountNonZero returns the number of non-zero elements in mtx:
See also: mean() , meanStdDev() , norm() , minMaxLoc() , calcCovarMatrix()
Computes cube root of the argument
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The function cubeRoot computes . Negative arguments are handled correctly, NaN and are not handled. The accuracy approaches the maximum possible accuracy for single-precision data.
Converts CvMat, IplImage or CvMatND to cv::Mat.
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The function cvarrToMat converts CvMat , IplImage or CvMatND header to Mat() header, and optionally duplicates the underlying data. The constructed header is returned by the function.
When copyData=false , the conversion is done really fast (in O(1) time) and the newly created matrix header will have refcount=0 , which means that no reference counting is done for the matrix data, and user has to preserve the data until the new header is destructed. Otherwise, when copyData=true , the new buffer will be allocated and managed as if you created a new matrix from scratch and copy the data there. That is, cvarrToMat(src, true) :math:`\sim` cvarrToMat(src, false).clone() (assuming that COI is not set). The function provides uniform way of supporting CvArr paradigm in the code that is migrated to use new-style data structures internally. The reverse transformation, from Mat() to CvMat or IplImage can be done by simple assignment:
CvMat* A = cvCreateMat(10, 10, CV_32F);
cvSetIdentity(A);
IplImage A1; cvGetImage(A, &A1);
Mat B = cvarrToMat(A);
Mat B1 = cvarrToMat(&A1);
IplImage C = B;
CvMat C1 = B1;
// now A, A1, B, B1, C and C1 are different headers
// for the same 10x10 floating-point array.
// note, that you will need to use "&"
// to pass C & C1 to OpenCV functions, e.g:
printf("
Normally, the function is used to convert an old-style 2D array ( CvMat or IplImage ) to Mat , however, the function can also take CvMatND on input and create Mat() for it, if it’s possible. And for CvMatND A it is possible if and only if A.dim[i].size*A.dim.step[i] == A.dim.step[i-1] for all or for all but one i, 0 < i < A.dims . That is, the matrix data should be continuous or it should be representable as a sequence of continuous matrices. By using this function in this way, you can process CvMatND using arbitrary element-wise function. But for more complex operations, such as filtering functions, it will not work, and you need to convert CvMatND to MatND() using the corresponding constructor of the latter.
The last parameter, coiMode , specifies how to react on an image with COI set: by default it’s 0, and then the function reports an error when an image with COI comes in. And coiMode=1 means that no error is signaled - user has to check COI presence and handle it manually. The modern structures, such as Mat() and MatND() do not support COI natively. To process individual channel of an new-style array, you will need either to organize loop over the array (e.g. using matrix iterators) where the channel of interest will be processed, or extract the COI using mixChannels() (for new-style arrays) or extractImageCOI() (for old-style arrays), process this individual channel and insert it back to the destination array if need (using mixChannel() or insertImageCOI() , respectively).
See also: cvGetImage() , cvGetMat() , cvGetMatND() , extractImageCOI() , insertImageCOI() , mixChannels()
Performs a forward or inverse discrete cosine transform of 1D or 2D array
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The function dct performs a forward or inverse discrete cosine transform (DCT) of a 1D or 2D floating-point array:
Forward Cosine transform of 1D vector of elements:
where
and , for .
Inverse Cosine transform of 1D vector of N elements:
(since is orthogonal matrix, )
Forward Cosine transform of 2D matrix:
Inverse Cosine transform of 2D vector of elements:
The function chooses the mode of operation by looking at the flags and size of the input array:
Important note : currently cv::dct supports even-size arrays (2, 4, 6 ...). For data analysis and approximation you can pad the array when necessary.
Also, the function’s 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 computed via DFT of a vector of size N/2 , thus the optimal DCT size can be computed as:
size_t getOptimalDCTSize(size_t N) { return 2*getOptimalDFTSize((N+1)/2); }
See also: dft() , getOptimalDFTSize() , idct()
Performs a forward or inverse Discrete Fourier transform of 1D or 2D floating-point array.
Parameters: |
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Forward Fourier transform of 1D vector of N elements:
where and Inverse Fourier transform of 1D vector of N elements:
where Forward Fourier transform of 2D vector of elements:
Inverse Fourier transform of 2D vector of elements:
In the case of real (single-channel) data, the packed format called CCS (complex-conjugate-symmetrical) that was borrowed from IPL and used to represent the result of a forward Fourier transform or input for an inverse Fourier transform:
in the case of 1D transform of real vector, the output will look as the first row of the above matrix.
So, the function chooses the operation mode depending on the flags and size of the input array:
The scaling is done after the transformation if DFT_SCALE is set.
Unlike dct() , the function supports arrays of arbitrary size, but only those arrays are processed efficiently, which 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 computed using getOptimalDFTSize() method.
Here is the sample on how to compute DFT-based convolution of two 2D real arrays:
void convolveDFT(const Mat& A, const Mat& B, Mat& 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;
// compute 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,
// we need only the first C.rows of them, and thus we
// 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
}
What can be optimized in the above sample?
since we passed to the forward transform calls and
since we copied
A / B to the top-left corners of tempA / tempB , respectively,
it’s 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.
especially if
B is significantly smaller than A or vice versa.
Instead, we can compute convolution by parts. For that we need to split the destination array
C into multiple tiles and for each tile estimate, which parts of A and B are required to compute 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 slowdown because of bad cache locality. So there is optimal tile size somewhere in the middle.
if the convolution is done by parts, since different tiles in C can be computed in parallel, the loop can be threaded.
All of the above improvements have been implemented in matchTemplate() and filter2D() , therefore, by using them, you can get even better performance than with the above theoretically optimal implementation (though, those two functions actually compute cross-correlation, not convolution, so you will need to “flip” the kernel or the image around the center using flip() ).
See also: dct() , getOptimalDFTSize() , mulSpectrums() , filter2D() , matchTemplate() , flip() , cartToPolar() , magnitude() , phase()
Performs per-element division of two arrays or a scalar by an array.
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The functions divide divide one array by another:
or a scalar by array, when there is no src1 :
The result will have the same type as src1 . When src2(I)=0 , dst(I)=0 too.
See also: multiply() , add() , subtract() , Matrix Expressions
Returns determinant of a square floating-point matrix.
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The function determinant computes and returns 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.
For symmetric positive-determined matrices, it is also possible to compute SVD() : and then calculate the determinant as a product of the diagonal elements of .
See also: SVD() , trace() , invert() , solve() , Matrix Expressions
Computes eigenvalues and eigenvectors of a symmetric matrix.
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The functions eigen compute just eigenvalues, or eigenvalues and eigenvectors of symmetric matrix src :
src*eigenvectors(i,:)' = eigenvalues(i)*eigenvectors(i,:)' (in MATLAB notation)
If either low- or highindex is supplied the other is required, too. Indexing is 0-based. Example: To calculate the largest eigenvector/-value set lowindex = highindex = 0. For legacy reasons this function always returns a square matrix the same size as the source matrix with eigenvectors and a vector the length of the source matrix with eigenvalues. The selected eigenvectors/-values are always in the first highindex - lowindex + 1 rows.
See also: SVD() , completeSymm() , PCA()
Calculates the exponent of every array element.
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The function exp calculates the exponent of every element of the input array:
The maximum relative error is about for single-precision and less than for double-precision. Currently, the function converts denormalized values to zeros on output. Special values (NaN, ) are not handled.
See also: log() , cartToPolar() , polarToCart() , phase() , pow() , sqrt() , magnitude()
Extract the selected image channel
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The function extractImageCOI is used to extract image COI from an old-style array and put the result to the new-style C++ matrix. As usual, the destination matrix is reallocated using Mat::create if needed.
To extract a channel from a new-style matrix, use mixChannels() or split() See also: mixChannels() , split() , merge() , cvarrToMat() , cvSetImageCOI() , cvGetImageCOI()
Calculates the angle of a 2D vector in degrees
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The function fastAtan2 calculates the full-range angle of an input 2D vector. The angle is measured in degrees and varies from to . The accuracy is about .
Flips a 2D array around vertical, horizontal or both axes.
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The function flip flips the array in one of three different ways (row and column indices are 0-based):
The example scenarios of function use are:
See also: transpose() , repeat() , completeSymm()
Performs generalized matrix multiplication.
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The function performs generalized matrix multiplication and similar to the corresponding functions *gemm in BLAS level 3. For example, gemm(src1, src2, alpha, src3, beta, dst, GEMM_1_T + GEMM_3_T) corresponds to
The function can be replaced with a matrix expression, e.g. the above call can be replaced with:
dst = alpha*src1.t()*src2 + beta*src3.t();
See also: mulTransposed() , transform() , Matrix Expressions
Returns conversion function for a single pixel
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The functions getConvertElem and getConvertScaleElem return pointers to the functions for converting individual pixels from one type to another. While the main function purpose is to convert single pixels (actually, for converting sparse matrices from one type to another), you can use them to convert the whole row of a dense matrix or the whole matrix at once, by setting cn = matrix.cols*matrix.rows*matrix.channels() if the matrix data is continuous.
See also: Mat::convertTo() , MatND::convertTo() , SparseMat::convertTo()
Returns optimal DFT size for a given vector size.
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DFT performance is not a monotonic function of a vector size, therefore, when you compute convolution of two arrays or do a spectral analysis of 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, which size is a power-of-two (2, 4, 8, 16, 32, ...) are the fastest to process, though, the arrays, which size is a product of 2’s, 3’s and 5’s (e.g. 300 = 5*5*3*2*2), are also processed quite efficiently.
The function getOptimalDFTSize returns the minimum number N that is greater than or equal to vecsize , such that the DFT of a vector of size N can be computed efficiently. In the current implementation , for some , , .
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 computed as getOptimalDFTSize((vecsize+1)/2)*2 .
See also: dft() , dct() , idft() , idct() , mulSpectrums()
Computes inverse Discrete Cosine Transform of a 1D or 2D array
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idct(src, dst, flags) is equivalent to dct(src, dst, flags | DCT_INVERSE) . See dct() for details.
See also: dct() , dft() , idft() , getOptimalDFTSize()
Computes inverse Discrete Fourier Transform of a 1D or 2D array
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idft(src, dst, flags) is equivalent to dct(src, dst, flags | DFT_INVERSE) . See dft() for details. Note, that none of dft and idft scale the result by default. Thus, 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()
Checks if array elements lie between the elements of two other arrays.
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The functions inRange do the range check for every element of the input array:
for single-channel arrays,
for two-channel arrays and so forth. dst (I) is set to 255 (all 1 -bits) if src (I) is within the specified range and 0 otherwise.
Finds the inverse or pseudo-inverse of a matrix
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The function invert inverts matrix src and stores the result in dst . When the matrix src is singular or non-square, the function computes the pseudo-inverse matrix, i.e. the matrix dst , such that is minimal.
In the case of DECOMP_LU method, the function returns the src determinant ( src must be square). If it is 0, the matrix is not inverted and dst is filled with zeros.
In the case of DECOMP_SVD method, the function returns the inversed 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. In this case the function stores the inverted matrix in dst and returns non-zero, otherwise it returns 0.
See also: solve() , SVD()
Calculates the natural logarithm of every array element.
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The function log calculates the natural logarithm of the absolute value of every element of the input array:
Where C is a large negative number (about -700 in the current implementation). The maximum relative error is about for single-precision input and less than for double-precision input. Special values (NaN, ) are not handled.
See also: exp() , cartToPolar() , polarToCart() , phase() , pow() , sqrt() , magnitude()
Performs a look-up table transform of an array.
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The function LUT fills the destination array with values from the look-up table. Indices of the entries are taken from the source array. That is, the function processes each element of src as follows:
where
See also: convertScaleAbs() , Mat::convertTo
Calculates magnitude of 2D vectors.
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The function magnitude calculates magnitude of 2D vectors formed from the corresponding elements of x and y arrays:
See also: cartToPolar() , polarToCart() , phase() , sqrt()
Calculates the Mahalanobis distance between two vectors.
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The function cvMahalonobis calculates and returns the weighted distance between two vectors:
The covariance matrix may be calculated using the calcCovarMatrix() function and then inverted using the invert() function (preferably using DECOMP _ SVD method, as the most accurate).
Calculates per-element maximum of two arrays or array and a scalar
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The functions max compute per-element maximum of two arrays:
or array and a scalar:
In the second variant, when the source array is multi-channel, each channel is compared with value independently.
The first 3 variants of the function listed above are actually a part of Matrix Expressions , they return the expression object that can be further transformed, or assigned to a matrix, or passed to a function etc.
See also: min() , compare() , inRange() , minMaxLoc() , Matrix Expressions
Calculates average (mean) of array elements
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The functions mean compute mean value M of array elements, independently for each channel, and return it:
When all the mask elements are 0’s, the functions return Scalar::all(0) .
See also: countNonZero() , meanStdDev() , norm() , minMaxLoc()
Calculates mean and standard deviation of array elements
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The functions meanStdDev compute the mean and the standard deviation M of array elements, independently for each channel, and return it via the output parameters:
When all the mask elements are 0’s, the functions return mean=stddev=Scalar::all(0) . Note that the computed 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 to the single-channel array (only possible when the matrix is continuous) and then pass the matrix to calcCovarMatrix() .
See also: countNonZero() , mean() , norm() , minMaxLoc() , calcCovarMatrix()
Composes a multi-channel array from several single-channel arrays.
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The functions merge merge several single-channel arrays (or rather interleave their elements) to make a single multi-channel array.
The function split() does the reverse operation and if you need to merge several multi-channel images or shuffle channels in some other advanced way, use mixChannels() See also: mixChannels() , split() , reshape()
Calculates per-element minimum of two arrays or array and a scalar
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The functions min compute per-element minimum of two arrays:
or array and a scalar:
In the second variant, when the source array is multi-channel, each channel is compared with value independently.
The first 3 variants of the function listed above are actually a part of Matrix Expressions , they return the expression object that can be further transformed, or assigned to a matrix, or passed to a function etc.
See also: max() , compare() , inRange() , minMaxLoc() , Matrix Expressions
Finds global minimum and maximum in a whole array or sub-array
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The functions ninMaxLoc find 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 functions do not work with multi-channel arrays. If you need to find minimum or maximum elements across all the channels, use reshape() first to reinterpret the array as single-channel. Or you may extract the particular channel using extractImageCOI() or mixChannels() or split() .
in the case of a sparse matrix the minimum is found among non-zero elements only.
See also: max() , min() , compare() , inRange() , extractImageCOI() , mixChannels() , split() , reshape() .
Copies specified channels from input arrays to the specified channels of output arrays
Parameters: |
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npairs
The functions mixChannels provide an advanced mechanism for shuffling image channels. split() and merge() and some forms of cvtColor() are partial cases of mixChannels .
As an example, this code splits a 4-channel RGBA image into a 3-channel BGR (i.e. with R and B channels swapped) and separate alpha channel image:
Mat rgba( 100, 100, CV_8UC4, Scalar(1,2,3,4) );
Mat bgr( rgba.rows, rgba.cols, CV_8UC3 );
Mat alpha( rgba.rows, rgba.cols, CV_8UC1 );
// forming array of matrices is quite efficient operations,
// because the matrix data is not copied, only the headers
Mat out[] = { bgr, alpha };
// rgba[0] -> bgr[2], rgba[1] -> bgr[1],
// rgba[2] -> bgr[0], rgba[3] -> alpha[0]
int from_to[] = { 0,2, 1,1, 2,0, 3,3 };
mixChannels( &rgba, 1, out, 2, from_to, 4 );
Note that, unlike many other new-style C++ functions in OpenCV (see the introduction section and Mat::create() ), mixChannels requires the destination arrays be pre-allocated before calling the function.
See also: split() , merge() , cvtColor()
Performs per-element multiplication of two Fourier spectrums.
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The function mulSpectrums performs 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 conj=false ) or correlation (pass conj=false ) of two arrays rapidly. When the arrays are complex, they are simply multiplied (per-element) with optional conjugation of the second array elements. When the arrays are real, they assumed to be CCS-packed (see dft() for details).
Calculates the per-element scaled product of two arrays
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The function multiply calculates the per-element product of two arrays:
There is also Matrix Expressions -friendly variant of the first function, see Mat::mul() .
If you are looking for a matrix product, not per-element product, see gemm() .
See also: add() , substract() , divide() , Matrix Expressions , scaleAdd() , addWeighted() , accumulate() , accumulateProduct() , accumulateSquare() , Mat::convertTo()
Calculates the product of a matrix and its transposition.
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The function mulTransposed calculates the product of src and its transposition:
if aTa=true , and
otherwise. The function is used to compute covariance matrix and with zero delta can be used as a faster substitute for general matrix product when .
See also: calcCovarMatrix() , gemm() , repeat() , reduce()
Calculates absolute array norm, absolute difference norm, or relative difference norm.
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The functions norm calculate the absolute norm of src1 (when there is no src2 ):
or an absolute or relative difference norm if src2 is there:
or
The functions norm return the calculated norm.
When there is mask parameter, and it is not empty (then it should have type CV_8U and the same size as src1 ), the norm is computed only over the specified by the mask region.
A multiple-channel source arrays are treated as a single-channel, that is, the results for all channels are combined.
Normalizes array’s norm or the range
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The functions normalize scale and shift the source array elements, so that
(where , 1 or 2) when normType=NORM_INF , NORM_L1 or NORM_L2 , or so that
when normType=NORM_MINMAX (for dense arrays only).
The optional mask specifies the sub-array to be normalize, that is, the norm or min-n-max are computed over the sub-array and then this sub-array is modified to be normalized. If you want to only use the mask to compute the norm or min-max, but modify the whole array, you can use norm() and Mat::convertScale() / MatND::convertScale() /cross{SparseMat::convertScale} separately.
in the 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.
See also: norm() , Mat::convertScale() , MatND::convertScale() , SparseMat::convertScale()
Class for Principal Component Analysis
class PCA
{
public:
// default constructor
PCA();
// computes PCA for a set of vectors stored as data rows or columns.
PCA(const Mat& data, const Mat& mean, int flags, int maxComponents=0);
// computes PCA for a set of vectors stored as data rows or columns
PCA& operator()(const Mat& data, const Mat& mean, int flags, int maxComponents=0);
// projects vector into the principal components space
Mat project(const Mat& vec) const;
void project(const Mat& vec, Mat& result) const;
// reconstructs the vector from its PC projection
Mat backProject(const Mat& vec) const;
void backProject(const Mat& vec, Mat& result) const;
// eigenvectors of the PC space, stored as the matrix rows
Mat eigenvectors;
// the corresponding eigenvalues; not used for PCA compression/decompression
Mat eigenvalues;
// mean vector, subtracted from the projected vector
// or added to the reconstructed vector
Mat mean;
};
The class PCA is used to compute the special basis for a set of vectors. The basis will consist of eigenvectors of the covariance matrix computed from the input set of vectors. And also the class PCA can transform vectors to/from the new coordinate space, defined by the basis. Usually, in this new coordinate system each vector from the original set (and any linear combination of such vectors) can be quite accurately approximated by taking just the first few its components, corresponding to the eigenvectors of the largest eigenvalues of the covariance matrix. Geometrically it means that we compute projection of the vector to a subspace formed by a few eigenvectors corresponding to the dominant eigenvalues of the covariation matrix. And usually such a projection is very close to the original vector. That is, we can represent the original vector from a high-dimensional space with a much shorter vector consisting of the projected vector’s coordinates in the subspace. Such a transformation is also known as Karhunen-Loeve Transform, or KLT. See http://en.wikipedia.org/wiki/Principal_component_analysis The following sample is the function that takes two matrices. The first one stores the set of vectors (a row per vector) that is used to compute PCA, the second one stores another “test” set of vectors (a row per vector) that are first compressed with PCA, then reconstructed back and then the reconstruction error norm is computed and printed for each vector.
PCA compressPCA(const Mat& pcaset, int maxComponents,
const Mat& testset, Mat& compressed)
{
PCA pca(pcaset, // pass the data
Mat(), // we do not have a pre-computed mean vector,
// so let the PCA engine to compute it
CV_PCA_DATA_AS_ROW, // indicate that the vectors
// are stored as matrix rows
// (use CV_PCA_DATA_AS_COL if the vectors are
// the matrix columns)
maxComponents // specify, how many principal components to retain
);
// if there is no test data, just return the computed basis, ready-to-use
if( !testset.data )
return pca;
CV_Assert( testset.cols == pcaset.cols );
compressed.create(testset.rows, maxComponents, testset.type());
Mat reconstructed;
for( int i = 0; i < testset.rows; i++ )
{
Mat vec = testset.row(i), coeffs = compressed.row(i);
// compress the vector, the result will be stored
// in the i-th row of the output matrix
pca.project(vec, coeffs);
// and then reconstruct it
pca.backProject(coeffs, reconstructed);
// and measure the error
printf("
}
return pca;
}
See also: calcCovarMatrix() , mulTransposed() , SVD() , dft() , dct()
PCA constructors
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The default constructor initializes empty PCA structure. The second constructor initializes the structure and calls PCA::operator () .
Performs Principal Component Analysis of the supplied dataset.
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The operator performs PCA of the supplied dataset. It is safe to reuse the same PCA structure for multiple dataset. That is, if the structure has been previously used with another dataset, the existing internal data is reclaimed and the new eigenvalues , eigenvectors and mean are allocated and computed.
The computed eigenvalues are sorted from the largest to the smallest and the corresponding eigenvectors are stored as PCA::eigenvectors rows.
Project vector(s) to the principal component subspace
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The methods project one or more vectors to the principal component subspace, where each vector projection is represented by coefficients in the principal component basis. The first form of the method returns the matrix that the second form writes to the result. So the first form can be used as a part of expression, while the second form can be more efficient in a processing loop.
Reconstruct vectors from their PC projections.
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The methods are inverse operations to PCA::project() . They take PC coordinates of projected vectors and reconstruct the original vectors. Of course, unless all the principal components have been retained, the reconstructed vectors will be different from the originals, but typically the difference will be small is if the number of components is large enough (but still much smaller than the original vector dimensionality) - that’s why PCA is used after all.
Performs perspective matrix transformation of vectors.
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The function perspectiveTransform transforms every element of src , by treating it as 2D or 3D vector, in the following way (here 3D vector transformation is shown; in the case of 2D vector transformation the component is omitted):
where
and
Note that 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 task, i.e. want to compute the most probable perspective transformation out of several pairs of corresponding points, you can use getPerspectiveTransform() or findHomography() .
See also: transform() , warpPerspective() , getPerspectiveTransform() , findHomography()
Calculates the rotation angle of 2d vectors
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The function phase computes the rotation angle of each 2D vector that is formed from the corresponding elements of x and y :
The angle estimation accuracy is , when x(I)=y(I)=0 , the corresponding angle (I) is set to .
See also:
Computes x and y coordinates of 2D vectors from their magnitude and angle.
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The function polarToCart computes the cartesian coordinates of each 2D vector represented by the corresponding elements of magnitude and angle :
The relative accuracy of the estimated coordinates is .
See also: cartToPolar() , magnitude() , phase() , exp() , log() , pow() , sqrt()
Raises every array element to a power.
Parameters: |
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The function pow raises every element of the input array to p :
That is, 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, as the following example, 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 p , such as integer values, 0.5, and -0.5, specialized faster algorithms are used.
See also: sqrt() , exp() , log() , cartToPolar() , polarToCart()
Random number generator class.
class CV_EXPORTS RNG
{
public:
enum { A=4164903690U, UNIFORM=0, NORMAL=1 };
// constructors
RNG();
RNG(uint64 state);
// returns 32-bit unsigned random number
unsigned next();
// return random numbers of the specified type
operator uchar();
operator schar();
operator ushort();
operator short();
operator unsigned();
// returns a random integer sampled uniformly from [0, N).
unsigned operator()(unsigned N);
unsigned operator()();
operator int();
operator float();
operator double();
// returns a random number sampled uniformly from [a, b) range
int uniform(int a, int b);
float uniform(float a, float b);
double uniform(double a, double b);
// returns Gaussian random number with zero mean.
double gaussian(double sigma);
// fills array with random numbers sampled from the specified distribution
void fill( Mat& mat, int distType, const Scalar& a, const Scalar& b );
void fill( MatND& mat, int distType, const Scalar& a, const Scalar& b );
// internal state of the RNG (could change in the future)
uint64 state;
};
The class RNG implements random number generator. It encapsulates the RNG state (currently, a 64-bit integer) and has methods to return scalar random values and to fill arrays with random values. Currently it supports uniform and Gaussian (normal) distributions. The generator uses Multiply-With-Carry algorithm, introduced by G. Marsaglia ( http://en.wikipedia.org/wiki/Multiply-with-carry ). Gaussian-distribution random numbers are generated using Ziggurat algorithm ( http://en.wikipedia.org/wiki/Ziggurat_algorithm ), introduced by G. Marsaglia and W. W. Tsang.
RNG constructors
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These are the RNG constructors. The first form sets the state to some pre-defined value, equal to 2**32-1 in the current implementation. The second form sets the state to the specified value. If the user passed state=0 , the constructor uses the above default value instead, to avoid the singular random number sequence, consisting of all zeros.
Returns the next random number
The method updates the state using MWC algorithm and returns the next 32-bit random number.
Returns the next random number of the specified type
Each of the methods updates the state using MWC algorithm and returns the next random number of the specified type. In the case of integer types the returned number is from the whole available value range for the specified type. In the case of floating-point types the returned value is from [0,1) range.
Returns the next random number
Parameters: |
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The methods transforms the state using MWC algorithm and returns the next random number. The first form is equivalent to RNG::next() , the second form returns the random number modulo N , i.e. the result will be in the range [0, N) .
Returns the next random number sampled from the uniform distribution
Parameters: |
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The methods transforms the state using MWC algorithm and returns the next uniformly-distributed random number of the specified type, deduced from the input parameter type, from the range [a, b) . There is one nuance, illustrated by the following sample:
cv::RNG rng;
// will always produce 0
double a = rng.uniform(0, 1);
// will produce double from [0, 1)
double a1 = rng.uniform((double)0, (double)1);
// will produce float from [0, 1)
double b = rng.uniform(0.f, 1.f);
// will produce double from [0, 1)
double c = rng.uniform(0., 1.);
// will likely cause compiler error because of ambiguity:
// RNG::uniform(0, (int)0.999999)? or RNG::uniform((double)0, 0.99999)?
double d = rng.uniform(0, 0.999999);
That is, the compiler does not take into account type of the variable that you assign the result of RNG::uniform to, the only thing that matters to it is the type of a and b parameters. So if you want a floating-point random number, but the range boundaries are integer numbers, either put dots in the end, if they are constants, or use explicit type cast operators, as in a1 initialization above.
Returns the next random number sampled from the Gaussian distribution
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The methods transforms the state using MWC algorithm and returns the next random number from the Gaussian distribution N(0,sigma) . That is, the mean value of the returned random numbers will be zero and the standard deviation will be the specified sigma .
Fill arrays with random numbers
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Each of the methods fills the matrix with the random values from the specified distribution. As the new numbers are generated, the RNG state is updated accordingly. In the case of multiple-channel images every channel is filled independently, i.e. RNG can not generate samples from multi-dimensional Gaussian distribution with non-diagonal covariation matrix directly. To do that, first, generate matrix from the distribution , i.e. Gaussian distribution with zero mean and identity covariation matrix, and then transform it using transform() and the specific covariation matrix.
Generates a single uniformly-distributed random number or array of random numbers
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The template functions randu generate and return the next uniformly-distributed random value of the specified type. randu<int>() is equivalent to (int)theRNG(); etc. See RNG() description.
The second non-template variant of the function fills the matrix mtx with uniformly-distributed random numbers from the specified range:
See also: RNG() , randn() , theRNG() .
Fills array with normally distributed random numbers
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The function randn fills the matrix mtx with normally distributed random numbers with the specified mean and standard deviation. is applied to the generated numbers (i.e. the values are clipped)
See also: RNG() , randu()
Shuffles the array elements randomly
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The function randShuffle shuffles the specified 1D array by randomly choosing pairs of elements and swapping them. The number of such swap operations will be mtx.rows*mtx.cols*iterFactor See also: RNG() , sort()
Reduces a matrix to a vector
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The function reduce reduces 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 an raster image. In the case of CV_REDUCE_SUM and CV_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.
See also: repeat()
Fill the destination array with repeated copies of the source array.
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The functions repeat() duplicate the source array one or more times along each of the two axes:
The second variant of the function is more convenient to use with Matrix Expressions See also: reduce() , Matrix Expressions
Template function for accurate conversion from one primitive type to another
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The functions saturate_cast resembles the standard C++ cast operations, such as static_cast<T>() etc. They perform an efficient and accurate conversion from one primitive type to another, see the introduction. “saturate” in the name means that when the input value v is out of range of the target type, the result will not be formed just by taking low bits of the input, but instead the value will be clipped. For example:
uchar a = saturate_cast<uchar>(-100); // a = 0 (UCHAR_MIN)
short b = saturate_cast<short>(33333.33333); // b = 32767 (SHRT_MAX)
Such clipping is done when the target type is unsigned char, signed char, unsigned short or signed short - for 32-bit integers no clipping is done.
When the parameter is floating-point value and the target type is an integer (8-, 16- or 32-bit), the floating-point value is first rounded to the nearest integer and then clipped if needed (when the target type is 8- or 16-bit).
This operation is used in most simple or complex image processing functions in OpenCV.
See also: add() , subtract() , multiply() , divide() , Mat::convertTo()
Calculates the sum of a scaled array and another array.
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The function cvScaleAdd 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:
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);
See also: add() , addWeighted() , subtract() , Mat::dot() , Mat::convertTo() , Matrix Expressions
Initializes a scaled identity matrix
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The function setIdentity() initializes a scaled identity matrix:
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]]
See also: Mat::zeros() , Mat::ones() , Matrix Expressions , Mat::setTo() , Mat::operator=() ,
Solves one or more linear systems or least-squares problems.
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The function 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 ):
If DECOMP_LU or DECOMP_CHOLESKY method is used, the function returns 1 if src1 (or ) is non-singular and 0 otherwise; in the latter case dst is not valid. Other methods find some pseudo-solution in the case of singular left-hand side part.
Note that if you want to find unity-norm solution of an under-defined singular system , the function solve will not do the work. Use SVD::solveZ() instead.
See also: invert() , SVD() , eigen()
Finds the real roots of a cubic equation.
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The function solveCubic finds the real roots of a cubic equation:
(if coeffs is a 4-element vector)
or (if coeffs is 3-element vector):
The roots are stored to roots array.
Finds the real or complex roots of a polynomial equation
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The function solvePoly finds real and complex roots of a polynomial equation:
Sorts each row or each column of a matrix
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The function sort sorts each matrix row or each matrix column in ascending or descending order. If you want to sort matrix rows or columns lexicographically, you can use STL std::sort generic function with the proper comparison predicate.
See also: sortIdx() , randShuffle()
Sorts each row or each column of a matrix
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The function sortIdx sorts each matrix row or each matrix column in ascending or descending order. Instead of reordering the elements themselves, it stores the indices of sorted elements in the destination array. For example:
Mat A = Mat::eye(3,3,CV_32F), B;
sortIdx(A, B, CV_SORT_EVERY_ROW + CV_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]]
See also: sort() , randShuffle()
Divides multi-channel array into several single-channel arrays
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The functions split split multi-channel array into separate single-channel arrays:
If you need to extract a single-channel or do some other sophisticated channel permutation, use mixChannels() See also: merge() , mixChannels() , cvtColor()
Calculates square root of array elements
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The functions sqrt calculate square root of each source array element. in the case of multi-channel arrays each channel is processed independently. The function accuracy is approximately the same as of the built-in std::sqrt .
See also: pow() , magnitude()
Calculates per-element difference between two arrays or array and a scalar
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The functions subtract compute
the difference between two arrays
the difference between array and a scalar:
the difference between scalar and an array:
where I is multi-dimensional index of array elements.
The first function in the above list can be replaced with matrix expressions:
dst = src1 - src2;
dst -= src2; // equivalent to subtract(dst, src2, dst);
See also: add() , addWeighted() , scaleAdd() , convertScale() , Matrix Expressions , .
Class for computing Singular Value Decomposition
class SVD
{
public:
enum { MODIFY_A=1, NO_UV=2, FULL_UV=4 };
// default empty constructor
SVD();
// decomposes A into u, w and vt: A = u*w*vt;
// u and vt are orthogonal, w is diagonal
SVD( const Mat& A, int flags=0 );
// decomposes A into u, w and vt.
SVD& operator ()( const Mat& A, int flags=0 );
// finds such vector x, norm(x)=1, so that A*x = 0,
// where A is singular matrix
static void solveZ( const Mat& A, Mat& x );
// does back-subsitution:
// x = vt.t()*inv(w)*u.t()*rhs ~ inv(A)*rhs
void backSubst( const Mat& rhs, Mat& x ) const;
Mat u; // the left orthogonal matrix
Mat w; // vector of singular values
Mat vt; // the right orthogonal matrix
};
The class SVD is used to compute Singular Value Decomposition of a floating-point matrix and then use it to solve least-square problems, under-determined linear systems, invert matrices, compute condition numbers etc. For a bit faster operation you can pass flags=SVD::MODIFY_A|... to modify the decomposed matrix when it is not necessarily to preserve it. If you want to compute condition number of a matrix or absolute value of its determinant - you do not need u and vt , so you can pass flags=SVD::NO_UV|... . Another flag FULL_UV indicates that full-size u and vt must be computed, which is not necessary most of the time.
See also: invert() , solve() , eigen() , determinant()
SVD constructors
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The first constructor initializes empty SVD structure. The second constructor initializes empty SVD structure and then calls SVD::operator () .
Performs SVD of a matrix
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The operator performs singular value decomposition of the supplied matrix. The u , vt and the vector of singular values w are stored in the structure. The same SVD structure can be reused many times with different matrices. Each time, if needed, the previous u , vt and w are reclaimed and the new matrices are created, which is all handled by Mat::create() .
Solves under-determined singular linear system
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The method finds unit-length solution x of the under-determined system . Theory says that such system has infinite number of solutions, so the algorithm finds the unit-length solution as the right singular vector corresponding to the smallest singular value (which should be 0). In practice, because of round errors and limited floating-point accuracy, the input matrix can appear to be close-to-singular rather than just singular. So, strictly speaking, the algorithm solves the following problem:
Performs singular value back substitution
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The method computes back substitution for the specified right-hand side:
Using this technique you can either get a very accurate solution of convenient linear system, or the best (in the least-squares terms) pseudo-solution of an overdetermined linear system. Note that explicit SVD with the further back substitution only makes sense if you need to solve many linear systems with the same left-hand side (e.g. A ). If all you need is to solve a single system (possibly with multiple rhs immediately available), simply call solve() add pass cv::DECOMP_SVD there - it will do absolutely the same thing.
Calculates sum of array elements
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The functions sum calculate and return the sum of array elements, independently for each channel.
See also: countNonZero() , mean() , meanStdDev() , norm() , minMaxLoc() , reduce()
Returns the default random number generator
The function theRNG returns the default random number generator. For each thread there is 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 will be much faster to use this function to retrieve the generator and then use RNG::operator _Tp() .
See also: RNG() , randu() , randn()
Performs matrix transformation of every array element.
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The function transform performs matrix transformation of every element of array src and stores the results in dst :
(when mtx.cols=src.channels() ), or
(when mtx.cols=src.channels()+1 )
That is, every element of an N -channel array src is considered as N -element vector, which is transformed using a or matrix mtx into an element of M -channel array dst .
The function may be used for geometrical transformation of -dimensional points, arbitrary linear color space transformation (such as various kinds of RGB YUV transforms), shuffling the image channels and so forth.
See also: perspectiveTransform() , getAffineTransform() , estimateRigidTransform() , warpAffine() , warpPerspective()
Transposes a matrix
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The function transpose() transposes the matrix src :
Note that no complex conjugation is done in the case of a complex matrix, it should be done separately if needed.