Merge pull request #9574 from saskatchewancatch:i9482

This commit is contained in:
Vadim Pisarevsky 2017-09-13 13:59:43 +00:00
commit f1aa180a40
4 changed files with 83 additions and 57 deletions

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@ -6,6 +6,7 @@ MathJax.Hub.Config(
matTT: [ "\\[ \\left|\\begin{array}{ccc} #1 & #2 & #3\\\\ #4 & #5 & #6\\\\ #7 & #8 & #9 \\end{array}\\right| \\]", 9], matTT: [ "\\[ \\left|\\begin{array}{ccc} #1 & #2 & #3\\\\ #4 & #5 & #6\\\\ #7 & #8 & #9 \\end{array}\\right| \\]", 9],
fork: ["\\left\\{ \\begin{array}{l l} #1 & \\mbox{#2}\\\\ #3 & \\mbox{#4}\\\\ \\end{array} \\right.", 4], fork: ["\\left\\{ \\begin{array}{l l} #1 & \\mbox{#2}\\\\ #3 & \\mbox{#4}\\\\ \\end{array} \\right.", 4],
forkthree: ["\\left\\{ \\begin{array}{l l} #1 & \\mbox{#2}\\\\ #3 & \\mbox{#4}\\\\ #5 & \\mbox{#6}\\\\ \\end{array} \\right.", 6], forkthree: ["\\left\\{ \\begin{array}{l l} #1 & \\mbox{#2}\\\\ #3 & \\mbox{#4}\\\\ #5 & \\mbox{#6}\\\\ \\end{array} \\right.", 6],
forkfour: ["\\left\\{ \\begin{array}{l l} #1 & \\mbox{#2}\\\\ #3 & \\mbox{#4}\\\\ #5 & \\mbox{#6}\\\\ #7 & \\mbox{#8}\\\\ \\end{array} \\right.", 8],
vecthree: ["\\begin{bmatrix} #1\\\\ #2\\\\ #3 \\end{bmatrix}", 3], vecthree: ["\\begin{bmatrix} #1\\\\ #2\\\\ #3 \\end{bmatrix}", 3],
vecthreethree: ["\\begin{bmatrix} #1 & #2 & #3\\\\ #4 & #5 & #6\\\\ #7 & #8 & #9 \\end{bmatrix}", 9], vecthreethree: ["\\begin{bmatrix} #1 & #2 & #3\\\\ #4 & #5 & #6\\\\ #7 & #8 & #9 \\end{bmatrix}", 9],
hdotsfor: ["\\dots", 1], hdotsfor: ["\\dots", 1],

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@ -28,7 +28,14 @@
#3 & \mbox{#4}\\ #3 & \mbox{#4}\\
#5 & \mbox{#6}\\ #5 & \mbox{#6}\\
\end{array} \right.} \end{array} \right.}
\newcommand{\forkthree}[8]{
\left\{
\begin{array}{l l}
#1 & \mbox{#2}\\
#3 & \mbox{#4}\\
#5 & \mbox{#6}\\
#7 & \mbox{#8}\\
\end{array} \right.}
\newcommand{\vecthree}[3]{ \newcommand{\vecthree}[3]{
\begin{bmatrix} \begin{bmatrix}
#1\\ #1\\

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@ -640,43 +640,50 @@ Scalar_ 's.
CV_EXPORTS_W void meanStdDev(InputArray src, OutputArray mean, OutputArray stddev, CV_EXPORTS_W void meanStdDev(InputArray src, OutputArray mean, OutputArray stddev,
InputArray mask=noArray()); InputArray mask=noArray());
/** @brief Calculates an absolute array norm, an absolute difference norm, or a /** @brief Calculates the absolute norm of an array.
relative difference norm.
The function cv::norm calculates an absolute norm of src1 (when there is no This version of cv::norm calculates the absolute norm of src1. The type of norm to calculate is specified using cv::NormTypes.
src2 ):
\f[norm = \forkthree{\|\texttt{src1}\|_{L_{\infty}} = \max _I | \texttt{src1} (I)|}{if \(\texttt{normType} = \texttt{NORM_INF}\) } As example for one array consider the function \f$r(x)= \begin{pmatrix} x \\ 1-x \end{pmatrix}, x \in [-1;1]\f$.
{ \| \texttt{src1} \| _{L_1} = \sum _I | \texttt{src1} (I)|}{if \(\texttt{normType} = \texttt{NORM_L1}\) } The \f$ L_{1}, L_{2} \f$ and \f$ L_{\infty} \f$ norm for the sample value \f$r(-1) = \begin{pmatrix} -1 \\ 2 \end{pmatrix}\f$
{ \| \texttt{src1} \| _{L_2} = \sqrt{\sum_I \texttt{src1}(I)^2} }{if \(\texttt{normType} = \texttt{NORM_L2}\) }\f] is calculated as follows
\f{align*}
or an absolute or relative difference norm if src2 is there: \| r(-1) \|_{L_1} &= |-1| + |2| = 3 \\
\| r(-1) \|_{L_2} &= \sqrt{(-1)^{2} + (2)^{2}} = \sqrt{5} \\
\f[norm = \forkthree{\|\texttt{src1}-\texttt{src2}\|_{L_{\infty}} = \max _I | \texttt{src1} (I) - \texttt{src2} (I)|}{if \(\texttt{normType} = \texttt{NORM_INF}\) } \| r(-1) \|_{L_\infty} &= \max(|-1|,|2|) = 2
{ \| \texttt{src1} - \texttt{src2} \| _{L_1} = \sum _I | \texttt{src1} (I) - \texttt{src2} (I)|}{if \(\texttt{normType} = \texttt{NORM_L1}\) } \f}
{ \| \texttt{src1} - \texttt{src2} \| _{L_2} = \sqrt{\sum_I (\texttt{src1}(I) - \texttt{src2}(I))^2} }{if \(\texttt{normType} = \texttt{NORM_L2}\) }\f] and for \f$r(0.5) = \begin{pmatrix} 0.5 \\ 0.5 \end{pmatrix}\f$ the calculation is
\f{align*}
or \| 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} \\
\f[norm = \forkthree{\frac{\|\texttt{src1}-\texttt{src2}\|_{L_{\infty}} }{\|\texttt{src2}\|_{L_{\infty}} }}{if \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_INF}\) } \| r(0.5) \|_{L_\infty} &= \max(|0.5|,|0.5|) = 0.5.
{ \frac{\|\texttt{src1}-\texttt{src2}\|_{L_1} }{\|\texttt{src2}\|_{L_1}} }{if \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_L1}\) } \f}
{ \frac{\|\texttt{src1}-\texttt{src2}\|_{L_2} }{\|\texttt{src2}\|_{L_2}} }{if \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_L2}\) }\f] The following graphic shows all values for the three norm functions \f$\| r(x) \|_{L_1}, \| r(x) \|_{L_2}\f$ and \f$\| r(x) \|_{L_\infty}\f$.
It is notable that the \f$ L_{1} \f$ norm forms the upper and the \f$ L_{\infty} \f$ norm forms the lower border for the example function \f$ r(x) \f$.
The function cv::norm returns the calculated norm. ![Graphs for the different norm functions from the above example](pics/NormTypes_OneArray_1-2-INF.png)
When the mask parameter is specified and it is not empty, the norm is 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. calculated only over the region specified by the mask.
A multi-channel input arrays are treated as a single-channel, that is, Multi-channel input arrays are treated as single-channel arrays, that is,
the results for all channels are combined. the results for all channels are combined.
Hamming norms can only be calculated with CV_8U depth arrays.
@param src1 first input array. @param src1 first input array.
@param normType type of the norm (see cv::NormTypes). @param normType type of the norm (see cv::NormTypes).
@param mask optional operation mask; it must have the same size as src1 and CV_8UC1 type. @param mask optional operation mask; it must have the same size as src1 and CV_8UC1 type.
*/ */
CV_EXPORTS_W double norm(InputArray src1, int normType = NORM_L2, InputArray mask = noArray()); CV_EXPORTS_W double norm(InputArray src1, int normType = NORM_L2, InputArray mask = noArray());
/** @overload /** @brief 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 cv::NormTypes.
@param src1 first input array. @param src1 first input array.
@param src2 second input array of the same size and the same type as src1. @param src2 second input array of the same size and the same type as src1.
@param normType type of the norm (cv::NormTypes). @param normType type of the norm (cv::NormTypes).

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@ -152,46 +152,57 @@ enum DecompTypes {
}; };
/** norm types /** norm types
- For one array:
\f[norm = \forkthree{\|\texttt{src1}\|_{L_{\infty}} = \max _I | \texttt{src1} (I)|}{if \(\texttt{normType} = \texttt{NORM_INF}\) }
{ \| \texttt{src1} \| _{L_1} = \sum _I | \texttt{src1} (I)|}{if \(\texttt{normType} = \texttt{NORM_L1}\) }
{ \| \texttt{src1} \| _{L_2} = \sqrt{\sum_I \texttt{src1}(I)^2} }{if \(\texttt{normType} = \texttt{NORM_L2}\) }\f]
- Absolute norm for two arrays src1 and src2 denote input arrays.
\f[norm = \forkthree{\|\texttt{src1}-\texttt{src2}\|_{L_{\infty}} = \max _I | \texttt{src1} (I) - \texttt{src2} (I)|}{if \(\texttt{normType} = \texttt{NORM_INF}\) }
{ \| \texttt{src1} - \texttt{src2} \| _{L_1} = \sum _I | \texttt{src1} (I) - \texttt{src2} (I)|}{if \(\texttt{normType} = \texttt{NORM_L1}\) }
{ \| \texttt{src1} - \texttt{src2} \| _{L_2} = \sqrt{\sum_I (\texttt{src1}(I) - \texttt{src2}(I))^2} }{if \(\texttt{normType} = \texttt{NORM_L2}\) }\f]
- Relative norm for two arrays
\f[norm = \forkthree{\frac{\|\texttt{src1}-\texttt{src2}\|_{L_{\infty}} }{\|\texttt{src2}\|_{L_{\infty}} }}{if \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_INF}\) }
{ \frac{\|\texttt{src1}-\texttt{src2}\|_{L_1} }{\|\texttt{src2}\|_{L_1}} }{if \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_L1}\) }
{ \frac{\|\texttt{src1}-\texttt{src2}\|_{L_2} }{\|\texttt{src2}\|_{L_2}} }{if \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_L2}\) }\f]
As example for one array consider the function \f$r(x)= \begin{pmatrix} x \\ 1-x \end{pmatrix}, x \in [-1;1]\f$.
The \f$ L_{1}, L_{2} \f$ and \f$ L_{\infty} \f$ norm for the sample value \f$r(-1) = \begin{pmatrix} -1 \\ 2 \end{pmatrix}\f$
is calculated as follows
\f{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
\f}
and for \f$r(0.5) = \begin{pmatrix} 0.5 \\ 0.5 \end{pmatrix}\f$ the calculation is
\f{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.
\f}
The following graphic shows all values for the three norm functions \f$\| r(x) \|_{L_1}, \| r(x) \|_{L_2}\f$ and \f$\| r(x) \|_{L_\infty}\f$.
It is notable that the \f$ L_{1} \f$ norm forms the upper and the \f$ L_{\infty} \f$ norm forms the lower border for the example function \f$ r(x) \f$.
![Graphs for the different norm functions from the above example](pics/NormTypes_OneArray_1-2-INF.png)
*/ */
enum NormTypes { NORM_INF = 1,
enum NormTypes {
/**
\f[
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 \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_INF}\) }
\f]
*/
NORM_INF = 1,
/**
\f[
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 \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_L1}\) }
\f]*/
NORM_L1 = 2, NORM_L1 = 2,
/**
\f[
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 \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_L2}\) }
\f]
*/
NORM_L2 = 4, NORM_L2 = 4,
/**
\f[
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 \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_L2}\) }
\f]
*/
NORM_L2SQR = 5, NORM_L2SQR = 5,
/**
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_HAMMING = 6, NORM_HAMMING = 6,
/**
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_HAMMING2 = 7, NORM_HAMMING2 = 7,
NORM_TYPE_MASK = 7, NORM_TYPE_MASK = 7, //!< bit-mask which can be used to separate norm type from norm flags
NORM_RELATIVE = 8, //!< flag NORM_RELATIVE = 8, //!< flag
NORM_MINMAX = 32 //!< flag NORM_MINMAX = 32 //!< flag
}; };