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Merge pull request opencv#9574 from saskatchewancatch:i9482
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‎doc/mymath.js

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

‎doc/mymath.sty

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

‎modules/core/include/opencv2/core.hpp

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

‎modules/core/include/opencv2/core/base.hpp

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};
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/** norm types
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- For one array:
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\f[norm = \forkthree{\|\texttt{src1}\|_{L_{\infty}} = \max _I | \texttt{src1} (I)|}{if \(\texttt{normType} = \texttt{NORM_INF}\) }
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{ \| \texttt{src1} \| _{L_1} = \sum _I | \texttt{src1} (I)|}{if \(\texttt{normType} = \texttt{NORM_L1}\) }
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{ \| \texttt{src1} \| _{L_2} = \sqrt{\sum_I \texttt{src1}(I)^2} }{if \(\texttt{normType} = \texttt{NORM_L2}\) }\f]
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- Absolute norm for two arrays
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\f[norm = \forkthree{\|\texttt{src1}-\texttt{src2}\|_{L_{\infty}} = \max _I | \texttt{src1} (I) - \texttt{src2} (I)|}{if \(\texttt{normType} = \texttt{NORM_INF}\) }
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{ \| \texttt{src1} - \texttt{src2} \| _{L_1} = \sum _I | \texttt{src1} (I) - \texttt{src2} (I)|}{if \(\texttt{normType} = \texttt{NORM_L1}\) }
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{ \| \texttt{src1} - \texttt{src2} \| _{L_2} = \sqrt{\sum_I (\texttt{src1}(I) - \texttt{src2}(I))^2} }{if \(\texttt{normType} = \texttt{NORM_L2}\) }\f]
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- Relative norm for two arrays
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\f[norm = \forkthree{\frac{\|\texttt{src1}-\texttt{src2}\|_{L_{\infty}} }{\|\texttt{src2}\|_{L_{\infty}} }}{if \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_INF}\) }
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{ \frac{\|\texttt{src1}-\texttt{src2}\|_{L_1} }{\|\texttt{src2}\|_{L_1}} }{if \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_L1}\) }
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{ \frac{\|\texttt{src1}-\texttt{src2}\|_{L_2} }{\|\texttt{src2}\|_{L_2}} }{if \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_L2}\) }\f]
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As example for one array consider the function \f$r(x)= \begin{pmatrix} x \\ 1-x \end{pmatrix}, x \in [-1;1]\f$.
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The \f$ L_{1}, L_{2} \f$ and \f$ L_{\infty} \f$ norm for the sample value \f$r(-1) = \begin{pmatrix} -1 \\ 2 \end{pmatrix}\f$
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is calculated as follows
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\f{align*}
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\| r(-1) \|_{L_1} &= |-1| + |2| = 3 \\
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\| r(-1) \|_{L_2} &= \sqrt{(-1)^{2} + (2)^{2}} = \sqrt{5} \\
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\| r(-1) \|_{L_\infty} &= \max(|-1|,|2|) = 2
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\f}
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and for \f$r(0.5) = \begin{pmatrix} 0.5 \\ 0.5 \end{pmatrix}\f$ the calculation is
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\f{align*}
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\| r(0.5) \|_{L_1} &= |0.5| + |0.5| = 1 \\
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\| r(0.5) \|_{L_2} &= \sqrt{(0.5)^{2} + (0.5)^{2}} = \sqrt{0.5} \\
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\| r(0.5) \|_{L_\infty} &= \max(|0.5|,|0.5|) = 0.5.
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\f}
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The following graphic shows all values for the three norm functions \f$\| r(x) \|_{L_1}, \| r(x) \|_{L_2}\f$ and \f$\| r(x) \|_{L_\infty}\f$.
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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$.
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![Graphs for the different norm functions from the above example](pics/NormTypes_OneArray_1-2-INF.png)
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*/
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enum NormTypes { NORM_INF = 1,
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src1 and src2 denote input arrays.
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*/
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enum NormTypes {
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/**
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\f[
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norm = \forkthree
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{\|\texttt{src1}\|_{L_{\infty}} = \max _I | \texttt{src1} (I)|}{if \(\texttt{normType} = \texttt{NORM_INF}\) }
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{\|\texttt{src1}-\texttt{src2}\|_{L_{\infty}} = \max _I | \texttt{src1} (I) - \texttt{src2} (I)|}{if \(\texttt{normType} = \texttt{NORM_INF}\) }
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{\frac{\|\texttt{src1}-\texttt{src2}\|_{L_{\infty}} }{\|\texttt{src2}\|_{L_{\infty}} }}{if \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_INF}\) }
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\f]
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*/
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NORM_INF = 1,
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/**
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\f[
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norm = \forkthree
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{\| \texttt{src1} \| _{L_1} = \sum _I | \texttt{src1} (I)|}{if \(\texttt{normType} = \texttt{NORM_L1}\)}
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{ \| \texttt{src1} - \texttt{src2} \| _{L_1} = \sum _I | \texttt{src1} (I) - \texttt{src2} (I)|}{if \(\texttt{normType} = \texttt{NORM_L1}\) }
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{ \frac{\|\texttt{src1}-\texttt{src2}\|_{L_1} }{\|\texttt{src2}\|_{L_1}} }{if \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_L1}\) }
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\f]*/
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NORM_L1 = 2,
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/**
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\f[
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norm = \forkthree
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{ \| \texttt{src1} \| _{L_2} = \sqrt{\sum_I \texttt{src1}(I)^2} }{if \(\texttt{normType} = \texttt{NORM_L2}\) }
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{ \| \texttt{src1} - \texttt{src2} \| _{L_2} = \sqrt{\sum_I (\texttt{src1}(I) - \texttt{src2}(I))^2} }{if \(\texttt{normType} = \texttt{NORM_L2}\) }
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{ \frac{\|\texttt{src1}-\texttt{src2}\|_{L_2} }{\|\texttt{src2}\|_{L_2}} }{if \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_L2}\) }
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\f]
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*/
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NORM_L2 = 4,
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/**
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\f[
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norm = \forkthree
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{ \| \texttt{src1} \| _{L_2} ^{2} = \sum_I \texttt{src1}(I)^2} {if \(\texttt{normType} = \texttt{NORM_L2SQR}\)}
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{ \| \texttt{src1} - \texttt{src2} \| _{L_2} ^{2} = \sum_I (\texttt{src1}(I) - \texttt{src2}(I))^2 }{if \(\texttt{normType} = \texttt{NORM_L2SQR}\) }
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{ \left(\frac{\|\texttt{src1}-\texttt{src2}\|_{L_2} }{\|\texttt{src2}\|_{L_2}}\right)^2 }{if \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_L2}\) }
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\f]
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*/
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NORM_L2SQR = 5,
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/**
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In the case of one input array, calculates the Hamming distance of the array from zero,
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In the case of two input arrays, calculates the Hamming distance between the arrays.
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*/
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NORM_HAMMING = 6,
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/**
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Similar to NORM_HAMMING, but in the calculation, each two bits of the input sequence will
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be added and treated as a single bit to be used in the same calculation as NORM_HAMMING.
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*/
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NORM_HAMMING2 = 7,
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NORM_TYPE_MASK = 7,
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NORM_TYPE_MASK = 7, //!< bit-mask which can be used to separate norm type from norm flags
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NORM_RELATIVE = 8, //!< flag
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NORM_MINMAX = 32 //!< flag
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};

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