diff --git a/doc/mymath.js b/doc/mymath.js index fb65fab1e770ccac4d623b46d0160ca7181c6f6a..0b65bd16d8ba9aa307d61660715f22ee9b1b155d 100644 --- a/doc/mymath.js +++ b/doc/mymath.js @@ -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], 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], + 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], vecthreethree: ["\\begin{bmatrix} #1 & #2 & #3\\\\ #4 & #5 & #6\\\\ #7 & #8 & #9 \\end{bmatrix}", 9], hdotsfor: ["\\dots", 1], diff --git a/doc/mymath.sty b/doc/mymath.sty index 08ab50d2b41e3532d0b26ac0a14ec42858126ffe..04aedf6302575e5351c0ef428095c960e877387b 100644 --- a/doc/mymath.sty +++ b/doc/mymath.sty @@ -28,7 +28,14 @@ #3 & \mbox{#4}\\ #5 & \mbox{#6}\\ \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]{ \begin{bmatrix} #1\\ diff --git a/modules/core/include/opencv2/core.hpp b/modules/core/include/opencv2/core.hpp index b077d06dcd00644dff1407676025db934c354604..34297b8adbfd3878c907a5cf461ad80f05f1b07b 100644 --- a/modules/core/include/opencv2/core.hpp +++ b/modules/core/include/opencv2/core.hpp @@ -640,34 +640,44 @@ Scalar_ 's. CV_EXPORTS_W void meanStdDev(InputArray src, OutputArray mean, OutputArray stddev, InputArray mask=noArray()); -/** @brief Calculates an absolute array norm, an absolute difference norm, or a -relative difference norm. +/** @brief Calculates an absolute array norm. -The function cv::norm calculates an absolute norm of src1 (when there is no -src2 ): +This version of cv::norm calculates the absolute norm of src1. The type of norm to calculate is specified using cv::NormTypes. -\f[norm = \forkthree{\|\texttt{src1}\|_{L_{\infty}} = \max _I | \texttt{src1} (I)|}{if \(\texttt{normType} = \texttt{NORM_INF}\) } +\f[norm = \forkfour{\|\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] +{ \| \texttt{src1} \| _{L_2} = \sqrt{\sum_I \texttt{src1}(I)^2} }{if \(\texttt{normType} = \texttt{NORM_L2}\) } +{ \| \texttt{src1} \| _{L_2} ^{2} = \sum_I \texttt{src1}(I)^2} {if \(\texttt{normType} = \texttt{NORM_L2SQR}\)}\f] + +If normType is not specified, NORM_L2 is used. or an absolute or relative difference norm if src2 is there: -\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] -or - -\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) The function cv::norm returns the calculated norm. When the mask parameter is specified and it is not empty, the norm is 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. @param src1 first input array. @@ -676,7 +686,24 @@ the results for all channels are combined. */ 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. + +\f[norm = \forkfour{\|\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 \(\texttt{normType} = \texttt{NORM_L2}\) } +{ \| \texttt{src1} - \texttt{src2} \| _{L_2} ^{2} = \sum_I (\texttt{src1}(I) - \texttt{src2}(I))^2 }{if \(\texttt{normType} = \texttt{NORM_L2SQR}\) } +\f] + +or + +\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] + @param src1 first input array. @param src2 second input array of the same size and the same type as src1. @param normType type of the norm (cv::NormTypes). diff --git a/modules/core/include/opencv2/core/base.hpp b/modules/core/include/opencv2/core/base.hpp index 0aeb055019b5b8c4a30aaab40e16704a19dbd4a7..0973aae0aa18c02a1adbdee1afbf583052901269 100644 --- a/modules/core/include/opencv2/core/base.hpp +++ b/modules/core/include/opencv2/core/base.hpp @@ -167,23 +167,6 @@ enum DecompTypes { { \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, NORM_L1 = 2,