From 3e0b1f284536818a5d6696a5f656234b1f647c95 Mon Sep 17 00:00:00 2001 From: "Jan S. (Milania1)" Date: Thu, 15 Oct 2015 19:16:07 +0200 Subject: [PATCH] Added example to the documentation for the NormTypes enum (L1, L2, INF) --- .../doc/pics/NormTypes_OneArray_1-2-INF.png | Bin 0 -> 15830 bytes modules/core/include/opencv2/core/base.hpp | 20 +++++++++++++++++- 2 files changed, 19 insertions(+), 1 deletion(-) create mode 100644 modules/core/doc/pics/NormTypes_OneArray_1-2-INF.png diff --git a/modules/core/doc/pics/NormTypes_OneArray_1-2-INF.png b/modules/core/doc/pics/NormTypes_OneArray_1-2-INF.png new file mode 100644 index 0000000000000000000000000000000000000000..ec4304d8c6d5223e9f4d04d13555f0adb7eb2fd3 GIT binary patch literal 15830 zcmb`u1yI&q^e*}$A_&r5(jna`pmeu%OG|g7NJ&adOM{fOv~;(0OE=Q}o{fCp_n&*_ z&fJ-E&kW-D`u_HB?O1C)&$HJ4q$n?ej7We8fk2R@Bt?}WkVixi2#g)VBk+lrFlPez z>#3cjrXvJ`gn9o529lJ52R>wT64P)}u{CvaHFPk6sM}hZIv84$${9MDn^+qJ1DU{%8%KN8998ADBZEZ+ZEv!u-Y%Hvte5@>dtQ@3l zYSQYSA-kW5m}Jjq?DnHJ?9fDh4$|3- zY{eqH*iJ^9)d;EJ`VY=jxy!5ypWLOLi95rot~HL@gE&4ll}CGHscabOjV6f|XdrMf 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zzx&g5No8*jXMP^b_eoIK*H|6FJ$eV;^{I81A;PAwV3b0O8=S^h|Cy$+QitkJN>&+f zrgS^sWe+Z4ZfeG7=GNfkCLJK_Z(e^QaYN!f;17$eTskZ`<0!fQ%>Ob+Xz~cM)4bJ7 z>jy{Fz4oK&HVorQI4T7SS#?XqsFI_;7T$?N=#m~MA*RZ Fe*r#1PB{Po literal 0 HcmV?d00001 diff --git a/modules/core/include/opencv2/core/base.hpp b/modules/core/include/opencv2/core/base.hpp index 3ab0982ceb..8fabf5fffa 100644 --- a/modules/core/include/opencv2/core/base.hpp +++ b/modules/core/include/opencv2/core/base.hpp @@ -164,7 +164,25 @@ enum DecompTypes { \f[norm = \forkthree{\frac{\|\texttt{src1}-\texttt{src2}\|_{L_{\infty}} }{\|\texttt{src2}\|_{L_{\infty}} }}{if \(\texttt{normType} = \texttt{NORM_RELATIVE_INF}\) } { \frac{\|\texttt{src1}-\texttt{src2}\|_{L_1} }{\|\texttt{src2}\|_{L_1}} }{if \(\texttt{normType} = \texttt{NORM_RELATIVE_L1}\) } { \frac{\|\texttt{src1}-\texttt{src2}\|_{L_2} }{\|\texttt{src2}\|_{L_2}} }{if \(\texttt{normType} = \texttt{NORM_RELATIVE_L2}\) }\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, NORM_L2 = 4,