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Ranklet : ウィキペディア英語版
Ranklet

In statistics, a ranklet is an orientation-selective non-parametric feature which is based on the computation of Mann–Whitney–Wilcoxon (MWW) rank-sum test statistics. Ranklets achieve similar response to Haar wavelets as they share the same pattern of orientation-selectivity, multi-scale nature and a suitable notion of completeness.
Rank-based (non-parametric) features have become popular in the field of image processing for their robustness in detecting outliers and invariance to monotonic transformations such as brightness, contrast changes and gamma correction.
The MWW is a combination of Wilcoxon rank-sum test and Mann–Whitney U-test. It is a non-parametric alternative to the t-test used to test the hypothesis for the comparison of two independent distributions. It assesses whether two samples of observations, usually referred as Treatment ''T'' and Control ''C'', come from the same distribution but do not have to be normally distributed.
The Wilcoxon rank-sum statistics ''W''''s'' is determined as:
: W_s=\sum^N_\pi_i V_i \text\pi_i = \texti\textV_i
= \begin
0 & \text\pi_i\in C \\()
1 & \text\pi_i\in T
\end

Subsequently, let ''MW'' be the Mann–Whitney statistics defined by:
: MW=W_s-\frac
where ''m'' is the number of Treatment values.
A ranklet ''R'' is defined as the normalization of ''MW'' in the range ():
: R = \frac-1
where a positive value means that the Treatment region is brighter than the Control region, and a negative value otherwise.
==Example==
Suppose T=\lbrace 5,9,1,10,15\rbrace and C=\lbrace 20,4,7,13,19,11\rbrace then


*W_s=\Big\lbrace 1+3+5+6+9\Big\rbrace =24
*MW=24-(\times (5+1)/2 )=9
*R=[9/[5 \times 6/2]]-1=-0.4
Hence, in the above example the Control region was a little bit brighter than the Treatment region.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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