Ranklet

<h2 id="example">Example</h2>
<p>Suppose 
  
    
      
        T
        =
        {
        5
        ,
        9
        ,
        1
        ,
        10
        ,
        15
        }
      
    
    {\displaystyle T=\lbrace 5,9,1,10,15\rbrace }
  
 and 
  
    
      
        C
        =
        {
        20
        ,
        4
        ,
        7
        ,
        13
        ,
        19
        ,
        11
        }
      
    
    {\displaystyle C=\lbrace 20,4,7,13,19,11\rbrace }
  
 then
</p>
<table><tbody><tr><td>Intensity</td><td>1</td><td>4</td><td>5</td><td>7</td><td>9</td><td>10</td><td>11</td><td>13</td><td>15</td><td>19</td><td>20</td></tr><tr><td>Sample</td><td>T</td><td>C</td><td>T</td><td>C</td><td>T</td><td>T</td><td>C</td><td>C</td><td>T</td><td>C</td><td>C</td></tr><tr><td>Rank</td><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td><td>9</td><td>10</td><td>11</td></tr></tbody></table>
<ul><li>
  
    
      
        
          W
          
            s
          
        
        =
        
          
            {
          
        
        1
        +
        3
        +
        5
        +
        6
        +
        9
        
          
            }
          
        
        =
        24
      
    
    {\displaystyle W_{s}={\Big \lbrace }1+3+5+6+9{\Big \rbrace }=24}
  
</li>
<li>
  
    
      
        M
        W
        =
        24
        −
        [
        5
        ×
        (
        5
        +
        1
        )
        
          /
        
        2
        ]
        =
        9
      
    
    {\displaystyle MW=24-[5\times (5+1)/2]=9}
  
</li>
<li>
  
    
      
        R
        =
        [
        9
        
          /
        
        [
        5
        ×
        6
        
          /
        
        2
        ]
        ]
        −
        1
        =
        −
        0.4
      
    
    {\displaystyle R=[9/[5\times 6/2]]-1=-0.4}
  
</li></ul>
<p>Hence, in the above example the Control region was a little bit brighter than the Treatment region.
</p>
<h2 id="method">Method</h2>
<p>Since Ranklets are non-linear filters, they can only be applied in the spatial domain. Filtering with Ranklets involves dividing an image window <i>W</i> into Treatment and Control regions as shown in the image below:
</p>

<p>Subsequently, Wilcoxon rank-sum test statistics are computed in order to determine the intensity variations among conveniently
chosen regions (according to the required orientation) of the samples in <i>W</i>. The intensity values of both regions are then
replaced by the respective ranking scores. These ranking scores determine a pairwise comparison between the <i>T</i> and <i>C</i> regions. This means that a ranklet essentially counts the number of TxC pairs which are brighter in the <i>T</i> set. Hence a positive value means that the Treatment values are brighter than the Control values, and vice versa.
</p>

<h2 id="external-links">External links</h2>
<ul><li><a href="/facts/Matlab/qPjLISCk">Matlab</a> <a href="https://web.archive.org/web/20110722070312/http://www.cs.rug.nl/~george/RankletFilter.m">RankletFilter.m -> source file to decompose an image into Intensity Ranklets</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>"www.Ranklets.net". www.eecs.qmul.ac.uk. Retrieved 2022-06-05. <a href="http://www.eecs.qmul.ac.uk/~fabri/www.ranklets.net/index.html" target="_blank">http://www.eecs.qmul.ac.uk/~fabri/www.ranklets.net/index.html</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Smeraldi, Fabrizio (2002). "Ranklets: Orientation Selective Non-Parametric Features Applied to Face Detection". 16th International Conference on Pattern Recognition, ICPR 2002, Quebec, Canada, August 11–15, 2002. IEEE Computer Society. pp. 379–382. doi:10.1109/ICPR.2002.1047924. <a href="https://hh.diva-portal.org/smash/record.jsf?pid=diva2%3A290965" target="_blank">https://hh.diva-portal.org/smash/record.jsf?pid=diva2%3A290965</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>"www.Ranklets.net". www.eecs.qmul.ac.uk. Retrieved 2022-06-05. <a href="http://www.eecs.qmul.ac.uk/~fabri/www.ranklets.net/nonZim/wilcoxon/computation.html" target="_blank">http://www.eecs.qmul.ac.uk/~fabri/www.ranklets.net/nonZim/wilcoxon/computation.html</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
</ol>

Ranklet open-in-new

Ranklet