title: Median variance in background subtraction
body: <p>I am facing some issues in implementation of the paper <em><a href="http://academic.research.microsoft.com/Publication/1796345/statistical-background-subtraction-for-a-mobile-observer" rel="nofollow noreferrer">Statistical Background Subtraction for a Mobile Observer</a></em>.</p>
  
  <p><strong>Question 1</strong>:</p>
  
  <p>In Section 4.1, it talks about "... the median variance is computed over the entire image from the first components ..."</p>
  
  <p>I am confused what the authors actually mean by this.</p>
  
  <p>According to <strong>Stauffer &amp; Grimson</strong>'s paper Adaptive Background Mixture Models for Real-Time Tracking(1999), for every background model a variance gets initialized (say with value 36) and then it gets updated for each pixel. Should the median of the first model's variance across all the pixels for that frame should be taken?</p>
  
  <pre><code>                  OR
  </code></pre>
  
  <p>We compute the <strong>variance</strong> for each pixel based on its history of intensity values of those which belong to the first model and then take m<a href="https://stackoverflow.com/questions/49263/approximate-string-matching-algorithms">e</a>dian of all these variances.</p>
  
  <p><strong>Question 2</strong>:</p>
  
  <p>I am facing difficulty in understanding equation (12) in section 4.1</p>
  
  <p>a) Is 'i' from <code>1</code> to <code>H+1</code>? If yes, how does the (H+1)th model fits in the equation? </p>
  
  <p>i) Just after equation (13), <code>P(A_1 | B_(H+1),M)</code> is defined. Shouldn't <code>rho_(H+1) = min(1, N_tot/N_max)</code> instead of max which could make <code>P(A_1 | B_(H+1),M)</code>  (-)ve?</p>
  
  <p>ii) For the (H+1)th model should we have <code>P(A_1 | B_(H+1),M) * P(B_(H+1) | N) to P(A_1 | Z,M)</code> for equation (12)?</p>
  
  <p>b) when H=1, does <code>P(A1|Z,M)</code> becomes 1?</p>
  
  <p>My <strong>implementation</strong> is <a href="https://sites.google.com/site/learningcomputervision/background-subtraction/grimsongmm" rel="nofollow noreferrer">here</a>.</p>
  
  <p>Please check my trial in the <strong>MATLAB</strong> files which I have mentioned in my <a href="https://sites.google.com/site/learningcomputervision/background-subtraction/grimsongmm" rel="nofollow noreferrer">webpage</a>.</p>