title: How sobel operator mask matrix is created?
body: <p><a href="http://www.cis.rit.edu/people/faculty/rhody/EdgeDetection.htm" rel="nofollow">http://www.cis.rit.edu/people/faculty/rhody/EdgeDetection.htm</a></p>
  
  <p>This seems the only article tries to describe how the sobel operator comes from equation. But i am certainly not understanding the aspects.</p>
  
  <p>In that page , they let</p>
  
  <pre><code>A = array of actual image , B = grayscale version
  
  Horizontal gradient B(j ,k) = taking column values = A ( j,k+1 ) - A (j,k)
  </code></pre>
  
  <p>My question , why taking column values for horizontal ?</p>
  
  <p>Then again , they said :</p>
  
  <pre><code>This can be represented by a filter array as shown below: as a matrix [-1,1]
  </code></pre>
  
  <p>How this filter array comes from that equation ? Also , i am having hard time to understand why [-1,1] becomes [-1,0,1] and then this horizontal and vertical matrices are not "multiplied" to get the sobel operator , they are product of 2-dimensional convolution operation. What the hack that means ?</p>