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POWhat is the difference between 1x2 and 1x3 image gradient kernel filter definition
 

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  1. POWhat is the difference between 1x2 and 1x3 image gradient kernel filter definition
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    <p>Recently I have a debate with my colleague on image gradient operation.</p> <p>Normally, the image gradient is defined as:</p> <p><code>dI_dx(j,k) = I(j,k+1) - I(j,k) # x partial derivative of image</code></p> <p><code>dI_dy(j,k) = I(j+1,k) - I(j,k) # y partial derivative of image</code></p> <p>For x partial derivative of image, this operation can be represented by a 1x2 filter array:</p> <p><code>[1 -1]</code></p> <p>But there is also another definition:</p> <p><code>dI_dx(j,k) = I(j,k+1) - I(j,k-1)</code> => <code>[1 0 -1]</code> (filter array)</p> <p><strong>So my colleague asked: What is the difference between them, and why is the latter 1x3 filter more often used than the 1x2 filter?</strong></p> <p>We have discussed some possible reasons:</p> <ol> <li><p>1x3 sampling is more robust than 1x2</p> <p>My colleague : No, they both sample 2 pixels for each image gradient pixel, the probability that a noise occurs on the sampled pixels is the same among these filters.</p></li> <li><p>1x3 is smoother than 1x2</p> <p>My colleague : No, the definition of the 1x2 and 1x3 filters are not smoothed at all. The Sobel filter is the one smoothed by a gaussian...</p></li> </ol> <p>Extended question: <strong>Does image gradient's spatial filter kernel have so called "window size"?</strong></p> <p>By the way, I and my colleague are not persuaded by the following reference webpage...</p> <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>
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