Notes
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Outline
1
Convolution
  • A convolution operation is a cross-correlation where the filter is flipped both horizontally and vertically before being applied to the image:




  • It is written:



  • Suppose H is a Gaussian or mean kernel.  How does convolution differ from cross-correlation?
2
Continuous filtering
  • We can also apply continuous filters to continuous images.
  • In the case of cross correlation:




  • In the case of convolution:





  • Note that the image and filter are infinite.
3
Image gradient
  • The gradient of an image:



  • The gradient points in the direction of most rapid change in intensity
4
Effects of noise
  • Consider a single row or column of the image
    • Plotting intensity as a function of position gives a signal
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Solution:  smooth first
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Derivative theorem of convolution
  • This saves us one operation:
7
Laplacian of Gaussian
  • Consider
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2D edge detection filters
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Edge detection by subtraction
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Edge detection by subtraction
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Edge detection by subtraction
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Gaussian - image filter