9/14/2001
CS 461, Copyright G.D. Hager
The Fourier Transform and Convolution
•If H and G are images, and F(.) represents Fourier transform, then
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•Thus, one way of thinking about the properties of a convolution is by thinking of how it modifies the frequencies of the image to which it is applied.
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•In particular, if we look at the power spectrum, then we see that convolving image H by G attenuates frequencies where G has low power, and amplifies those which have high power.
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•This is referred to as the Convolution Theorem
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F(H*G) = F(H)F(G)