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
•
•
•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.
•
•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.
•
•
•This
is referred to as the Convolution Theorem
•
F(H*G) = F(H)F(G)