EE4206/EE5806 The Fourier transform X(jw1, jw2) of the image

EE4206/EE5806 The Fourier transform X(jw1, jw2) of the image

1. The Fourier transform X(jw1,jw2) of the image represents a decomposition of the image into complex exponential components of the form e^(jw1*t1) * e^(jw2*t2) that capture the spatial variations of x(t1,t2) AT different frequencies in EACH of the two coordinate directions.

2. In viewing a picture, some of the most important visual information is contained in the EDGES and REGIONS of high contrast.

3. Intuitively, regions of maximum and minimum intensity in a picture are places at which complex exponentials at different frequencies are in phase.

4. Therefore, it seems plausible to expect the phase of the Fourier transform of a picture to contain much of the information in the picture, and in particular, the phase should capture the information about the edges.