I am trying to understand some really basics of image processing. One of them is the DFT ( Discrte Fourier Tranform). I have seen code segments, read stuff but still I don’t get how the image produced is related to the first one. For example, I take an image with vertical black and white stripes, and I get an image (after applying DFT) that has some dots in it. Now how does the mapping works? What do I mean? How does point (1,0) of the first image relates to point (1,0) of the DFT image? How does the mapping works?
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The correlation between an image and the DFT exists, of course, but it has nothing to do with point(1,0) being mapped to dft_point(1,0)
The Fourier transform is said to take one image from the space domain to the frequency domain. That is to say that the numbers on the transform represent the fundamental frequencies that compose the image.
To really understand what that means, you have to at least be comfortable with calculus. But stating that in a more simple term:
If the image was composed by a summation of sinusoids, the DFT would return the amplitude and phase of the sinusoids that, summed up, would yield the original image.
Applet
In that applet, click on Sine, and then you can increase or decrease the values of the fourier transform and see what happens. There you can see the correlation in 1d 🙂