how to do FFT for PART on an image?

I want to compare the following two images based on their Fourier Transform. However, I am only interested in the circular region. Is it possible to do FFT for part on an image?

tnx in advance

Answer 1

[Image Analyst]

Not sure what you're looking for. Since your second image has a circular mask multiplied by the first image, your second spectrum will be the same as the first spectrum, just convolved with a narrow sombrero function.

[ramin bba]

yes, the second image has a mask but I just used it to show which regions I am NOT interested in. the question might be better stated as:

how can I find out which regions on an image, are mapped to which regions of the transformed image? if I was doing only fft, I would not have a problem! however, I am doing 2D DFT (discrete Fourier Transform) on the indicator function of the binary image (this will result into a probability space).

tnx and sry for the confusion

[Image Analyst]

I think you do not understand what the Fourier transform represents. There is no one-to-one correspondence with a region in the spatial domain with a certain finite, compact region in the Fourier domain. There is no "mapping" as you called it. Low frequencies are near the center and high frequencies are away from the center, but that's about as "mapped" as you can call it.

[ramin bba]

you are right, I meant "mapping" not from pixel to pixel.

Let's say I provide you with two copies of the image on the right hand side. In the one of them, the gray region is replaced with disks of various sizes (and this is the only change). Now, if you take FFT of the two copies, the results will NOT be the same WHILE the two images are identical given MY REGION OF INTEREST. How can use FFT of two images to make the decision that "whether they are the same given a region of interest"?

I hope I made myself clearer.

thanks for your thorough comments.