Can Fourier Transforms of both images tell anything about "likeliness" of two pictures? If yes, how precise? Can it still work if only several pixels are different or can it tell they are same if one of images is rotated, scaled or distorted(up to some degree)?

  • $\begingroup$ Fourier and spatial domains are related uniquely in a one to one fashion. For most fundamental operations and operators (such as multiplication, convolution, integration (sum), differentiation (difference) ) there will be a corresponding operation/operator in Fourier domain as well. However, an operation very simple in one domain may be quite complex to implement in the reciprocal domain. Finding an image inside another is traditionally a space domain problem and forcing that into frequency domain could be an overkill, unless otherwise is proven for a particular application. $\endgroup$ – Fat32 Feb 13 '19 at 19:09
  • $\begingroup$ Thank you. I should look for "frequency operators" then. $\endgroup$ – huseyin tugrul buyukisik Feb 13 '19 at 20:19
  • $\begingroup$ no possibly you should not. What's the reason you are looking for Frequency domain techniques ? Why do not you use spatial domain ? $\endgroup$ – Fat32 Feb 13 '19 at 20:46
  • $\begingroup$ Because in spatial domain, I just guessed, that I have to apply more transform types to match/align shapes to start measuring their similarity compared to some magical single step in Fourier Space. For example, comparing ellipse to circle. Spatial could need to distort ellipse into a circle first and also scale the circles to have same radius. Then what to do if we don't even know what shape is this? What if its something like an apple vs car? $\endgroup$ – huseyin tugrul buyukisik Feb 13 '19 at 20:54
  • $\begingroup$ ok, but (afaik) there is no magical one step frequency domain operation that would yield the similarity between two images under all condtions. Consider looking into object recognition, pattern recognition, template matching and similar techniques... All of them are exhaustive however. No simple technique exists. Parallel processing might improve that however. $\endgroup$ – Fat32 Feb 13 '19 at 21:00

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