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I am facing problem in reading Fourier domain of a given image. I don't understand what to interpret from it. For instance, consider this image.

enter image description here

Ok, so there is a dot in the middle, with some striking vertical and horizontal lines and there are also some circulating white lines which are low in intensity. What do I interpret from them? I basically converted the image to a monochrome image and then took the fourier transform of the monochrome image and displayed it along with original RGB image. Please help me to understand this. I tried every other resource but nothing got into my head. What are the uses of this interpretation? Also, in one of the answers here on DSP stackexchange, the images of sine and cosine were taken and then converted to spectrum which resulted white dots in it. I don't want to know that. I know that these dot represents the frequency component present in the sine and cosine. I want to understand everything with respect to my image only.

Thanks in advance!!

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    $\begingroup$ My suggestion is to read any introductory textbook on signals and systems. Since you don't provide any reason why you calculated the image's FT in the first place, I'll assume it's a homework problem and then my second suggestion is, ask your instructor. $\endgroup$
    – MBaz
    Apr 8, 2018 at 16:10
  • $\begingroup$ In the meantime, you might find this somewhat helpful. $\endgroup$
    – A_A
    Apr 8, 2018 at 22:08
  • $\begingroup$ I know the concepts of signals and systems, Fourier transform, Laplace transform, etc. I am an electrical engineering student. I just want to know what does magnitude spectrum of an image means. $\endgroup$
    – Himanshu Sharma
    Apr 9, 2018 at 0:29

1 Answer 1

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Many people face the same issues. Your image is far from showing stationarity: quite edgy, with circular features, so the Fourier analysis might not be so enlightening, without showing the unwrapped phase, which might contain many interesting features for this class of images. However:

  • so there is a dot in the middle: standard images have integer values between $0$ and $255$, hence the average is not zero. The average is the center dot. Remove it, and the global contrast may be better
  • some striking vertical and horizontal lines: FFT generally uses periodic extension, and the differences between the bottom and top, and right and left, might obfuscate details.

In the following pictures, you get space data and the Fourier spectrum. The first line is your image, with an horizontal/vertical cross. When you window the image (second line), those disappear, and the most luminous decreasing slope is, probably, due to the index finger, and the parallel lines from the two biggest gears. On the third row, the windowed image is subtracted from its median filtered version. One begins to see circles, related to locally oriented teeth.

fourier transforms

So, to interpret complicated data, remove first order artifacts, and slow background features, to better interpret details.

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