How to interpret the results of 2D Fourier Transform on an image?

Question

I am following a signal processing course (mostly filtering of sounds and images).

I roughly understand the results of a Fourier transform for sounds, but I don't really get the meaning for the resulting image of a 2D Fourier transform on an image. Generally, we use that on grayscale images, and it just gives seemingly random white/grey points on a black background, but I don't understand what information I can extract from that. Basically, I'd like someone to explain to me how this is useful and what important informations I can get from such an image.

Answer 1

Fourier transform on image represent the image in the frequency domain so you extract information with some kind of image.

For example:

• Denoising: You can remove (reduce) noise by removing high frequency from FT.
• Analysis: If image is simple in that it is composed of periodic shapes then you can extract geometric features (extract space of diagonal stripes).
• image reconstruction: tomography
• image compression: deimation in time and frequency (Radix-$2^n$ Fast Fourier transform).

In any case, image must not have too much information (it should have low frequency domain or distinct frequency domain ...) because in fourier domain it becomes difficult to find features of image we want.