Take the image and spectrum below. If I look at the spectrum, it just look like noise.... How to make sense of it intuitively?
Frequency spectrum of image (using Fourier Transform):
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As stated by @tomasz, the fourier transform relates only globally to the image since the pixels of the transform correspond to frequencies in the original image (which you may intuitively understand - somewhat - as speed of color variation as you move on the original image). This is well explained on the web : An Intuitive Explanation of Fourier Theory
Look in particular at the bottom of the page.