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I am relatively new to FFT analysis of images and have a question about them. I like to think I understand the basics but many of the properties shown in a FFT image are beyond me.

My main question is what is what is the meaning of the length of diagonal lines in a fourier transform? What is the meaning of the length of a diagonal line on the image domain or in the Fourier domain? The diagonal lines are related to the edges in the image but what kind of property does the length describe?

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If asking these questions means that I don't fully understand FFT, are there any resources that would help me dig deeper?

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The length of the diagonal line will be, in a sense, a measurement of the sharpness of the sharpest edge in that direction. If you apply the proper coordinates to your axes, you could quantify this.

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  • $\begingroup$ Thank you very much, Joe. I had done some research on the question and stumbled onto this (smallpond.ca/jim/misc/resolution/fft). It shows there is a correlation between the "sharpness" of the image and the length of those lines. What does the length actually describe? The antialiasing of the image or the resolution? Or is it just a correlation? Sorry if this sounds fussy but I want to understand this phenomenon in its entirety. $\endgroup$
    – Jorge Diaz
    Sep 20, 2019 at 19:26
  • $\begingroup$ I would argue it corresponds to the containing frequencies along this direction while the middle is nyquiest and goes to lower on the outside. So you have to take it's density into account as well not just it's end. Every dot basically means how much energy a specific frequency along this line has. $\endgroup$
    – OuttaSpaceTime
    Jan 10, 2022 at 23:47
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If you rotate an image, Also its 2D Fourier transform will rotate.

Those lines mean you have something like a barcode oriented in that direction in your image. In one direction it has lots of variations and behaves like a white noise with flat spectrum and in the other direction it has very slow variations.

I'm not sure what do you mean by the length of diagonals, but it's a visual measure of maximum frequency available in those directions.

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  • $\begingroup$ I do not really understand the first part of your answer but your last sentence makes a lot of sense. I understand that the frequency is represented in FFT and that those lines represent the edges since it show the change of frequency in a certain direction. But my question is what does having different lengths tell us about the image in the spatial domain. $\endgroup$
    – Jorge Diaz
    Sep 20, 2019 at 19:17

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