Fourier spectrum of an image

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I don't quite understand fourier spectrum and it's properties of an image. Can anybody helps me to solve the follwing questions?

For question e,I think a larger distance of bright point will give a larger frequency , so c to a. However I dont quit understand the meaning of the 3 point.

For question c ii, I think the magnitude of fourier spectrum will roate and the phase will not change as the position is the same. For c iii, the magnitude of fourier spectrum will be the same in c ii but the phase changed due to the change in position. Is it right?

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Another one here : enter image description here

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image-processing
what is it you don't understand? provide what you understand or what you think how it could be understood. This is not a free service for solving text book questions or homework – Piglet
For question e,I think a larger distance of bright point will give a larger frequency , so c to a. However I dont quit understand the meaning of the 3 point. – Zhetao Zhuang
For question c ii, I think the magnitude of fourier spectrum will roate and the phase will not change as the position is the same. For c iii, the magnitude of fourier spectrum will be the same in c ii but the phase changed due to the change in position. Is it right? – Zhetao Zhuang
@ZhetaoZhuang you need to add @nick to your comment so user nick is notified of your message. The smaller details on the image the higher the used frequencies with high magnitude. Sharp images (edges and non periodic details) produce cascade of frequencies. Overall DFT magnitude encode also the image overall brightness. – Spektre

1 Answers

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To help with understanding here are some DFT response examples:

DFT responses

All input images are 64x64 hand drawed in paint so they may be misplaced by few pixels. The DFT response images are wrapped and magnitude is emphasized many times so it is visible and match shapes from the books (raw DFT unwrapped images looks a bit different).

  1. Integrated magnitude should correspond to image integrated magnitude. Hence more bright image has bigger magnitudes.

  2. The smaller the detail the higher the frequencies have bigger magnitudes (black space is also detail)

  3. position do not affect frequencies so much but the amplitude distribution instead

  4. rotation rotates also the frequency domain but centered on the wrapped center or the 4 corners in unwrapped images

  5. sharp non periodic edged detail provide many frequencies

  6. smooth periodic shapes provide fewer frequencies response

Do not forget that input image si real only so the response is always symetrical/mirrored in both x,y directions

For more info see related QA: