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First time studying image processing...
I just don't understand what does fourier transformed image of an image describe?
For example consider given following pictures, The first one is the image, and the second one is the fourier transformation of the image.

The Lena image The fourier transformation of lena

Now my question is:
By given the fourier transformation image, what am i suppose to comprehend from that?

I would really appreciate any help here, i just cannot proceed with my studies without understanding this.

Thanks in advance.

dariush
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  • It's the frequency content in the image - but you've jumped straight into the deep end with a photograph, maybe look at some simpler examples first! e.g. [image](http://homepages.inf.ed.ac.uk/rbf/HIPR2/images/stp2.gif) and [transform](http://homepages.inf.ed.ac.uk/rbf/HIPR2/images/stp2fur1.gif) – wim Feb 21 '14 at 16:52
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    Check out [this](https://www.cs.unm.edu/~brayer/vision/fourier.html) website. – wbest Feb 21 '14 at 16:56
  • @wim thanks, but with images you've gave, the question still remains, what are those 3 dots means, i know those are the frequency content in the image, but what does `frequency content in the images` means actually? – dariush Feb 21 '14 at 17:13
  • @tom10 not according to [this](http://stackoverflow.com/questions/1424701/image-processing-related-discussion-forum)!!! – dariush Feb 22 '14 at 01:15
  • Voted to close as off-topic. I'm not sure how my original comment got deleted, so I'm restating it. (Certainly many image processing questions are on topic for this forum, but interpretations of mathematical algorithms seems off topic to me. I find this question very interesting, btw, so no offense intended towards the OP or the question.) – tom10 Feb 22 '14 at 17:41

1 Answers1

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The central part includes the low frequency components. The bright pixels in frequency image (right) indicate strong intensity at the corresponding positions in spatial image (left). Note that there is no one-on-one mapping from the pixel in frequency domain and spatial domain. One frequency pixel consists all the spatial pixels that have the corresponding frequency.

The low frequency domain corresponds to the smooth areas in the image (such as skin, hat, background, etc). The high frequency domain, which is shown in the image away from the central part, includes those sharp edges or some structure with the changes of intensity dramatically along one orientation (such as the hairs, boundary of hat, etc). But since the intensity for those parts is not high enough compared with the smooth structure, the corresponding regions appear dark on the right image.

Note that the camera lens focuses on Lenna, so the background is blurred. If the focus region is at background, the vertical lines behind Lenna would be clear, and the sharp edges of the lines will contribute to high frequency magnitude, thus region away from the center on the right image would be bright.

lennon310
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    Thanks, and what about the horizontal and vertical white lines in the transformed picture(right), what is the meaning of them and what causes them? – dariush Feb 22 '14 at 04:08
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    That's the DC offset along x and y direction (0-x-frequency and 0-y- frequency ). If you eliminate the mean value of each column, then each row on Lenna, the two white lines are supposed to disappear. – lennon310 Feb 22 '14 at 04:11