I am learning image processing. I want to ask very basic question related to FFT topic
Which information do we actually get from "phase spectrum" and "magnitude spectrum" about an image?
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$\begingroup$ Hi ! It is not really clear what is the question under #3, so, if you can, elaborate :) $\endgroup$– SektorJun 9, 2014 at 19:43
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1$\begingroup$ It's best to only ask one question per post. #1 is likely a duplicate of this previous question. #2 is probably answered in many places (frequency-domain filtering can yield improved speed for large filters). I'm not sure what you're asking in #3. #4 is a very vague question, so you'd need to clarify. $\endgroup$– Jason RJun 9, 2014 at 20:23
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$\begingroup$ ieeexplore.ieee.org/iel5/5/31301/01456290.pdf?arnumber=1456290 $\endgroup$– geometrikalJun 10, 2014 at 6:53
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$\begingroup$ @Jason R sir i have edited my 3rd question $\endgroup$– sagarJun 10, 2014 at 9:49
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1 Answer
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You get the exact same information you will receive if you analyse a 1-D signal using the Fourier analysis tools, for example. To illustrate this consider the following examples
We perform Fourier Transform on it and obtain the following spectrum
As you can see there are two symmetric dots representing the frequency that is present in the image and the central, DC, component.
Next up
Again the Fourier Transform
It is obvious that the higher frequencies are further away from the DC, central, component. To understand the logic behind this you shall remember that we are actually working with complex numbers and their properties kick in.
To answer your second question: You are usually working with sparse data structures (vectors, arrays, tensors, etc.) in the frequency domain. Now you tell me which is easier: Working on the original data set consisting of 500 different values or the transformed one with half of them 0s ?
Now, the importance of phase - drum rolls - it is the same, meaning HUGE
Again, a sample image
Fourier Magnitude Spectrum
Fourier Phase Spectrum
Now, we inverse the transformation by using just the amplitude and then just the phase information
Inverted amplitude spectrum
Inverted phase spectrum
I think you get the idea :D
Now, here are some sample images and their respective amplitude and phase spectra, so you can practice a wee bit
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$\begingroup$ @Sektir To elaborate on the meaning of the magnitude and phase. The magnitude corresponds to the (values) of the pixels in the time domain. While the phase, tells us how these values should be organized to get the full picture. Therefore; the phase is dominant to the magnitude. +1 for the effort! $\endgroup$ Jun 9, 2014 at 20:37