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?
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.
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
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