Why shift, take absolute value and perform log transform to the frequency spectrum of an image obtained by fft2?

I have to obtain the frequency spectrum of a grayscale image using FFT in MATLAB and plot the spectrum. I used fft2() and plotted the output.

I watched a tutorial on plotting frequency spectrum and in that, they perform fftshit(), take the absolute value, apply a log transformation, scale pixels using mat2gray() and then convert into uint8 before plotting the spectrum.

im2uint8(mat2gray(log(abs(fft_shifted)+1)))

My question is, is that necessary to perform all those steps before plotting the frequency spectrum?

I know fftshift() is used to center the spectrum around 0th frequency coefficient. But what is the use of performing other functions?

I plotted the frequency spectrum without shifting, after shifting, and after applying the above-mentioned steps.

After this, I have to apply a low pass filter to the grayscale image and compare frequency spectrums. (This is a homework question)

Any advice is much appreciated. Thank you!

Answer 1

[yanqi liu]

im2uint8(mat2gray(log(abs(fft_shifted)+1)))

sir，i think

abs(fft_shifted)+1 to avoid log(0) or log(neg)

log to display result in log space，to avoid some data too big with some data too small

Answer 2

[Chris]

take the absolute value

The log of a negative number is undefined, which would make for a boring image.

apply a log transformation

It's likely some intensities will be orders of magnitude higher than some others. Applying a log scale allows you to see the smaller values as well. Otherwise, the image will be boring.

scale pixels using mat2gray() and then convert into uint8

I don't know what function you're using to display the image, but functions like imshow() expect integers on a 0 to 255 scale (an 8-bit pixel map). im2uint8(mat2gray()) accomplishes that scaling.

[Ilya Grishanovich]

How to take the absolute value for 2D spectrum?

I have 2D spectrum with positive and negative signals, I want to make all signals positive.

How to make it?

[Chris]

If it's in matrix form, like an image, abs() will make all points positive.