1/f amplitude frequency plot

I'm running an image analysis using fourier transform.

I want to use spectral amplitude as a measure of naturalness of an image.

It is said that the i/f amplitude-frequency scaling is modulated by the naturalness of scenes, with steeper slops for naturalistics compared to artifactual scenes.

I just want to run this in matlab and test on two images, naturalistic and artifactual to see how it is.

Please share a simple code to read an image and run this 1/f amplitude - frequency scaling.

I'm here so far:

clear all; close all; clc

imdata = imread('C:\....\ab.jpg');

figure(1);imshow(imdata); title('Original Image');

imdata = rgb2gray(imdata);

figure(2); imshow(imdata); title('Gray Image');

%get fourier transform of an image

F = fft2(imdata);

%fourier transform of an image

S = abs(F);

figure(3);imshow(S,[]);title('Fourier Transform of an Image');

%get the centered spectrium

Fsh = fftshift(F);

figure(4);imshow(abs(Fsh),[]);title('Centered Fourier Transform of Image')

%apply log transform

S2 = log(1+abs(Fsh));

figure(5);imshow(S2,[]);title('log transformed image')

%reconstruct our image

F = ifftshift(Fsh);

f =ifft2(F);

figure(6);imshow(f,[]),title('reconstruct image')

If I'm missing something, too, please explain how to go about it.

Answer 1

[Hari]

Hi Ayesha,

I understand that you want to analyze the naturalness of images using 1/f amplitude-frequency scaling through Fourier transform.

I assume you want to compare the amplitude spectrum of naturalistic and artifactual images by analyzing their frequency content.

In order to perform 1/f amplitude-frequency scaling analysis, you can follow the below steps:

Read and Preprocess Images:

Load your images and convert them to grayscale.

imdata_natural = rgb2gray(imread('path_to_natural_image.jpg'));
imdata_artificial = rgb2gray(imread('path_to_artificial_image.jpg'));

Compute Fourier Transform:

Calculate the 2D Fourier transform to get frequency representation.

F_natural = fft2(imdata_natural);
F_artificial = fft2(imdata_artificial);

Calculate Amplitude Spectrum:

Shift the zero-frequency component to the center and compute amplitude.

amplitude_natural = abs(fftshift(F_natural));
amplitude_artificial = abs(fftshift(F_artificial));

Plot 1/f Amplitude-Frequency Scaling:

Compute and plot the radial average of the amplitude spectrum.

radial_natural = mean(amplitude_natural, 2);
radial_artificial = mean(amplitude_artificial, 2);
loglog(radial_natural, 'b'); hold on;
loglog(radial_artificial, 'r');
legend('Natural', 'Artificial');

Interpret Results:

Compare slopes on the log-log plot; steeper slopes suggest more natural scenes.

Refer to the documentation of “fft2” and “fftshift” functions to know more about their usage:

• https://www.mathworks.com/help/matlab/ref/fft2.html
• https://www.mathworks.com/help/matlab/ref/fftshift.html

Hope this helps!