1/f amplitude frequency plot

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Ayesha Batool
Ayesha Batool 2019-2-5
回答： Hari 2025-2-24
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.

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回答（1 个）

Hari
Hari 2025-2-24
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:
Hope this helps!

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