What does phase spectrum of image signal mean?????

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ramdas patil 2014-5-22

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编辑： ramdas patil 2014-6-10

Hello everyone....!!!

I take phase spectrum of an image using Fourier transform, but I don't understand what it represents. So I have some basic doubts:

1.What does phase spectrum of Image actually mean?

2.What information do we get about each pixel from phase spectrum?

3.suppose u are given two phase spectrum instead of actual images,So can u recognize rotation of one image occurred in the second image using phase spectrum only? i have added my code and figure for reference

clc;
clear all;
close all;
i=imread('C:\Users\Public\Pictures\Sample Pictures\index.jpg');
i1=rgb2gray(i);
figure,
subplot(1,2,1);imshow(i1);title('Test image 1');
f1=fftshift(fft2(i1));
phase1=angle(f1);
subplot(1,2,2);imshow(phase1,[]),title('phase spectrum 1');
i2=imrotate(i,45);
i2=rgb2gray(i2);
figure,
subplot(1,2,1);imshow(i2);title('Test image 2');
f2=fftshift(fft2(i2));
phase2=angle(f2);
subplot(1,2,2);imshow(phase2,[]);title('phase spectrum 2');

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Answer 1

Image Analyst 2014-6-3

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The magnitude of the FFT is like how much energy there is in the sine waves used to build up your image. The phase is like how those sine waves are positioned. For a real, unsymmetrical image, your FFT will be Hermitian. See table about a quarter of the way down this page: http://www.cv.nrao.edu/course/astr534/FourierTransforms.html

Also see Steve's blogs: http://blogs.mathworks.com/steve/category/fourier-transforms/

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ramdas patil 2014-6-3

编辑：ramdas patil 2014-6-10

@Image Analyst ,thank u sir but can u comment on my 3rd question given above.??

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Answer 2

JB Braendel 2014-6-8

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I'm currently taking a course on continuous time signals, and our prof provided a visual interpretation behind the magnitude and phase spectrum of images:

My confusion however comes from how 2d signal processing works for images. What portion of the image does the FFT represent? Is it an FFT for each row of the image? Each column? An overall mix?

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ramdas patil 2014-6-10

@JB Braendel A full two-dimensional Fourier transform performs a 1-D transform on every scan-line or row of the image, and another 1-D transform on every column of the image, producing a 2-D Fourier transform of the same size as the original image

ramdas patil 2014-6-10

@JB Braendel sir, from the figures that u uploaded,....i can come to conclusion that phase part is dominant over magnitude part. can u tell me why is it so.???

also i have reconstructed image (partially) from the phase spectrum alone.but is it possible to reconstruct an image from magnitude spectrum only??

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