image rotation in frequency domain

Question

I found a code about image rotation in frequency domain. But I couldn't understand this code. This code works correct. Can anyone describe this code? Actually I have to write a code to rotate an image in frequency domain in polar coordinates. Do you think this code meet the requirements.

clear;
img=imread('cameraman.tif');
imshow(img); title('original image');
theta=26,5;
N=size(img,1);
M=size(img,2);                                      

fimg=fftshift(fft2(fftshift(img)));

p=ones(N,1)*[-N/2:(N-1)/2];               % horizontal axis
q=-p';                                                     % vertical axis

theta=2*pi*theta/360;
g=1/(N^2).*fimg;
z1=exp(i*pi/N.*((p.^2-q.^2)*cos(theta)-2*p.*q*sin(theta)));
z2=exp(-i*pi/N.*((p.^2-q.^2)*cos(theta)-2*p.*q*sin(theta)));
k=ifft2(fft2(g.*z1).*(fft2(z2)));
figure,
imshow(abs(fftshift(flipud(k))), [0 255]); 
title(['Cameraman rotated at ' num2str(theta*360/(2*pi))  ' Degrees']); axis off

Answer 1

As you can see here.

For the rotation, there is no properties. But this code using the shift properties to apply the rotation.

In z1, you have the coordinate (p,q) compute normaly as well, but just by applying the 2D rotation matrix to your coordinate, you can use the shift properties.

And notice, this code change a the sign every where, that why there no minus in z1 instead of z2.

Rotation : [cos(theta) -sin(theta);
            sin(theta) cos(theta)];