How To Find The X & Y Shift Of An Image

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Pranjal Pathak 2012-8-24

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https://ww2.mathworks.cn/matlabcentral/answers/46650-how-to-find-the-x-y-shift-of-an-image

Hi,

I need some help regarding the following code:

fx = 3.5:3.5:56;
fy = 2;
a=128;
b=128;
c=512;
[x1,y1]=meshgrid(-1:2/511:+1,-1:2/511:+1);
circ1=sqrt(x1.^1+y1.^1)<1;
% Aberration
z8=sqrt(8).*(3.*(x1.^2+y1.^2)-2).*x1; 
% Generation Of Holograms
[x,y] = meshgrid(-1:2/127:+1,-1:2/127:+1);
circ=sqrt(x.^2+y.^2)<1;
for j1 = numel(fx):-1:1
    h{j1} = circ.*cos(pi*(x*fx(j1) + y*fy));
end
% An Array Of 4x4 Holograms(Concatenation)
M = cell(c/a);
M(:) = h;
M = cell2mat(M');
%figure(1) 
imagesc(M),colormap gray; axis image; axis off 
title('Array Of 4x4 Holograms');   
%Fourier Transform Before Adding Aberration
z1=fftshift(fft2(M,512,512));
q1=abs(z1);    
figure(2)
imagesc(q1); colormap gray; axis image; axis off
title('Focal Spots Of Grating Array');
%Fourier Transform After Adding Aberration
N=exp(sqrt(-1).*(M+z8));
z2=fftshift(fft2(N,512,512));
q2=abs(z2);    
figure(3)
imagesc(q2); colormap gray; axis image; axis off
title('Focal Spots Of Grating Array Shifted');

******* If you run the above code, you will get two figures: fig(2) & fig(3). In fig(3), the spots gets shifted from the ideal position in fig(2) due to aberration added. So, can anyone help me how to calculate both the horizontal and vertical shift (slope) of each spot in fig(3) with respect to fig(2) using Matlab coding. It will be a great help for me.

Thanking You!

[EDITED, Code formatted, Jan S]