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2026-09-17 19:39:08 +09:00 · 2026-08-07 15:56:42 +09:00
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+% IMSHEAR_FFT fft-based image shearing function for a stack of images along given axis 
+% 
+% img_stack = imshear_fft(img_stack, theta, shear_axis)
+%
+% Inputs: 
+%   **img_stack  - stack of 2D images 
+%   **theta      - shear angle, scalar 
+%   **shear_axis - image axis along which the image will be shared 
+% *returns*: 
+%   ++img        - shreared image 
+%
+
+
+%*-----------------------------------------------------------------------*
+%|                                                                       |
+%|  Except where otherwise noted, this work is licensed under a          |
+%|  Creative Commons Attribution-NonCommercial-ShareAlike 4.0            |
+%|  International (CC BY-NC-SA 4.0) license.                             |
+%|                                                                       |
+%|  Copyright (c) 2017 by Paul Scherrer Institute (http://www.psi.ch)    |
+%|                                                                       |
+%|       Author: CXS group, PSI                                          |
+%*-----------------------------------------------------------------------*
+% You may use this code with the following provisions:
+%
+% If the code is fully or partially redistributed, or rewritten in another
+%   computing language this notice should be included in the redistribution.
+%
+% If this code, or subfunctions or parts of it, is used for research in a 
+%   publication or if it is fully or partially rewritten for another 
+%   computing language the authors and institution should be acknowledged 
+%   in written form in the publication: “Data processing was carried out 
+%   using the “cSAXS matlab package” developed by the CXS group,
+%   Paul Scherrer Institut, Switzerland.” 
+%   Variations on the latter text can be incorporated upon discussion with 
+%   the CXS group if needed to more specifically reflect the use of the package 
+%   for the published work.
+%
+% A publication that focuses on describing features, or parameters, that
+%    are already existing in the code should be first discussed with the
+%    authors.
+%   
+% This code and subroutines are part of a continuous development, they 
+%    are provided “as they are” without guarantees or liability on part
+%    of PSI or the authors. It is the user responsibility to ensure its 
+%    proper use and the correctness of the results.
+
+
+function img = imshear_fft(img, theta, shear_axis)
+    
+    if theta == 0; return ; end
+    
+    assert(any(shear_axis == [1,2]), 'Shear axis has to be 1 or 2' )
+    
+    isReal = isreal(img); 
+    
+    if abs(theta) > 45
+        error('Out of valid angle range [-45,45], use rot90 to get into the valid range')
+    end
+    
+    [M, N, ~] = size(img); 
+    theta = reshape(theta,1,1,[]); % allow different theta for each slice 
+
+    Nx = -sind(theta) .* ifftshift(-fix(M/2):ceil(M/2)-1)/M; 
+    Ny = tand(theta/2).* ifftshift(-fix(N/2):ceil(N/2)-1)/N;
+    Mgrid = 2i*pi*((1:M)'-floor(M/2)) * ones(1,'like',img); 
+    Ngrid = 2i*pi*((1:N)'-floor(N/2)) * ones(1,'like',img); 
+    
+    % rotate images by a combination of shears 
+    switch shear_axis
+        case 1, img=ifft(fft(img,[],2).*exp(-Mgrid.*Ny), [],2);
+        case 2, img=ifft(fft(img,[],1).*exp( Ngrid.*Nx)',[],1);
+        otherwise
+            error('Shear axis has to be 1 or 2')
+    end
+
+    if isReal
+        img = real(img); 
+    end
+   
+end