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+utils/find_shift_fast_3D.m

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+% FIND_SHIFT_FAST_3D uses crosscorelation to find shift between o1 nd
+% o2 patterns in 3D space 
+%
+% shift = find_shift_fast_3D(o1, o2, sigma, apply_fft)
+%
+% Inputs:
+%   **o1            - aligned array  3D - return only single shift vector [x,y,z]
+%   **o2            - template for alignement  3D
+%   **sigma         - filtering intensity [0-1 range],  sigma <= 0 no filtering, recommended sigma < 0.05 
+%   **apply_fft     - if false, assume o1 and o2 to be already in fourier domain 
+% *returns*
+%   ++shift         - displacement of the 3D volumes 
+
+%*-----------------------------------------------------------------------*
+%|                                                                       |
+%|  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 
+% 
+
+
+function shift = find_shift_fast_3D(o1, o2, sigma, apply_fft)   
+    
+
+    import math.*
+    
+    assert(ndims(o1) == 3, 'Inputs has to be 3D matrix')
+    assert(ndims(o2) == 3, 'Inputs has to be 3D matrix')
+    
+   if nargin < 4 
+       apply_fft = true;
+   end
+   if nargin < 3
+       sigma = 0.01;
+   end
+  
+   
+   if apply_fft
+
+        [nx, ny, nz] = size(o1);
+
+        % suppress edge effects of the registration procedure
+        spatial_filter = tukeywin(nx,0.5) * tukeywin(ny,0.5)' .* reshape(tukeywin(nz,0.5),1,1,[]); 
+        
+        o1 = bsxfun(@times, o1, spatial_filter);
+        o2 = bsxfun(@times, o2, spatial_filter);
+
+        clear spatial_filter
+        
+        o1 = fftn(o1);
+        o2 = fftn(o2);
+        
+   end
+   
+    [nx, ny, ~] = size(o1);
+
+    if sigma > 0 
+        % remove low frequencies 
+        [X,Y,Z] = meshgrid( (-nx/2:nx/2-1)/nx, (-ny/2:ny/2-1)/ny, (-nz/2:nz/2-1)/nz);
+        spectral_filter = fftshift(exp(1./(-(X.^2+Y.^2+Z.^2)/sigma^2)));
+        o1 = bsxfun(@times, o1, spectral_filter);
+        o2 = bsxfun(@times, o2, spectral_filter);  
+        clear spectral_filter
+    end
+  
+    
+    % fast subpixel cross correlation 
+    xcorrmat = fftshift(abs(ifftn(o1.*conj(o2)))); 
+    
+
+    %% take only small region around maximum 
+
+    WIN = 5; 
+    kernel_size = [WIN,WIN,WIN];
+    xcorrmat = xcorrmat / max(xcorrmat(:)); 
+    xcorrmat = xcorrmat .* convn(xcorrmat == 1, ones(kernel_size,'single'), 'same'); 
+    [x,y,z] = find_center_fast(xcorrmat.^2);
+    shift = [x,y,z];
+
+end
+
+function [x,y,z] = find_center_fast(xcorrmat)
+    MASS = squeeze(sum(xcorrmat(:)));
+    [N,M,O] = size(xcorrmat); 
+    x = squeeze(sum(sum(sum(xcorrmat .* (1:M),1)))) ./ MASS - floor(M/2)-1;
+    y = squeeze(sum(sum(sum(xcorrmat .* (1:N)',2)))) ./ MASS - floor(N/2)-1;
+    z = squeeze(sum(sum(sum(xcorrmat .* reshape(1:O,1,1,[]),3) ))) ./ MASS - floor(O/2)-1;
+end