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116 lines
4.5 KiB
Matlab
116 lines
4.5 KiB
Matlab
% FIND_SHIFT_FAST_3D uses crosscorelation to find shift between o1 nd
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% o2 patterns in 3D space
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%
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% shift = find_shift_fast_3D(o1, o2, sigma, apply_fft)
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%
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% Inputs:
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% **o1 - aligned array 3D - return only single shift vector [x,y,z]
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% **o2 - template for alignement 3D
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% **sigma - filtering intensity [0-1 range], sigma <= 0 no filtering, recommended sigma < 0.05
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% **apply_fft - if false, assume o1 and o2 to be already in fourier domain
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% *returns*
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% ++shift - displacement of the 3D volumes
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%*-----------------------------------------------------------------------*
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%| |
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%| Except where otherwise noted, this work is licensed under a |
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%| Creative Commons Attribution-NonCommercial-ShareAlike 4.0 |
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%| International (CC BY-NC-SA 4.0) license. |
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%| |
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%| Copyright (c) 2017 by Paul Scherrer Institute (http://www.psi.ch) |
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%| |
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%| Author: CXS group, PSI |
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%*-----------------------------------------------------------------------*
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% You may use this code with the following provisions:
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%
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% If the code is fully or partially redistributed, or rewritten in another
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% computing language this notice should be included in the redistribution.
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%
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% If this code, or subfunctions or parts of it, is used for research in a
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% publication or if it is fully or partially rewritten for another
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% computing language the authors and institution should be acknowledged
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% in written form in the publication: “Data processing was carried out
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% using the “cSAXS matlab package” developed by the CXS group,
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% Paul Scherrer Institut, Switzerland.”
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% Variations on the latter text can be incorporated upon discussion with
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% the CXS group if needed to more specifically reflect the use of the package
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% for the published work.
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%
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% A publication that focuses on describing features, or parameters, that
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% are already existing in the code should be first discussed with the
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% authors.
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%
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% This code and subroutines are part of a continuous development, they
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% are provided “as they are” without guarantees or liability on part
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% of PSI or the authors. It is the user responsibility to ensure its
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%
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function shift = find_shift_fast_3D(o1, o2, sigma, apply_fft)
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import math.*
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assert(ndims(o1) == 3, 'Inputs has to be 3D matrix')
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assert(ndims(o2) == 3, 'Inputs has to be 3D matrix')
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if nargin < 4
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apply_fft = true;
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end
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if nargin < 3
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sigma = 0.01;
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end
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if apply_fft
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[nx, ny, nz] = size(o1);
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% suppress edge effects of the registration procedure
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spatial_filter = tukeywin(nx,0.5) * tukeywin(ny,0.5)' .* reshape(tukeywin(nz,0.5),1,1,[]);
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o1 = bsxfun(@times, o1, spatial_filter);
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o2 = bsxfun(@times, o2, spatial_filter);
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clear spatial_filter
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o1 = fftn(o1);
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o2 = fftn(o2);
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end
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[nx, ny, ~] = size(o1);
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if sigma > 0
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% remove low frequencies
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[X,Y,Z] = meshgrid( (-nx/2:nx/2-1)/nx, (-ny/2:ny/2-1)/ny, (-nz/2:nz/2-1)/nz);
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spectral_filter = fftshift(exp(1./(-(X.^2+Y.^2+Z.^2)/sigma^2)));
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o1 = bsxfun(@times, o1, spectral_filter);
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o2 = bsxfun(@times, o2, spectral_filter);
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clear spectral_filter
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end
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% fast subpixel cross correlation
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xcorrmat = fftshift(abs(ifftn(o1.*conj(o2))));
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%% take only small region around maximum
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WIN = 5;
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kernel_size = [WIN,WIN,WIN];
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xcorrmat = xcorrmat / max(xcorrmat(:));
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xcorrmat = xcorrmat .* convn(xcorrmat == 1, ones(kernel_size,'single'), 'same');
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[x,y,z] = find_center_fast(xcorrmat.^2);
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shift = [x,y,z];
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end
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function [x,y,z] = find_center_fast(xcorrmat)
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MASS = squeeze(sum(xcorrmat(:)));
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[N,M,O] = size(xcorrmat);
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x = squeeze(sum(sum(sum(xcorrmat .* (1:M),1)))) ./ MASS - floor(M/2)-1;
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y = squeeze(sum(sum(sum(xcorrmat .* (1:N)',2)))) ./ MASS - floor(N/2)-1;
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z = squeeze(sum(sum(sum(xcorrmat .* reshape(1:O,1,1,[]),3) ))) ./ MASS - floor(O/2)-1;
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end
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