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% FIND_SHIFT_FAST_2D 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_2D(o1, o2, sigma, apply_fft)
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%
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% Inputs:
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% **o1 - aligned array 2D or 3D, (for stack of images, alignment is done along 3rd axis)
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% **o2 - template for alignment 2D or 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 2D 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_2D(o1, o2, sigma, apply_fft, method)
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import math.*
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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 nargin < 5
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method = 'full_range';
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end
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if apply_fft
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[nx, ny, ~] = 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)';
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o1 = bsxfun(@times, o1, spatial_filter);
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o2 = bsxfun(@times, o2, spatial_filter);
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o1 = fft2(o1);
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o2 = fft2(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] = meshgrid( (-nx/2:nx/2-1)/nx, (-ny/2:ny/2-1)/ny);
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spectral_filter = fftshift(exp(1./(-(X.^2+Y.^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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end
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% fast subpixel cross correlation
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xcorrmat = fftshift_2D(abs(ifft2(o1.*conj(o2))));
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% %% just for testing
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% subplot(3,1,1)
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% imagesc(abs(fft2(o1(:,:,1)))); axis off image; colormap bone
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% subplot(3,1,2)
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% imagesc(abs(fft2(o2(:,:,1)))); axis off image; colormap bone
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% subplot(3,1,3)
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% imagesc(xcorrmat(:,:,1)); axis off image; colormap bone
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% drawnow
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% pause(0.1)
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switch method
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case 'full_range'
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%% take only small region around maximum
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WIN = 5;
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kernel_size = [WIN,WIN];
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% convolution may be quite slow ?
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mask = convn(single(bsxfun(@eq, xcorrmat, max2(xcorrmat))), ones(kernel_size,'single'), 'same');
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xcorrmat(~mask) = nan;
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xcorrmat = max(0, bsxfun(@minus, xcorrmat, min2(xcorrmat)));
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xcorrmat(~mask) = 0;
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xcorrmat = bsxfun(@times, xcorrmat, 1./max2(xcorrmat)).^2;
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%% get CoM of the central peak only !!, assume a single peak
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xcorrmat = max(0, xcorrmat - 0.5).^2;
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[x,y] = find_center_fast(xcorrmat);
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shift = [x,y];
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case 'limited_range'
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% second option: assume that the shifts are only small, it is faster
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mxcorr = mean(xcorrmat,3);
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[m,n] = find(mxcorr == max(mxcorr(:)));
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MAX_SHIFT = 10; % +-10px search
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MAX_SHIFT_X = min(floor(nx/2-0.5),MAX_SHIFT);
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MAX_SHIFT_Y = min(floor(ny/2-0.5),MAX_SHIFT);
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xrange = (-MAX_SHIFT_X:MAX_SHIFT_X);
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yrange = (-MAX_SHIFT_Y:MAX_SHIFT_Y);
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idx = { m + xrange,n+yrange,':'};
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xcorrmat = xcorrmat(idx{:});
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MAX = max(max(xcorrmat));
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xcorrmat = bsxfun(@times, xcorrmat, 1. / MAX);
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%% get CoM of the central peak only !!, assume a single peak
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xcorrmat = max(0, xcorrmat - 0.5).^2;
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[x,y] = find_center_fast(xcorrmat);
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shift = [x,y]+[n,m]-floor([ny,nx]/2)-1;
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end
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if any(isnan(gather(shift)))
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keyboard
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end
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end
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function [x,y,MASS] = find_center_fast(xcorrmat)
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MASS = squeeze(sum(sum(xcorrmat)));
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[N,M,~] = size(xcorrmat);
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x = squeeze(sum( bsxfun(@times, sum(xcorrmat,1), 1:M), 2)) ./ MASS - floor(M/2)-1;
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y = squeeze(sum(bsxfun(@times, sum(xcorrmat,2), (1:N)'),1)) ./ MASS - floor(N/2)-1;
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end
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