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141 lines
5.4 KiB
Matlab
141 lines
5.4 KiB
Matlab
% FIND_SHIFT_FAST_1D uses cross-correlation to find shift between 1D patterns o1 and
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% o2, if the patterns are 2D, perform the search along the axis `ax`
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%
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% shift = find_shift_fast_1D(o1, o2, ax, sigma)
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%
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% Inputs:
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% **o1 - aligned array 1D/2D (will be aligned along 1st axis)
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% **o2 - template for alignment 1D or 2D
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% **ax - perform search along this axis
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% *optional*
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% **sigma - filtering intensity [0-1 range], sigma <= 0 no filtering, recommended sigma < 0.05
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% **padding - pading [in pixels] the provided array by zeros, prevent circular boundary condition in FFT, default = 0
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% *returns*
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% ++shift - (vector) displacement of the 1D/2D arrays
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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_1D(o1, o2, ax, sigma, padding)
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if nargin < 3
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ax = 2;
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end
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if nargin < 4
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sigma = 0;
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end
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if nargin < 5
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padding = 0;
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else
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padding = ceil(padding/2)*2;
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end
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max_shift = size(o1,ax)/3; % avoid too large corrections !!!
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Ndims = ndims(o1);
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if ax ~= 1
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error('FIXME: Not tested axis')
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end
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%% symmetrize before spectral filtering !!
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o1 = cat(ax, o1, flipud(o1));
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o2 = cat(ax, o2, flipud(o2));
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Npix = size(o1);
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shape = ones(1,Ndims);
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shape(ax) = Npix(ax);
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if sigma > 0
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%% high pass filter
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o1 = fft(o1, [],ax);
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o2 = fft(o2, [],ax);
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x = reshape((-Npix(ax)/2+1:Npix(ax)/2)/Npix(ax), shape);
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spectral_filter = fftshift(exp(1./(-(x.^2)/(sigma^2))));
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spectral_filter(floor(end/2+[-3:3])) = 0; %% remove some strange artefacts
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o1 = bsxfun(@times, o1, spectral_filter);
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o2 = bsxfun(@times, o2, spectral_filter);
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o1 = ifft(o1, [],ax);
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o2 = ifft(o2, [],ax);
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end
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% remove symetrization !!
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o1 = o1(1:end/2,:);
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o2 = o2(1:end/2,:);
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o1 = padarray(o1, padding/2, 'both');
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o2 = padarray(o2, padding/2, 'both');
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Npix = size(o1);
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shape = ones(1,Ndims);
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shape(ax) = Npix(ax);
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%% remove edge issues (after symetrized filtering )
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spatial_filter = reshape(tukeywin(prod(shape)), shape);
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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 = fft(o1, [],ax);
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o2 = fft(o2, [],ax);
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%% cross-correlation
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xcorrmat = abs(ifft(o1.*conj(o2),[],ax));
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%% 1D fftshift
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xcorrmat = circshift(xcorrmat, floor(Npix(ax)/2), ax);
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if ax == 2; error('FIXME: Not tested axis'); end
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% choose only optimim withing reduced range
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xcorrmat([1:ceil(end/2-max_shift), ceil(end/2+max_shift):end],:) = 0;
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%% take only small region around maximum
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WIN = 10;
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kernel_size = [1,1];
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kernel_size(ax) = WIN;
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mask = conv2(single(bsxfun(@eq, xcorrmat, max(xcorrmat,[],ax))), ones(kernel_size), 'same');
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xcorrmat(~mask) = nan;
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xcorrmat = max(0, bsxfun(@minus, xcorrmat, min(xcorrmat,[],ax)));
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xcorrmat(~mask) = 0;
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xcorrmat = bsxfun(@times, xcorrmat, 1./max(xcorrmat,[],ax)).^4;
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%% find center of mass
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MASS = sum(xcorrmat,ax);
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grid = reshape(1:Npix(ax),shape);
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shift = sum(bsxfun(@times, xcorrmat, grid),ax) ./ MASS - floor(Npix(ax)/2)-1;
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end
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