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119 lines
4.5 KiB
Matlab
119 lines
4.5 KiB
Matlab
% IMROTATE_AX_FFT fft-based image rotation for a stack of images along given axis
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% based on "Fast Fourier method for the accurate rotation of sampled images", Optic Communications, 1997
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% img_stack = imrotate_ax_fft(img, theta, ax)
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%
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% Inputs:
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% **img - stacked array of images to be rotated
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% **theta - rotation angle
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% *optional*
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% **axis - rotation axis (default=3)
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% returns:
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% ++img - rotated image
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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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% proper use and the correctness of the results.
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function img = imrotate_ax_fft(img, theta, axis)
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if all(theta == 0) || isempty(img); return ; end
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if nargin < 3
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axis = 3;
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end
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isReal = isreal(img);
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if axis == 1
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img = permute(img, [3,2,1]); theta = - theta;
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elseif axis == 2
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img = permute(img, [1,3,2]);
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end
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angle_90_offset = round(theta/90);
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if angle_90_offset ~= 0
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img = rot90(img, angle_90_offset);
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theta = theta - 90*angle_90_offset;
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end
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if theta == 0; return ; end
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[M, N, ~] = size(img);
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% make possible to rotate each slice with different angle
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theta = reshape(theta,1,1,[]) * ones(1,'like',img); % move to GPU if needed
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xgrid = (ifftshift(-fix(M/2):ceil(M/2)-1)'/M);
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ygrid = (ifftshift(-fix(N/2):ceil(N/2)-1) /N);
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Mgrid = (1:M)'-floor(M/2)-0.5; % the 0.5px offset is important to make the rotation equivalent to matlab imrotate
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Ngrid = (1:N) -floor(N/2)-0.5;
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if isa(theta, 'gpuArray')
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[M1, M2] = arrayfun(@aux_fun, theta, xgrid, ygrid, Mgrid, Ngrid);
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else
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[M1, M2] = aux_fun(theta, xgrid, ygrid, Mgrid, Ngrid);
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end
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% rotate images by a combination of shears
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img=ifft(fft(img,[],2).*M1,[],2);
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img=ifft(fft(img,[],1).*M2,[],1);
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img=ifft(fft(img,[],2).*M1,[],2);
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if isReal
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img = real(img);
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end
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if axis == 1
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img = permute(img, [3,2,1]);
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elseif axis == 2
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img = permute(img, [1,3,2]);
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end
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end
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% auxiliarly function to be used for GPU kernel merging
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function [M1, M2] = aux_fun(theta, xgrid, ygrid, Mgrid, Ngrid)
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% based on "Fast Fourier method for the accurate rotation of sampled images", Optic Communications, 1997
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Nx = -sind(theta) .* xgrid;
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Ny = tand(theta/2).* ygrid;
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M1 = exp(-2i*pi*Mgrid.*Ny);
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M2 = exp(-2i*pi*Ngrid.*Nx);
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end |