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+math/unwrap2D_fft2.m

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+%  UNWRAP2D_FFT2 simple and very fast 2D phase unwrapping based on FT
+%  integration of DIC signal (phase gradient) 
+%
+%  [phase, residues] = unwrap2D_fft2(img, empty_region=[], step=0, weights=[], polyfit_order=1)
+% 
+% Inputs: 
+%   **img           - either complex valued image or real valued phase gradient 
+% *optional*
+%   **empty_region  - 2x1 or 1x1 vector, size of empty region assumed around edges for phase offset removal 
+%   **step          - used to calculate finite difference gradient, 0 = analytical (default) expression
+%   **polyfit_order   -1 = dont assume anything about the removed phase,
+%                       subtract linear offset from each horizontal line separatelly
+%                      0 = assume that removed degree of freedom is only a constant offset
+%                      1 = assume that removed degree of freedom is a 2D plane 
+% *returns*: 
+%  ++phase          - unwrapped phase with subtracted phase ramp / offset 
+%  ++residues       - calculated binary map of phase residuas 
+%
+% See also: utils.findresidues, utils.remove_sinogram_ramp
+
+
+%*-----------------------------------------------------------------------*
+%|                                                                       |
+%|  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 
+%    proper use and the correctness of the results.
+
+
+
+
+function [phase, residues] = unwrap2D_fft2(img, empty_region, step, weights, polyfit_order)
+    import utils.* 
+    import math.* 
+    
+    if isreal(img)
+        error('Complex-valued input array was expected')
+    end
+    
+    if nargin < 3 || isempty(step)
+        step = 0; % use analytical method 
+    end
+    if nargin < 4 || isempty(weights)
+        weights = 1; 
+    end
+    if nargin < 5
+        polyfit_order = 1; % subtract 2D plane 
+    end
+    
+    weights = max(0, min(1, single(weights)));  % weights are assumed in range [0,1]
+    
+    img = weights .* img ./ (abs(img)+eps);
+    clear weights 
+    
+    padding = [64,64];  % padding to avoid periodic boundary artefacts 
+    if any(padding > 0)
+        img = padarray(img,padding,'symmetric','both'); 
+        img = smooth_edges(img, 5, [1,2]);
+    end
+
+    
+    [dX,dY] = get_phase_gradient_2D(img, step, 0);
+    clear img 
+        
+    phase = real(get_img_int_2D(dX,dY));
+    
+    if any(padding > 0)
+        % remove padding 
+        ind = {padding(1):size(phase,1)-padding(1)-1,padding(2):size(phase,2)-padding(2)-1, ':'};
+        phase = phase(ind{:}); 
+    end
+    
+    if exist('empty_region', 'var') && ~isempty(empty_region)
+       phase = remove_sinogram_ramp(phase,empty_region, polyfit_order);  
+    end
+    
+    if nargout > 1
+        residues = abs(findresidues(img)) > 0.1; 
+    end
+
+end