initial commit

+utils/find_img_rotation_2D.m

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+%   FIND_IMG_ROTATION_2D  find object rotation that provides in projection most sparse features 
+%
+% [angle] = find_img_rotation_2D(img) 
+%
+% Inputs: 
+%  **img - 2D image to be rotated 
+% *returns*: 
+%   ++angle - optimal rotation angle in degrees 
+
+%*-----------------------------------------------------------------------*
+%|                                                                       |
+%|  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  [angle_fine] = find_img_rotation_2D(img, max_range)
+    import math.argmin
+    if nargin < 2
+        max_range = [-22.5,22.5];
+    end
+    
+    %  grid search first => avoid local minimums
+    
+    test_img = abs(img);
+    test_img = max(0, test_img - median(test_img(:)));
+    N = 50;
+    score  = zeros(N,1);
+    alpha_range = linspace(max_range(1),max_range(end), N);
+    for i = 1:N
+        score(i) = gather(get_score(test_img, alpha_range(i)));
+    end
+    
+    alpha_range = alpha_range(argmin(score)) + (-1:0.1:1);
+    clear score
+    for i = 1:length(alpha_range)
+        score(i) = gather(get_score(test_img, alpha_range(i)));
+    end
+    angle = alpha_range(argmin(score));
+    
+    angle_fine = fminsearch(@(x)get_score(test_img, x), angle, struct('TolX', 1e-4)); 
+    
+
+    if isa(angle, 'gpuArray')
+        angle = gather(angle); 
+    end
+    fprintf('Optimal image rotation: %.3g°\n', angle_fine)
+  
+end
+
+function score = get_score(data, angle)
+    Npix = size(data);
+    [X,Y] = meshgrid(-ceil(Npix(2)/2):floor(Npix(2)/2)-1,-ceil(Npix(1)/2):floor(Npix(1)/2)-1);
+    data = data .* (X.^2 / (Npix(2)/2)^2 +Y.^2/(Npix(1)/2)^2 < 1/2); 
+    data = data - utils.imgaussfilt2_fft(data,5); 
+    
+    data = utils.imrotate_ax_fft(data, angle, 3);
+
+    data = data(ceil(end*0.1):floor(end*0.9), ceil(end*0.1):floor(end*0.9));   
+    data = (abs(math.fftshift_2D(fft2(data))));
+    score =  -mean([sparseness(nanmean(data,1)), ...
+        sparseness(nanmean(data,2))]);
+    score = gather(score);
+end
+
+function spars = sparseness(x)
+    %Hoyer's measure of sparsity for a vector
+    % from  scipy.linalg import norm
+
+    order_1 = 1;
+    order_2 = 2;
+    x = x(:);
+    sqrt_n = sqrt(length(x));
+    spars = (sqrt_n - norm(x, order_1) / norm(x, order_2)) / (sqrt_n - order_1);
+end