initial commit

+math/center.m

@@ -0,0 +1,46 @@
+function [pos_x, pos_y, mass, mu, sigma] = center(X, use_shift)
+% -----------------------------------------------------------------------
+% This file is part of the PTYCHOMAT Toolbox
+% Author: Michal Odstrcil, 2016
+% License: Open Source under GPLv3
+% Contact: ptychomat@gmail.com
+% Website: https://bitbucket.org/michalodstrcil/ptychomat
+% -----------------------------------------------------------------------
+% Description:  find center of mass of matrix X,  calculate variance if
+% needed 
+% inputs:
+%   X  2D stacked images 
+%   use_shift, if true, CoM will be calculated relatively to the center
+%   of the image, default == true 
+
+
+
+    if nargin < 2
+        use_shift = true;
+    end
+
+    [N,M,~] = size(X);
+    mass = sum(sum(X));
+    xgrid = (1:M);
+    ygrid = (1:N)';
+    pos_x =  (sum(sum(X,1).*xgrid)./mass);
+    pos_y =  (sum(sum(X,2).*ygrid)./mass);
+    if nargout > 3
+        mu = [pos_x, pos_y]';
+    end
+    
+    if nargout == 5
+        pos_xx = (sum(sum(X,1).*((1:M)-pos_x).^2)/mass);
+        pos_yy = (sum(sum(X,2).*((1:N)-pos_y)'.^2)/mass);
+        pos_xy = ((X*((1:M)-pos_x)')'*((1:N)-pos_y)'/mass);
+        pos_yx = ((X*((1:M)-pos_x)')'*((1:N)-pos_y)'/mass);
+        sigma =  [ pos_xx, pos_xy; pos_yx, pos_yy];
+    end
+    
+
+    if use_shift
+        pos_x = pos_x - M/2-0.5;  % defined so that center(ones(N),true) == [0,0]
+        pos_y = pos_y - N/2-0.5;
+    end
+              
+end