curveFilter

 curveFilter : calculates the curvatures of an image.

 INPUT : 
       im : image to be filtered
       filterWidth : filter width
 OUTPUT : 
       M_ : Mean curvature of the image without negative values
       G_ : Gaussian curvature of the image without negative values
       C1_ : Principal curvature 1 of the image without negative values
       C2_ : Principal curvature 2 of the image without negative values
       M : Mean curvature of the image
       G : Gaussian curvature of the image
       C1 : Principal curvature 1 of the image
       C2 : Principal curvature 2 of the image
       im_xx :
       im_yy :
       im_xy :

 Copyright (C) 2016 Wiggins Lab 
 Written by Connor Brennan & Paul Wiggins.
 University of Washington, 2016
 This file is part of SuperSegger.
 
 SuperSegger is free software: you can redistribute it and/or modify
 it under the terms of the GNU General Public License as published by
 the Free Software Foundation, either version 3 of the License, or
 (at your option) any later version.
 
 SuperSegger is distributed in the hope that it will be useful,
 but WITHOUT ANY WARRANTY; without even the implied warranty of
 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 GNU General Public License for more details.
 
 You should have received a copy of the GNU General Public License
 along with SuperSegger.  If not, see <http://www.gnu.org/licenses/>.

0001 function [M_, G_, C1_, C2_, M, G, C1, C2, im_xx, im_yy, im_xy] = curveFilter( im, filterWidth )
0002 % curveFilter : calculates the curvatures of an image.
0003 %
0004 % INPUT :
0005 %       im : image to be filtered
0006 %       filterWidth : filter width
0007 % OUTPUT :
0008 %       M_ : Mean curvature of the image without negative values
0009 %       G_ : Gaussian curvature of the image without negative values
0010 %       C1_ : Principal curvature 1 of the image without negative values
0011 %       C2_ : Principal curvature 2 of the image without negative values
0012 %       M : Mean curvature of the image
0013 %       G : Gaussian curvature of the image
0014 %       C1 : Principal curvature 1 of the image
0015 %       C2 : Principal curvature 2 of the image
0016 %       im_xx :
0017 %       im_yy :
0018 %       im_xy :
0019 %
0020 % Copyright (C) 2016 Wiggins Lab
0021 % Written by Connor Brennan & Paul Wiggins.
0022 % University of Washington, 2016
0023 % This file is part of SuperSegger.
0024 %
0025 % SuperSegger is free software: you can redistribute it and/or modify
0026 % it under the terms of the GNU General Public License as published by
0027 % the Free Software Foundation, either version 3 of the License, or
0028 % (at your option) any later version.
0029 %
0030 % SuperSegger is distributed in the hope that it will be useful,
0031 % but WITHOUT ANY WARRANTY; without even the implied warranty of
0032 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
0033 % GNU General Public License for more details.
0034 %
0035 % You should have received a copy of the GNU General Public License
0036 % along with SuperSegger.  If not, see <http://www.gnu.org/licenses/>.
0037 
0038 im = double(im);
0039 
0040 % filter width
0041 if ~exist( 'filterWidth', 'var' ) || isempty( filterWidth )
0042     filterWidth = 1.5;
0043 end
0044 
0045 
0046 % Make filter
0047 x = -floor(7*filterWidth):floor(7*filterWidth);
0048 %x = -10:10;
0049 [X,Y] = meshgrid( x, x);
0050 R2 = X.^2+Y.^2;
0051 
0052 v = filterWidth^2;
0053 
0054 gau = 1/(2*pi*v) * exp( -R2/(2*v) );
0055 f_xx = (2*pi*v^2)*((X/v).^2-1/v).*gau;
0056 f_yy = (2*pi*v^2)*((Y/v).^2-1/v).*gau;
0057 f_xy = (2*pi*v^2)*X.*Y.*gau/v^2;
0058 
0059 % Do filtering
0060 im_xx = imfilter( im, f_xx, 'replicate' );
0061 im_yy = imfilter( im, f_yy, 'replicate' );
0062 im_xy = imfilter( im, f_xy, 'replicate' );
0063 
0064 % gaussian curvature
0065 G = im_xx.*im_yy-im_xy.^2;
0066 
0067 % mean curvature
0068 M = -(im_xx+im_yy)/2;
0069 
0070 % compute principal curvatures
0071 C1 = (M-sqrt(abs(M.^2-G)));
0072 C2 = (M+sqrt(abs(M.^2-G)));
0073 
0074 % remove negative values
0075 G_ = G;
0076 G_(G<0) = 0;
0077 
0078 M_ = M;
0079 M_(M<0) = 0;
0080 
0081 C1_ = C1;
0082 C1_(C1<0) = 0;
0083 
0084 C2_ = C2;
0085 C2_(C2<0) = 0;
0086 
0087 end