Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / image-1.0.15 / radon.m

diff --git a/octave_packages/image-1.0.15/radon.m b/octave_packages/image-1.0.15/radon.m
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+## Copyright (C) 2007 Alexander Barth <barth.alexander@gmail.com>
+##
+##
+## This program 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.
+##
+## This program 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 this program; see the file COPYING.  If not, see
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {[@var{RT},@var{xp}] =} radon(@var{I}, @var{theta})
+## @deftypefnx {Function File} {[@var{RT},@var{xp}] =} radon(@var{I})
+##
+## Calculates the 2D-Radon transform of the matrix @var{I} at angles given in
+## @var{theta}. To each element of @var{theta} corresponds a column in @var{RT}. 
+## The variable @var{xp} represents the x-axis of the rotated coordinate.
+## If @var{theta} is not defined, then 0:179 is assumed.
+## @end deftypefn
+
+
+function [RT,xp] = radon (I,theta)
+
+  ## Input checking
+  if (nargin == 0 || nargin > 2)
+    print_usage ();
+  elseif (nargin == 1)
+    theta = 0:179;
+  endif
+  
+  if (!ismatrix(I) || ndims(I) != 2)
+    error("radon: first input must be a MxN matrix");
+  endif
+  
+  if (!isvector(theta))
+    error("radon: second input must be a vector");
+  endif
+
+  [m, n] = size (I);
+
+  # center of image
+  xc = floor ((m+1)/2);
+  yc = floor ((n+1)/2);
+
+  # divide each pixel into 2x2 subpixels
+
+  d = reshape (I,[1 m 1 n]);
+  d = d([1 1],:,[1 1],:);
+  d = reshape (d,[2*m 2*n])/4;
+
+  b = ceil (sqrt (sum (size (I).^2))/2 + 1);
+  xp = [-b:b]';
+  sz = size(xp);
+
+  [X,Y] = ndgrid (0.75 - xc + [0:2*m-1]/2,0.75 - yc + [0:2*n-1]/2);
+
+  X = X(:)';
+  Y = Y(:)';
+  d = d(:)';
+
+  th = theta*pi/180;
+
+  for l=1:length (theta)
+    # project each pixel to vector (-sin(th),cos(th))
+    Xp = -sin (th(l)) * X + cos (th(l)) * Y;
+    
+    ip = Xp + b + 1;
+
+    k = floor (ip);
+    frac = ip-k;
+
+    RT(:,l) = accumarray (k',d .* (1-frac),sz) + accumarray (k'+1,d .* frac,sz);
+  endfor
+
+endfunction
+
+%!test
+%! A = radon(ones(2,2),30);
+%! assert (A,[0 0 0.608253175473055 2.103325780167649 1.236538105676658 0.051882938682637 0]',1e-10)
+
+