## Copyright (C) 2007 Alexander Barth
##
##
## 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
## .
## -*- texinfo -*-
## @deftypefn {Function File} address@hidden,@var{xp}] =} radon(@var{I}, @var{theta})
## @deftypefnx {Function File} address@hidden,@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)
if (nargin == 0 | nargin > 2)
print_usage ();
elseif (nargin == 1)
theta = 0:179;
endif
m = size (I,1);
n = size (I,2);
# 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)