--- /dev/null
+## Copyright (C) 2004 Stefan van der Walt <stefan@sun.ac.za>
+##
+## This program is free software; redistribution and use in source and
+## binary forms, with or without modification, are permitted provided that
+## the following conditions are met:
+##
+## 1. Redistributions of source code must retain the above copyright
+## notice, this list of conditions and the following disclaimer.
+## 2. Redistributions in binary form must reproduce the above copyright
+## notice, this list of conditions and the following disclaimer in the
+## documentation and/or other materials provided with the distribution.
+##
+## THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
+## ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+## FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+## OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+## HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+## LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+## OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+## SUCH DAMAGE.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} fftconv2 (@var{a}, @var{b}, @var{shape})
+## @deftypefnx{Function File} fftconv2 (@var{v1}, @var{v2}, @var{a}, @var{shape})
+## Convolve 2 dimensional signals using the FFT.
+##
+## This method is faster but less accurate than @var{conv2} for large @var{a} and @var{b}.
+## It also uses more memory. A small complex component will be
+## introduced even if both @var{a} and @var{b} are real.
+## @seealso{conv2}
+## @end deftypefn
+
+## Author: Stefan van der Walt <stefan@sun.ac.za>
+## Date: 2004
+
+function X = fftconv2(varargin)
+ if (nargin < 2)
+ usage("fftconv2(a,b[,shape]) or fftconv2(v1, v2, a, shape)")
+ endif
+
+ shape = "full";
+ rowcolumn = 0;
+
+ if ((nargin > 2) && ismatrix(varargin{3}) && !ischar(varargin{3}))
+ ## usage: fftconv2(v1, v2, a[, shape])
+
+ rowcolumn = 1;
+ v1 = varargin{1}(:)';
+ v2 = varargin{2}(:);
+ orig_a = varargin{3};
+
+ if (nargin == 4) shape = varargin{4}; endif
+ else
+ ## usage: fftconv2(a, b[, shape])
+
+ a = varargin{1};
+ b = varargin{2};
+ if (nargin == 3) shape = varargin{3}; endif
+
+ endif
+
+ if (rowcolumn)
+ a = fftconv2(orig_a, v2);
+ b = v1;
+ endif
+
+ ra = rows(a);
+ ca = columns(a);
+ rb = rows(b);
+ cb = columns(b);
+
+ A = fft2(impad(a, [0 cb-1], [0 rb-1]));
+ B = fft2(impad(b, [0 ca-1], [0 ra-1]));
+
+ X = ifft2(A.*B);
+
+ if (rowcolumn)
+ rb = rows(v2);
+ ra = rows(orig_a);
+ cb = columns(v1);
+ ca = columns(orig_a);
+ endif
+
+ if strcmp(shape,"same")
+ r_top = ceil((rb + 1) / 2);
+ c_top = ceil((cb + 1) / 2);
+ X = X(r_top:r_top + ra - 1, c_top:c_top + ca - 1);
+ elseif strcmp(shape, "valid")
+ X = X(rb:ra, cb:ca);
+ endif
+endfunction
+
+%!# usage: fftconv2(a,b,[, shape])
+%!shared a,b
+%! a = repmat(1:10, 5);
+%! b = repmat(10:-1:3, 7);
+%!assert(norm(fftconv2(a,b)-conv2(a,b)), 0, 1e6*eps)
+%!assert(norm(fftconv2(b,a)-conv2(b,a)), 0, 1e6*eps)
+%!assert(norm(fftconv2(a,b,'full')-conv2(a,b,'full')), 0, 1e6*eps)
+%!assert(norm(fftconv2(b,a,'full')-conv2(b,a,'full')), 0, 1e6*eps)
+%!assert(norm(fftconv2(a,b,'same')-conv2(a,b,'same')), 0, 1e6*eps)
+%!assert(norm(fftconv2(b,a,'same')-conv2(b,a,'same')), 0, 1e6*eps)
+%!assert(isempty(fftconv2(a,b,'valid')));
+%!assert(norm(fftconv2(b,a,'valid')-conv2(b,a,'valid')), 0, 1e6*eps)
+
+%!# usage: fftconv2(v1, v2, a[, shape])
+%!shared x,y,a
+%! x = 1:4; y = 4:-1:1; a = repmat(1:10, 5);
+%!assert(norm(fftconv2(x,y,a)-conv2(x,y,a)), 0, 1e6*eps)
+%!assert(norm(fftconv2(x,y,a,'full')-conv2(x,y,a,'full')), 0, 1e6*eps)
+%!assert(norm(fftconv2(x,y,a,'same')-conv2(x,y,a,'same')), 0, 1e6*eps)
+%!assert(norm(fftconv2(x,y,a,'valid')-conv2(x,y,a,'valid')), 0, 1e6*eps)
+
+%!demo
+%! ## Draw a cross
+%! N = 100;
+%! [x,y] = meshgrid(-N:N, -N:N);
+%! z = 0*x;
+%! z(N,1:2*N+1) = 1; z(1:2*N+1, N) = 1;
+%! imshow(z);
+%!
+%! ## Draw a sinc blob
+%! n = floor(N/10);
+%! [x,y] = meshgrid(-n:n, -n:n);
+%! b = x.^2 + y.^2; b = max(b(:)) - b; b = b / max(b(:));
+%! imshow(b);
+%!
+%! ## Convolve the cross with the blob
+%! imshow(real(fftconv2(z, b, 'same')*N))
+
+
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff