/usr/share/octave/packages/image-2.4.1/fftconv2.m is in octave-image 2.4.1-1.
This file is owned by root:root, with mode 0o644.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 | ## Copyright (C) 2004 Stefan van der Walt <stefan@sun.ac.za>
## All rights reserved.
##
## 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 COPYRIGHT HOLDERS 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})
## @deftypefnx {Function File} {} fftconv2 (@var{v1}, @var{v2}, @var{a})
## @deftypefnx {Function File} {} fftconv2 (@dots{}, @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, fftconv, fft, ifft}
## @end deftypefn
function X = fftconv2 (varargin)
if (nargin < 2)
print_usage ();
endif
nargs = nargin; # nargin minus the shape option
if (ischar (varargin{end}))
shape = varargin{end};
nargs--;
else
shape = "full";
endif
rowcolumn = false;
if (nargs == 2)
## usage: fftconv2(a, b[, shape])
a = varargin{1};
b = varargin{2};
elseif (nargs == 3)
## usage: fftconv2 (v1, v2, a[, shape])
rowcolumn = true;
if (! isnumeric (varargin{3}) && ! islogical (varargin{3}))
error ("fftconv2: A must be a numeric or logical array");
endif
v1 = vec (varargin{1});
v2 = vec (varargin{2}, 2);
orig_a = varargin{3};
else
print_usage ();
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 (padarray (a, [rb-1 cb-1], "post"));
B = fft2 (padarray (b, [ra-1 ca-1], "post"));
X = ifft2 (A.*B);
if (rowcolumn)
rb = rows (v1);
ra = rows (orig_a);
cb = columns (v2);
ca = columns (orig_a);
endif
switch (tolower (shape))
case "full",
## do nothing
case "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);
case "valid",
X = X(rb:ra, cb:ca);
otherwise
error ("fftconv2: unknown convolution SHAPE `%s'", shape);
endswitch
endfunction
## usage: fftconv2(a,b,[, shape])
%!test
%! a = repmat (1:10, 5);
%! b = repmat (10:-1:3, 7);
%! assert (fftconv2 (a, b), conv2 (a, b), 1.3e4*eps)
%! assert (fftconv2 (b, a), conv2 (b, a), 1.3e4*eps)
%! assert (fftconv2 (a, b, "full"), conv2 (a, b, "full"), 1.3e4*eps)
%! assert (fftconv2 (b, a, "full"), conv2 (b, a, "full"), 1.3e4*eps)
%! assert (fftconv2 (a, b, "same"), conv2 (a, b, "same"), 1e4*eps)
%! assert (fftconv2 (b, a, "same"), conv2 (b, a, "same"), 1e4*eps)
%! assert (isempty (fftconv2 (a, b, "valid")));
%! assert (fftconv2 (b, a, "valid"), conv2 (b, a, "valid"), 1e4*eps)
## usage: fftconv2(v1, v2, a[, shape])
%!test
%! x = 1:4;
%! y = 4:-1:1;
%! a = repmat(1:10, 5);
%! assert (fftconv2 (x, y, a), conv2 (x, y, a), 1e4*eps)
%! assert (fftconv2 (x, y, a, "full"), conv2 (x, y, a, "full"), 1e4*eps)
%! assert (fftconv2 (x, y, a, "same"), conv2 (x, y, a, "same"), 1e4*eps)
%! assert (fftconv2 (x, y, a, "valid"), conv2 (x, y, a, "valid"), 1e4*eps)
%!demo
%! ## Draw a cross
%! z = zeros (101, 101);
%! z(50, :) = 1;
%! z(:, 50) = 1;
%! subplot (1, 3, 1)
%! imshow (z);
%! title ("Original thin cross")
%!
%! ## Draw a sinc blob
%! b = getheight (strel ("ball", 10, 1));
%! subplot (1, 3, 2)
%! imshow (b);
%! title ("Sync blob")
%!
%! ## Convolve the cross with the blob
%! fc = real (fftconv2 (z, b, "same"));
%! subplot (1, 3, 3)
%! imshow (fc, [min(fc(:)) max(fc(:))])
%! title ("Convolution in the frequency domain")
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