1## Copyright (C) 2008 Søren Hauberg <soren@hauberg.org> 2## 3## This program is free software; you can redistribute it and/or modify it under 4## the terms of the GNU General Public License as published by the Free Software 5## Foundation; either version 3 of the License, or (at your option) any later 6## version. 7## 8## This program is distributed in the hope that it will be useful, but WITHOUT 9## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or 10## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more 11## details. 12## 13## You should have received a copy of the GNU General Public License along with 14## this program; if not, see <http://www.gnu.org/licenses/>. 15 16## -*- texinfo -*- 17## @deftypefn {Function File} {@var{E} =} entropyfilt (@var{im}) 18## @deftypefnx{Function File} {@var{E} =} entropyfilt (@var{im}, @var{domain}) 19## @deftypefnx{Function File} {@var{E} =} entropyfilt (@var{im}, @var{domain}, @var{padding}, @dots{}) 20## Computes the local entropy in a neighbourhood around each pixel in an image. 21## 22## The entropy of the elements of the neighbourhood is computed as 23## 24## @example 25## @var{E} = -sum (@var{P} .* log2 (@var{P}) 26## @end example 27## 28## where @var{P} is the distribution of the elements of @var{im}. The distribution 29## is approximated using a histogram with @var{nbins} cells. If @var{im} is 30## @code{logical} then two cells are used. For other classes 256 cells 31## are used. 32## 33## When the entropy is computed, zero-valued cells of the histogram are ignored. 34## 35## The neighbourhood is defined by the @var{domain} binary mask. Elements of the 36## mask with a non-zero value are considered part of the neighbourhood. By default 37## a 9 by 9 matrix containing only non-zero values is used. 38## 39## At the border of the image, extrapolation is used. By default symmetric 40## extrapolation is used, but any method supported by the @code{padarray} function 41## can be used. Since extrapolation is used, one can expect a lower entropy near 42## the image border. 43## 44## @seealso{entropy, paddarray, stdfilt} 45## @end deftypefn 46 47function retval = entropyfilt (I, domain = true (9), padding = "symmetric", varargin) 48 ## Check input 49 if (nargin == 0) 50 error ("entropyfilt: not enough input arguments"); 51 endif 52 53 if (! isnumeric (I)) 54 error ("entropyfilt: I must be numeric"); 55 endif 56 57 if (! isnumeric (domain) && ! islogical (domain)) 58 error ("entropyfilt: DOMAIN must be a logical matrix"); 59 endif 60 domain = logical (domain); 61 62 ## Get number of histogram bins 63 if (islogical (I)) 64 nbins = 2; 65 else 66 nbins = 256; 67 endif 68 69 ## Convert to 8 or 16 bit integers if needed 70 ## (accepting single, int8, int16, int32, int64, uint64 is Octave-only) 71 switch (class (I)) 72 case {"double", "single", "int16", "int32", "int64", "uint16", "uint32", "uint64"} 73 I = im2uint8 (I); # because this is what Matlab seems to do 74 case {"logical", "int8", "uint8"} 75 ## Do nothing 76 otherwise 77 error ("entropyfilt: cannot handle images of class '%s'", class (I)); 78 endswitch 79 80 ## Pad image 81 pad = floor (size (domain)/2); 82 I = padarray (I, pad, padding, varargin {:}); 83 even = (round (size (domain)/2) == size (domain)/2); 84 idx = cell (1, ndims (I)); 85 for k = 1:ndims (I) 86 idx {k} = (even (k)+1):size (I, k); 87 endfor 88 I = I (idx {:}); 89 90 retval = __spatial_filtering__ (I, domain, "entropy", zeros (size (domain)), 91 nbins); 92endfunction 93 94%!test 95%! a = log2 (9) * ones (5, 5); 96%! b = -(2*log2 (2/9) + log2 (1/9))/3; 97%! a(1,2:4) = b; 98%! a(5,2:4) = b; 99%! a(2:4,1) = b; 100%! a(2:4,5) = b; 101%! c = -(4*log2 (4/9) + 4*log2 (2/9) + log2 (1/9))/9; 102%! a(1,1) = c; 103%! a(5,1) = c; 104%! a(1,5) = c; 105%! a(5,5) = c; 106%! assert (entropyfilt (uint8 (magic (5)), ones (3, 3)), a, 2*eps); 107 108%!test 109%! assert (entropyfilt (uint8 (ones (10, 10))), zeros (10, 10)); 110 111## some (Matlab compatible) tests on simple 2D-images (classes double, uint8, uint16): 112%!test 113%! A = zeros (3,3); 114%! B = ones (3,3); 115%! C = [1 1 1; 2 2 2; 3 3 3]; 116%! D = C'; 117%! E = ones (3,3); 118%! E(2,2) = 2; 119%! F = 3 .* ones (3,3); 120%! F(2,2) = 1; 121%! G = [-1 2 7; -5 2 8; -7 pi 9]; 122%! H = [5 2 8; 1 -3 1; 5 1 0]; 123%! Hf = mat2gray(H); 124%! X = uint8(abs(H)); 125%! P = [0.2 0.201 0.204; 0.202 0.203 0.205; 0.205 0.206 0.202]; 126%! Q = uint16([100 101 103; 100 105 102; 100 102 103]); 127%! R = uint8([1 2 3 4 5; 11 12 13 14 15; 21 22 4 5 6; 5 5 3 2 1; 15 14 14 14 14]); 128%! Aout = zeros (3); 129%! Bout = zeros (3); 130%! Cout = zeros (3); 131%! Dout = zeros (3); 132%! Eout = zeros (3); 133%! Fout = zeros (3); 134%! Gout_1 = -sum([2 7]./9.*log2([2 7]./9)); 135%! Gout_2 = -sum([3 6]./9.*log2([3 6]./9)); 136%! Gout_3 = -sum([4 5]./9.*log2([4 5]./9)); 137%! Gout = [Gout_1 Gout_2 Gout_3; Gout_1 Gout_2 Gout_3; Gout_1 Gout_2 Gout_3]; 138%! Hout_5 = -sum([2 7]./9.*log2([2 7]./9)) ; 139%! Hout = [0.8916 0.8256 0.7412; 0.8256 Hout_5 0.6913; 0.7412 0.6913 0.6355]; 140%! Hfout_5 = -sum([3 2 1 1 1 1]./9.*log2([3 2 1 1 1 1]./9)); 141%! Hfout = [2.3613 2.3296 2.2252; 2.4571 Hfout_5 2.3090; 2.4805 2.4488 2.3445]; 142%! Xout_5 = -sum([1 1 1 1 2 3]./9.*log2([1 1 1 1 2 3]./9)); 143%! Xout = [2.3613 2.3296 2.2252; 2.4571 Xout_5 2.3090; 2.4805 2.4488 2.3445]; 144%! Pout_5 = -sum([1 2 6]./9.*log2([1 2 6]./9)); 145%! Pout = [1.1137 1.1730 1.2251; 1.1595 Pout_5 1.2774; 1.1556 1.2183 1.2635]; 146%! Qout = zeros(3); 147%! Rout = [3.5143 3.5700 3.4871 3.4957 3.4825; 148%! 3.4705 3.5330 3.4341 3.4246 3.3890; 149%! 3.3694 3.4063 3.3279 3.3386 3.3030; 150%! 3.3717 3.4209 3.3396 3.3482 3.3044; 151%! 3.4361 3.5047 3.3999 3.4236 3.3879]; 152%! assert (entropyfilt (A), Aout); 153%! assert (entropyfilt (B), Bout); 154%! assert (entropyfilt (C), Cout); 155%! assert (entropyfilt (D), Dout); 156%! assert (entropyfilt (E), Eout); 157%! assert (entropyfilt (F), Fout); 158%! assert (entropyfilt (G), Gout, 1e-4); 159%! assert (entropyfilt (H), Hout, 1e-4); 160%! assert (entropyfilt (Hf), Hfout, 1e-4); 161%! assert (entropyfilt (X), Xout, 1e-4); 162%! assert (entropyfilt (P), Pout, 1e-4); 163%! assert (entropyfilt (Q), Qout); 164%! assert (entropyfilt (R), Rout, 1e-4); 165