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## Copyright (C) 2004 Josep Mones i Teixidor <jmones@puntbarra.com>
## Copyright (C) 2011 Adrián del Pino <delpinonavarrete@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; if not, see <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {@var{eul} = } bweuler (@var{BW}, @var{n})
## Calculate the Euler number of a binary image.
##
## This function calculates the Euler number @var{eul} of a binary
## image @var{BW}. This number is a scalar whose value represents the total
## number of objects in @var{BW} minus the number of holes.
##
## @var{n} is an optional argument that specifies the neighbourhood
## connectivity. Must either be 4 or 8. If omitted, defaults to 8.
##
## This function uses Bit Quads as described in "Digital Image
## Processing" to calculate euler number.
##
## References:
## W. K. Pratt, "Digital Image Processing", 3rd Edition, pp 593-595
##
## @seealso{bwmorph, bwperim, qtgetblk}
## @end deftypefn
function eul = bweuler (BW, n = 8)
if (nargin < 1 || nargin > 2)
print_usage;
elseif (!isbw (BW, "non-logical"))
error("first argument must be a Black and White image");
elseif (ndims (BW) != 2)
error ("bweuler: BW must have 2 dimensions");
endif
## lut_4=(q1lut-q3lut+2*qdlut)/4; # everything in one lut will be quicker
## lut_8=(q1lut-q3lut-2*qdlut)/4; # but only the final result is divided by four
## we precalculate this... # to save more time
if (!isnumeric (n) || !isscalar (n) || (n != 8 && n != 4))
error("second argument must either be 4 or 8");
elseif (n == 8)
lut = [0; 1; 1; 0; 1; 0; -2; -1; 1; -2; 0; -1; 0; -1; -1; 0];
elseif (n == 4)
lut = [0; 1; 1; 0; 1; 0; 2; -1; 1; 2; 0; -1; 0; -1; -1; 0];
endif
## Adding zeros to the top and left bordes to avoid errors when figures touch these borders.
## Notice that 1 0 is equivalent to 1 0 0 because there are implicit zeros in the bottom and right
## 0 1 0 1 0
## 0 0 0
## borders. Therefore, there are three one-pixel and one diagonal pixels. So, we get 3 * 1 - 2 = 1
## (error) instead of 6 * 1 - 2 = 4 (correct).
BWaux = false (size (BW) +1);
BWaux(2:end,2:end) = BW;
eul = sum (applylut (BWaux, lut) (:)) / 4;
endfunction
%!demo
%! A=zeros(9,10);
%! A([2,5,8],2:9)=1;
%! A(2:8,[2,9])=1
%! bweuler(A)
%! # Euler number (objects minus holes) is 1-2=-1 in an 8-like object
%!test
%! A=zeros(10,10);
%! A(2:9,3:8)=1;
%! A(4,4)=0;
%! A(8,8)=0; # not a hole
%! A(6,6)=0;
%! assert(bweuler(A),-1);
## This will test if n=4 and n=8 behave differently
%!test
%! A=zeros(10,10);
%! A(2:4,2:4)=1;
%! A(5:8,5:8)=1;
%! assert(bweuler(A,4),2);
%! assert(bweuler(A,8),1);
%! assert(bweuler(A),1);
%!error <2 dimensions> bweuler (true (5, 5, 1, 5))
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