bweuler.m

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function e = bweuler(a,n)
%BWEULER Compute the Euler number of binary image.
%   EUL = BWEULER(BW,N) returns the Euler number for the binary
%   image BW. EUL is a scalar whose value is the number of
%   objects in the image minus the total number of holes in those
%   objects.  N can have a value of either 4 or 8, where 4
%   specifies 4-connected objects and 8 specifies 8-connected
%   objects; if the argument is omitted, it defaults to 8. 
%
%   Class Support
%   -------------
%   BW can be of class uint8 or double. EUL is of class double.
%
%   Example
%   -------
%       BW = imread('circles.tif');
%       imshow(BW)
%       bweuler(BW)
%
%   See also BWPERIM, BWMORPH.

%   Clay M. Thompson 12-2-92
%   Revised Steven L. Eddins 1996
%   Copyright 1993-1998 The MathWorks, Inc.  All Rights Reserved.
%   $Revision: 5.9 $  $Date: 1997/11/24 15:34:05 $

% Reference: William Pratt, Digital Image Processing, John Wiley
% and Sons, 1991, pp. 630-634.

if nargin<2, n = 8; end

if n~=8 & n~=4, error('N must be either 4 or 8.'); end

if n==4,
  lut = 4*[0 0.25 0.25 0 0.25 0  .5 -0.25 0.25  0.5  0 -0.25 0 ...
              -0.25 -0.25 0] + 2;
else
  lut = 4*[0 0.25 0.25 0 0.25 0 -.5 -0.25 0.25 -0.5  0 -0.25 0 ...
              -0.25 -0.25 0] + 2;
end

% Need to zero-pad the input
b = repmat(uint8(0),size(a)+2);
b(2:end-1,2:end-1) = a;

weights = applylut(b,lut);
e = (sum(weights(:)) - 2*prod(size(b))) / 4;