function T = th_intermeans(I,n);
% T =  th_intermeans(I,n)
%
% Find a global threshold for a grayscale image using the intermeans method
% commonly known as Otsu's method.
%
% In:
%  I    grayscale image
%  n    maximum graylevel (defaults to 255)
%
% Out:
%  T    threshold
%
% References: 
%
% N. Otsu, "A threshold selection method from gray-level histogram," IEEE
% Transactions on Systems, Man, and Cybernetics, vol. 9, pp. 62-66, 1979.
%
% C. A. Glasbey, "An analysis of histogram-based thresholding algorithms,"
% CVGIP: Graphical Models and Image Processing, vol. 55, pp. 532-537, 1993.
%
%% Copyright (C) 2004-2013 Antti Niemistö
%%
%% This file is part of HistThresh toolbox.
%%
%% HistThresh toolbox 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.
%%
%% HistThresh toolbox 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 HistThresh toolbox.  If not, see <http://www.gnu.org/licenses/>.

if nargin == 1
  n = 255;
end

% This algorithm is implemented in the Image Processing Toolbox.
%I = uint8(I);
%T = n*graythresh(I);

% The implementation below uses the notations from the paper, but is
% significantly slower.

I = double(I);

% Calculate the histogram.
y = hist(I(:),0:n);

warning('off', 'MATLAB:divideByZero');
for j = 0:n
  mu = B(y,j)/A(y,j);
  nu = (B(y,n)-B(y,j))/(A(y,n)-A(y,j));
  vec(j+1) = A(y,j)*(A(y,n)-A(y,j))*(mu-nu)^2;
end
warning('on', 'MATLAB:divideByZero');

[maximum,ind] = max(vec);
T = ind-1;
