function T = th_minerror(I,n)
% T =  th_minerror(I,n)
%
% Find a global threshold for a grayscale image using the minimum error
% thresholding method.
%
% In:
%  I    grayscale image
%  n    maximum graylevel (defaults to 255)
%
% Out:
%  T    threshold
%
% References: 
%
% J. Kittler and J. Illingworth, "Minimum error thresholding," Pattern
% Recognition, vol. 19, pp. 41-47, 1986.
%
% 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

I = double(I);

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

warning_state = warning('off');

% The threshold is chosen such that the following expression is minimized.
for j = 0:n
  mu = B(y,j)/A(y,j);
  nu = (B(y,n)-B(y,j))/(A(y,n)-A(y,j));
  p = A(y,j)/A(y,n);
  q = (A(y,n)-A(y,j)) / A(y,n);
  sigma2 = C(y,j)/A(y,j)-mu^2;
  tau2 = (C(y,n)-C(y,j)) / (A(y,n)-A(y,j)) - nu^2;
  vec(j+1) = p*log10(sqrt(sigma2)/p) + q*log10(sqrt(tau2)/q);
end
warning(warning_state);     % Switch warning back to initial settings

vec(vec==-inf) = NaN;
[minimum,ind] = min(vec);
T = ind-1;
