output=nick(image, varargin)

%NICK local thresholding.
%   BW = NICK(IMAGE) performs local thresholding of a two-dimensional 
%   array IMAGE with Nick's algorithm.
%      
%   BW = NICK(IMAGE, [M N], THRESHOLD, PADDING) performs local 
%   thresholding with M-by-N neighbourhood (default is 15-by-15) and 
%   threshold THRESHOLD between -0.1 and -0.2 (default is -0.2). 
%   To deal with border pixels the image is padded with one of 
%   PADARRAY options (default is 'replicate').
%       
%   Example
%   -------
%       imshow(nick(imread('eight.tif'), [250 250]));
%
%   See also PADARRAY, RGB2GRAY.

%   For method description see:
%       http://dx.doi.org/10.1117/12.805827
%   Contributed by Jan Motl ([e-mail])
%   $Revision: 1.0 $  $Date: 2013/05/09 16:58:01 $

function output=nick(image, varargin)
% Initialization
numvarargs = length(varargin);      % only want 3 optional inputs at most
if numvarargs > 3
    error('myfuns:somefun2Alt:TooManyInputs', ...
     'Possible parameters are: (image, [m n], threshold, padding)');
end
 
optargs = {[15 15] -0.2 'replicate'}; % set defaults
 
optargs(1:numvarargs) = varargin;   % use memorable variable names
[window, k, padding] = optargs{:};

if ndims(image) ~= 2
    error('The input image must be a two-dimensional array.');
end

% Convert to double
image = double(image);

% Mean value
mean = averagefilter(image, window, padding);

% Standard deviation
meanSquare = averagefilter(image.^2, window, padding);
variance = meanSquare - mean.^2;

% Nick
threshold = mean + k*sqrt(variance + mean.^2);
output = (image > threshold);