function Y = vanherk(X,N,TYPE,varargin)
% VANHERK Fast max/min 1D filter
%
% Y = VANHERK(X,N,TYPE) performs the 1D max/min filtering of the row
% vector X using a N-length filter.
% The filtering type is defined by TYPE = 'max' or 'min'. This function
% uses the van Herk algorithm for min/max filters that demands only 3
% min/max calculations per element, independently of the filter size.
%
% If X is a 2D matrix, each row will be filtered separately.
%
% Y = VANHERK(...,'col') performs the filtering on the columns of X.
%
% Y = VANHERK(...,'shape') returns the subset of the filtering specified
% by 'shape' :
% 'full' - Returns the full filtering result,
% 'same' - (default) Returns the central filter area that is the
% same size as X,
% 'valid' - Returns only the area where no filter elements are outside
% the image.
%
% X can be uint8 or double. If X is uint8 the processing is quite faster, so
% dont't use X as double, unless it is really necessary.
%
% Initialization
[direc, shape] = parse_inputs(varargin{:});
if strcmp(direc,'col')
X = X';
end
if strcmp(TYPE,'max')
maxfilt = 1;
elseif strcmp(TYPE,'min')
maxfilt = 0;
else
error([ 'TYPE must be ' char(39) 'max' char(39) ' or ' char(39) 'min' char(39) '.'])
end
% Correcting X size
fixsize = 0;
addel = 0;
if mod(size(X,2),N) ~= 0
fixsize = 1;
addel = N-mod(size(X,2),N);
if maxfilt
f = [ X zeros(size(X,1), addel) ];
else
f = [X repmat(X(:,end),1,addel)];
end
else
f = X;
end
lf = size(f,2);
lx = size(X,2);
clear X
% Declaring aux. mat.
g = f;
h = g;
% Filling g & h (aux. mat.)
ig = 1:N:size(f,2);
ih = ig + N - 1;
g(:,ig) = f(:,ig);
h(:,ih) = f(:,ih);
if maxfilt
for i = 2 : N
igold = ig;
ihold = ih;
ig = ig + 1;
ih = ih - 1;
g(:,ig) = max(f(:,ig),g(:,igold));
h(:,ih) = max(f(:,ih),h(:,ihold));
end
else
for i = 2 : N
igold = ig;
ihold = ih;
ig = ig + 1;
ih = ih - 1;
g(:,ig) = min(f(:,ig),g(:,igold));
h(:,ih) = min(f(:,ih),h(:,ihold));
end
end
clear f
% Comparing g & h
if strcmp(shape,'full')
ig = [ N : 1 : lf ];
ih = [ 1 : 1 : lf-N+1 ];
if fixsize
if maxfilt
Y = [ g(:,1:N-1) max(g(:,ig), h(:,ih)) h(:,end-N+2:end-addel) ];
else
Y = [ g(:,1:N-1) min(g(:,ig), h(:,ih)) h(:,end-N+2:end-addel) ];
end
else
if maxfilt
Y = [ g(:,1:N-1) max(g(:,ig), h(:,ih)) h(:,end-N+2:end) ];
else
Y = [ g(:,1:N-1) min(g(:,ig), h(:,ih)) h(:,end-N+2:end) ];
end
end
elseif strcmp(shape,'same')
if fixsize
if addel > (N-1)/2
disp('hoi')
ig = [ N : 1 : lf - addel + floor((N-1)/2) ];
ih = [ 1 : 1 : lf-N+1 - addel + floor((N-1)/2)];
if maxfilt
Y = [ g(:,1+ceil((N-1)/2):N-1) max(g(:,ig), h(:,ih)) ];
else
Y = [ g(:,1+ceil((N-1)/2):N-1) min(g(:,ig), h(:,ih)) ];
end
else
ig = [ N : 1 : lf ];
ih = [ 1 : 1 : lf-N+1 ];
if maxfilt
Y = [ g(:,1+ceil((N-1)/2):N-1) max(g(:,ig), h(:,ih)) h(:,lf-N+2:lf-N+1+floor((N-1)/2)-addel) ];
else
Y = [ g(:,1+ceil((N-1)/2):N-1) min(g(:,ig), h(:,ih)) h(:,lf-N+2:lf-N+1+floor((N-1)/2)-addel) ];
end
end
else % not fixsize (addel=0, lf=lx)
ig = [ N : 1 : lx ];
ih = [ 1 : 1 : lx-N+1 ];
if maxfilt
Y = [ g(:,N-ceil((N-1)/2):N-1) max( g(:,ig), h(:,ih) ) h(:,lx-N+2:lx-N+1+floor((N-1)/2)) ];
else
Y = [ g(:,N-ceil((N-1)/2):N-1) min( g(:,ig), h(:,ih) ) h(:,lx-N+2:lx-N+1+floor((N-1)/2)) ];
end
end
elseif strcmp(shape,'valid')
ig = [ N : 1 : lx];
ih = [ 1 : 1: lx-N+1];
if maxfilt
Y = [ max( g(:,ig), h(:,ih) ) ];
else
Y = [ min( g(:,ig), h(:,ih) ) ];
end
end
if strcmp(direc,'col')
Y = Y';
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [direc, shape] = parse_inputs(varargin)
direc = 'lin';
shape = 'same';
flag = [0 0]; % [dir shape]
for i = 1 : nargin
t = varargin{i};
if strcmp(t,'col') & flag(1) == 0
direc = 'col';
flag(1) = 1;
elseif strcmp(t,'full') & flag(2) == 0
shape = 'full';
flag(2) = 1;
elseif strcmp(t,'same') & flag(2) == 0
shape = 'same';
flag(2) = 1;
elseif strcmp(t,'valid') & flag(2) == 0
shape = 'valid';
flag(2) = 1;
else
error(['Too many / Unkown parameter : ' t ])
end
end
