WORDFILT2 - Weighted order-statistic filtering.

Contents

Description

Perform (integer) weighted order-statistic filtering of an image (possibly multispectral).

Syntax

   WOI = WORDFILT2(I, wk);
   WOI = WORDFILT2(I, wk, order);

Inputs

I : input image, possibly multispectral.

wk : kernel defining the neighbourhood and the local integer weights used in the estimation of the weighted ordered statistics; a possibly negative weight indicates the position of the centre pixel (origin of the offset); otherwise, the kernel should be square-shaped with odd size and its barycenter will be considered as the centre.

order : optional argument stating the order statistics to be computed in the sorted set of neighbours specified by the nonzero elements in wk; it can be either:

note in particular that order='min' and order=1 are equivalent as well as order='max' and order=sum(wk(:)); however order='med' and order=sum(wk(:))/2 are not equivalent as in the latter case the value of the median pixel (and not the median value itself like when using MEDIAN) is output; default: order='med'.

Output

WOI : output weighted ordered statistics image with same size as the image I; each pixel in WOI contains the order statistics in the neighbourhood of I defined by the non-negative values of wk around corresponding pixel in I.

References

[Brown84] D.R.K. Brownrigg: "The weighted median filter", Image Processing and Computer Vision, Communications of the ACM, 27(8): 807-818, 1984. http://dl.acm.org/citation.cfm?id=358222&bnc=1

[Yaros94] L. Yaroslavsky: "Local criteria: a unified approach to local adaptive linear and rank filters for image restoration and enhancement", Proc. IEEE ICIP, pp. 517-521, 1994. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=413624&tag=1

[Yaros96] L. Yaroslavsky: "Local adaptative filters for image restauration and enhancement", LNCIS, vol. 219, pp. 31-39, 1996. http://www.springerlink.com/content/y45n7228700540n2/

[Soille02] P. Soille: "On morphological operators based on rank filters", Pattern Recognition, 35:527-535, 2002. http://www.sciencedirect.com/science/article/pii/S0031320301000474

[Yaros08] L. Yaroslavsky: "Local criteria and local adaptive filtering in image processing: a retrospective view", Proc. LNLAIP, 2008. http://www.eurasip.org/Proceedings/Ext/LNLA2008/papers/cr1005.pdf

See also

Ressembles: MEDFILT2, ORDFILT2, WMEDFILT2. Requires: WORDFILT2_BASE.

Function implementation

function WOI = wordfilt2(I,wk,varargin)

error(nargchk(2, 4, nargin, 'struct'));
error(nargoutchk(1, 1, nargout, 'struct'));

parsing and checking parameters

if ~isnumeric(I)
    error('wordfilt2:inputerror','matrice is required in input');
end

p = createParser('WORDFILT2');   % create an instance of the inputParser class.
% optional parameters
p.addOptional('order','med', @(x) (isscalar(x) && x>0) ||...
    (ischar(x)&& any(strcmpi(x,{'med','mod'}))));

% parse and validate all input arguments
p.parse(varargin{:});
p = getvarParser(p);

internal variables and further checking

C = size(I,3);
[x y c] = size(wk);
s = sum(abs(wk(:)));

if ~isequal(round(wk),wk)
    warning('wordfilt2:inputwarning',...
        'the input weighting matrix must have integer values');
end

if isscalar(p.order) && p.order>s
    error('wordfilt2:inputerror',...
        'the input rank must be <= to the sum of the elements in wk');
end

if c~=1 && c~=C
    error('wordfilt2:inputargument', ...
    'input kernel must have 1 channel or the same number as the input');
end

cpos = find(wk<0,1,'first');
if isempty(cpos) && (x~=y || mod(x,2)~=1)
    error('wordfilt2:inputargument',...
        'input kernel must be square shaped with odd size');
end

main processing

WOI = wordfilt2_base(I, wk, p.order);

display

if p.disp
    figure, imagesc(rescale(WOI,0,1)), axis image off;
    if C==1,  colormap gray; end;
    title('weighted order-statistic filtered image');
end

end % end of wordfilt2