GRANULOMETRY - Morphological granulometry representation of an image.

Contents

Description

Compute a granulometry through a series of morphological operations (filters) following the various approaches described in [Mathe75,Serra82,CD94,DC99].

Syntax

   G = GRANULOMETRY(I);
   G = GRANULOMETRY(I, op);
   G = GRANULOMETRY(I, op, 'Property', propertyvalue, ... );

Inputs

I : input image of size (X,Y,C), with C>1 when I is multispectral.

op : (optional) string setting the elementary operations performed at each step for computing the final granulometry; it can any of those strings: 'o' (or 'open'), 'c' (or 'close'), 'oc', 'co', 'oco', 'coc', 'ro', 'rc', 'roc', 'rco', 'rcoc', 'roco', 'e' (or 'erode') or 'd' (or 'dilate'), where the 'o' represents the opening operation (see function IMOPEN), the 'c' represents the closing operation (see function IMCLOSE), the prior 'r' means that the reconstruction version of these operators are considered (see functions IMROPEN and IMRCLOSE), and where the order of the letters represents the order those operators are applied for computing the elementary operation at each step; for instance, 'roco' means that at each step, an opening by reconstruction followed by a closing by reconstruction itself followed by another opening by reconstruction are applied on the input image; default: op='roc'.

se : (optional) string or cell of defining the structuring elements used for computing the granulometry; it can be either a cell of N structures of type STREL, each se{i} representing the SE used by the operator at step i<=N, or a string defining the shape of the elementary SE (see function FLATSTREL); in this latter case, the size of the SE needs to be passed in the variable s1 (see below); default: se='disk'.

Property [propertyname propertyvalues]

's1', 's2' : optional argument(s) further defining the series of SE's used by the elementary morphological operation at each step in the case the variable se (see above) was passed as a string (and not a cell of STREL structures); s1 is a vector of size N, each s1(i) providing the size of the SE used by the operator at step i<=N; s2 further completes the definition of the SE, depending on its type (see function FLATSTREL); default: s1=2:2:10 and s2=[].

Outputs

G : a cell of size N representing a granulometry.

References

[Mathe75] G. Matheron: "Random Sets and Integral Geometry", Wiley, New York (USA), 1975.

[Serra82] J. Serra: "Image Analysis and Mathematical Morphology", Academic Press, New York (USA), 1982.

[CD94] Y. Chen and E.R. Dougherty: "Gray-scale morphological granulometric texture classification", Opt. Eng. 33(8):2713-2722, 1994. http://spiedigitallibrary.org/oe/resource/1/opegar/v33/i8/p2713_s1

[DC99] E.R. Dougherty and Y. Chen: "Granulometric filters", in: "Nonlinear Image Filtering", E.R. Dougherty and J. Astola eds., SPIE and IEEE Presses, Belingham, pp. 121-162, 1999.

See also

Ressembles: MORPHPROFILE, WATERSHED. Requires: GRANULOMETRY_BASE, FLATSTREL.

Function implementation

function [G, varargout] = granulometry( I, varargin )

parsing parameters

if isempty(ver('images'))
    error('morphprofile:errortoolbox', 'Image Processing toolbox required');
end

error(nargchk(1, 16, nargin, 'struct'));
error(nargoutchk(1, 4, nargout, 'struct'));

if ~isnumeric(I)
    error('morphprofile:inputparameter','a matrix is required in input');
end

p = createParser('MORPHPROFILE');
p.addOptional('op', 'roc', @(x)ischar(x) && ...
    any(strcmpi(x,{'ro', 'ropen', 'rc', 'rclose', 'roc','rocmax', ...
    'o', 'open', 'c', 'close', 'oc', 'ocmax', ...
    'e', 'erode', 'd', 'dilate'})));
p.addOptional('se', 'disk', @(x) (iscell(x) && strcmp(class(x{1}),'strel')) || ...
    (ischar(x) && any(strcmpi(x,{'disk','rectangle','square','diamond', ...
                'line','periodicline','arbitrary','octagon','pair'}))));
p.addParamValue('s1', 2:2:10, @(x)isnumeric(x));
p.addParamValue('s2', [], @(x)isnumeric(x));

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

checking/setting variables

C = size(I,3);

if ischar(p.se)
    shape = p.se;
    N = length(p.s1);

    if ~iscell(p.s1),
        if any(strcmp(shape,{'disk'}))
            p.s1 = floor(p.s1/2);
        end
        p.s1 = num2cell(p.s1);
    end
    if ~iscell(p.s2),
        if isempty(p.s2)
            p.s2 = cell(N,1);
        else
            if isscalar(p.s2),  p.s2 = repmat(p.s2, 1, N);  end;
            p.s2 = num2cell(p.s2);
        end
    end

    p.se = cell(N,1);
    for i=1:N
        p.se{i} = flatstrel(shape, p.s1{i}, p.s2{i});
    end

end

main processing

G = granulometry_base( I, p.op, p.se );

if nargout==2,  varargout{1} = p.se;  end

display

if p.disp

    if any(strcmp(p.op,'o')),       p.op = 'open';
    elseif any(strcmp(p.op,'c')),   p.op = 'close';
    elseif strcmp(p.op,'oc'),       p.op = 'open-close';
    elseif strcmp(p.op,'co'),       p.op = 'close-open';
    elseif strcmp(p.op,'oco'),      p.op = 'open-close-open';
    elseif strcmp(p.op,'coc'),      p.op = 'close-open-close';
    elseif any(strcmp(p.op,'ro')),  p.op = 'open-by-rec';
    elseif any(strcmp(p.op,'rc')),  p.op = 'close-by-rec';
    elseif strcmp(p.op,'roc'),      p.op = 'open-close-by-rec';
    elseif strcmp(p.op,'rco'),      p.op = 'close-open-by-rec';
    elseif strcmp(p.op,'roco'),     p.op = 'open-close-open-by-rec';
    elseif strcmp(p.op,'rcoc'),     p.op = 'close-open-close-by-rec';
    end

    N = length(G);
    figure; ndisp = 3; mdisp = ceil(N/ndisp);
    for i=1:N
        subplot(mdisp, ndisp, i),  imagesc(rescale(G{i})), axis image off;
    end
    if C==1,  colormap gray; end
    suptitle(['MP of ' p.op]);
end

end % end of granulometry