GEOSUPERPIX - Geodesic superpixel segmentation.

Contents

Description

Compute geodesic superpixels following an approach similar to the Simple Linear Iterative Clustering superpixel segmentation technique of [ASSLFS10,LSALF10].

Syntax

  Q = GEOSUPERPIX(I);
  [Q, Ck, LabCk] = GEOSUPERPIX(I, K0, method, 'Property', propertyvalue, ... );

Inputs

I : input color image of size (X,Y,C) (multispectral with C=3 bands).

K0 : desired number of clusters, ie. of approximately equally-sized superpixels.

method : string defining the method used for computing the potential (and the metric) derived from the image; see function IM2POTENTIAL; it is either based on the image itself by setting it to 'pix' or 'pixinv', or based on the gradient of the image, by setting it to 'grd', 'grdorth' (or 'ani'), 'grdn' (or 'isoinv') or 'grdninv' (or 'iso'); whenever the image is a scalar (graylevel) image; when the image is multispectral (C>1), the GST is used to derive the potential function, which will depend on the chosen method: 'iso' (or 'gstninv'), 'gst', 'gstorth', 'ani', 'gstcoh' or 'gstiso'.

Property [propertyname propertyvalues]

'T' : stopping criterion; it is defined as a threshold on the errror for relocating all the superpixel regions' centers; default: T=eps.

'n' : multiplying factor used for the search area around each superpixel region's center; default: n=2.

'k' : size of the neighbourood considered when correcting the initial location of the superpixel regions' centers; when set to 0, the first initialization is kept as it is; default: k=3.

'iter' : maximum number of iterations; default: iter=Inf, ie. the segmentation process is iterated till convergence.

'a' : exponent used for amplyfying the strenght of the cost function (cases 'pix', 'pixinv', 'grdn', 'iso') or the strenght of the scaling function (cases 'gstninv', 'gstnorm'); default: a=1.

'rho' : integration scale for computing the GST; default: rho=1.

'sigma' : differentiation scale for estimating the directional derivatives; default: sigma=1.

'der' : string defining the method of pre-smoothing/differentiation used for estimating the directional derivatives of the input image; it is either (see GRDSMOOTH): 'matlab', 'vista', 'fast', 'conv', 'fleck', 'tap5', 'tap7', 'sob', 'opt' or 'ana'; default: der='fast'.

'int' : string defining the method used for the post-smoothing of the GST; it is either (see GRD2GST): 'matlab', 'conv' or 'fast' for isotropic Gaussian smoothing, or 'ani' for anisotropic Gaussian (using hourglass shaped Gaussian kernels) along the edges; this latter better captures edges anisotropy; default: int='fast'.

'samp' : scalar used as a sampling rate for the gradient when estimating the GST; default: samp=1.

'eign' : in the case the tensor norm estimated from the eigenvalues (l1 and l2, with l1>l2) is to be estimated , the string eign defines the method used for its approximation; it is either (see GSTFEATURE): 'l1' (or 'zen'), 'abs', 'sum' (or 'sap'), 'dif' (or 'koe') or 'ndi'; default: eign='l1'.

Outputs

Q : diagram of geodesic superpixels regions; it takes values in the range [1,K] where K is the final number of superpixel regions; it is a matrix of size (X,Y).

LabCk : representative Lab values of the superpixels; it is a matrix of size (K,3).

Ck : coordinates of the centers of the corresponding superpixels; it is a matrix of size (K,2).

References

[PC09] G. Peyre, and L. Cohen: "Geodesic methods for shape and surface processing", in "Advances in Computational Vision and Medical Image Processing: Methods and Applications", vol. 13 of "Computational Methods in Applied Sciences", pp. 29-56, Springer, 2009. http://www.springerlink.com/content/k15pkj1434003774/

[GSD10] J. Grazzini, P. Soille and S. Dillard: "Multichannel image regularisation using anisotropic geodesic filtering", Proc. ICPR, pp. 2664-2667, 2010. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5596008

[ASSLFS10] R. Achanta, A. Shaji, K. Smith, A. Lucchi, P. Fua and S. Susstrunk: "SLIC superpixels", EPFL Technical Report no. 149300, 2010. http://infoscience.epfl.ch/record/149300/files/SLIC_Superpixels_TR_2.pdf

[LSALF10] A. Lucchi, K. Smith, R. Achanta, V. Lepetit and P. Fua: "A fully automated approach to segmentation of irregularly shaped cellular structures in EM images", Proc. MICCAI, 2010. http://cvlab.epfl.ch/publications/publications/2010/LucchiSALF10.pdf

See also

Ressembles: SLICSUPERPIX, AMOEBASUPERPIX, GEODESICFILT, FMM. Requires: GEOSUPERPIX_BASE.

Function implementation

function [Q, varargout] = geosuperpix(I, varargin)

parsing parameters

error(nargchk(1, 37, nargin, 'struct'));
error(nargoutchk(1, 3, nargout, 'struct'));

% mandatory parameter
if ~isnumeric(I)
    error('geosuperpix:inputerror','a matrix is required in input');
end

% optional parameters
p = createParser('GEOSUPERPIX');   % create an instance of the inputParser class.
p.addOptional('K', 0.1, @(x)isscalar(x) && ((x>0 && x<1) || (x>1 && x==round(x))));
p.addOptional('method', 'ani',  @(x)ischar(x) && ...
    any(strcmpi(x,{'iso','isotropic','ani','anisotropic', ...
    'gstninv','gst','gstorth','gstn','gstn1','gstn2','gstn3','gstcoh'})));
% additional optional parameters
p.addParamValue('T', eps, @(x) isscalar(x) && x>=0);
p.addParamValue('n', 2, @(x)isscalar(x) && x>=1 && x==round(x));
p.addParamValue('k', 3, @(x)isscalar(x) && (x==0 || x>=3));
p.addParamValue('iter', Inf, @(x)isscalar(x) && x>=1);
% additional parameters used by IM2POTENTIAL_BASE
p.addParamValue('rho', 1, @(x)isscalar(x) && isfloat(x) && x>=0);
p.addParamValue('sigma', 1, @(x)isscalar(x) && isfloat(x) && x>=0);
p.addParamValue('der', 'fast', @(x)islogical(x) || (ischar(x) && ...
    any(strcmpi(x,{'matlab','vista','fast','conv','fleck', ...
    'tap5','tap7','sob','opt','ana'}))));
p.addParamValue('int', 'fast', @(x)islogical(x) || (ischar(x) && ...
    any(strcmpi(x,{'matlab','conv','fast','ani'}))));
p.addParamValue('samp',1, @(x)isscalar(x) && round(x)==x && x>=1);
p.addParamValue('eign','l1',@(x)ischar(x) && ...
    any(strcmpi(x,{'abs','zen','l1','sap','sum','ndi','dif','koe'})));
p.addParamValue('a', [1 1], @(x)isscalar(x) || ...
    (isvector(x) && length(x)==2));

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

setting variables

if p.K<1
    p.K = p.K * min(size(I,1),size(I,2)); % proportion
end

main computation

[Q, Ck, LabCk] = ...
    geosuperpix_base(I, p.K, p.T, p.n, p.k, p.iter, p.method, ...
    p.rho, p.sigma, p.a, p.der, p.int, p.samp, p.eign);

if nargout>=2
    varargout{1} = Ck;
    if nargout>=3,  varargout{2} = LabCk;  end
end

display

if p.disp
    figure;
    if isempty(ver('images')),       imagesc(Q), colormap jet;
    else  imagesc(label2rgb(Q.*(imdilate(Q,ones(3,3))-Q==0)));
    end
    axis image off, title('geodesic superpixel areas');
    rgb = Lab2RGB(LabCk(:,1),LabCk(:,2),LabCk(:,3));
    rgb = double(reshape(rgb(Q(:),:), size(I)));
    figure, imagesc(rescale(rgb)), axis image off,
    title('geodesic superpixel representation');
end

end % end of geosuperpix