IM2AMOEBA - Amoeba-like front propagation over an image.

Contents

Description

Perform a (multiple) front propagation from a set of seed points using a metric derived from the input image over its domain.

Algorithm

Let $d_{\mbox{pixel}}$ be a distance defined on the values of the image, for example a difference of gray-value, or a color distance. Let $P=(x=x_0,x_1,\cdots,x_n=y)$ a path between points $x$ and $y$. Let $\lambda$ be a real positive number. The length of the path $P$ is defined as

$$ L(P) = n + \lambda \cdot d_{\mbox{pixel}}(x_i,x_{i+1})$$

The "amoeba distance" with parameter $\lambda$ is thus defined as:

$$ \left\{ \begin{array}{l} d_\lambda (x,x) = 0 \\ d_\lambda (x,y) = \min_P \{ L(P) \} \end{array} \right. $$

Syntax

D = IM2AMOEBA(I, start_pts);
[D, Q] = IM2AMOEBA(I, start_pts, dfeat, dspace, lambda);

Inputs

I : input image of size (X,Y,C), possibly multichannel with C>1.

start_pts : array of size (2,k), where k is the number of starting points, ie. start_pts(:,i) are the coordinates of the i-th starting point.

dspace : (optional) string defining the distance over the spatial domain; it is either: 'l1', 'l2' or 'linf'; dspace: dspace='l2'.

dfeat : (optional) string defining the distance over the feature space (eg. a color distance); it is either: 'l1', 'l2' or 'linf'; default: dfeat='l2'.

lambda : (optional) real parameter used for weighting the relative influences of spatial domain and spectral range; default: lambda=1.

Outputs

D : distance map representing the propagated front from start_pts using the amoeba metric derived from the image.

Q : Voronoi-like (labelled) index map.

See also

Ressembles: IM2FRONT, FMM, DIJSKTRA, POTENTIAL2FRONT. Requires: IM2AMOEBA_BASE.

Function implementation

function [D, Q] = im2amoeba(I, start_pts, varargin)

parsing and checking parameters

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

% mandatory parameter
if ~isnumeric(I)
    error('im2amoeba:inputerror','a matrix is required in input');
end

p = createParser('IM2AMOEBA');   % create an instance of the inputParser class.
% additional optional parameters
p.addOptional('dfeat', 'l2', @(x) isa(x, 'function_handle') || ...
    (ischar(x) && any(strcmpi(x,{'l1','l2','linf'}))));
p.addOptional('lambda', 1, @(x)isscalar(x) && x>=0);
p.addOptional('dspace', 'l2', @(x) isa(x, 'function_handle') || ...
    (ischar(x) && any(strcmpi(x,{'l1','l2'}))));

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

checking/setting variables

if ischar(p.dfeat)
   switch p.dfeat
       case 'l1'
           p.dfeat = @(c0, c1) sum(abs(c1-c0), 2);
       case 'l2'
           p.dfeat = @(c0, c1) sqrt(sum((c1-c0).^2, 2));
       case 'linf'
           p.dfeat = @(c0, c1) max(c1-c0, [], 2);
   end
end

if ischar(p.dspace)
   switch p.dspace
       case 'l1' % Mahnattan (city-block) distance
           p.dspace = @(c0, c1) sum(abs(c1-c0), 2);
       case 'l2'
           p.dspace = @(c0, c1) sqrt(sum((c1-c0).^2, 2));
   end
end

main computation

[D, Q] = im2amoeba_base(I, start_pts, p.dfeat, p.lambda, p.dspace);

display

if p.disp
    figure;
    if isempty(ver('images'))
        subplot(1,3,1), imagesc(rescale(I));
        subplot(1,3,2), imagesc(Q), colormap jet;
    else
        M = (imdilate(Q,ones(3,3))-Q==0);
        subplot(1,3,2), imagesc(label2rgb(Q.*M)), axis image off;
        M = cat(3,M,M,M);
        subplot(1,3,1), imagesc(rescale(I.*M)+(1-M)), axis image off;
    end
    subplot(1,3,2), hold on, plot(start_pts(1,:),start_pts(2,:),'*r'),
    hold off;
    subplot(1,3,3), imagesc(rescale(D)), colormap gray, axis image off;
    hold on, plot(start_pts(1,:),start_pts(2,:),'*r'), hold off
    suptitle('amoeba neighbourhoods')
end

end % end of im2amoeba