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Geodesic Segmentation
This tour explores the use of Fast Marching methods for image segmentation.
Contents
Installing toolboxes and setting up the path.
You need to download the following files: signal toolbox, general toolbox and graph toolbox.
You need to unzip these toolboxes in your working directory, so that you have toolbox_signal, toolbox_general and toolbox_graph in your directory.
For Scilab user: you must replace the Matlab comment '%' by its Scilab counterpart '//'.
Recommandation: You should create a text file named for instance numericaltour.sce (in Scilab) or numericaltour.m (in Matlab) to write all the Scilab/Matlab command you want to execute. Then, simply run exec('numericaltour.sce'); (in Scilab) or numericaltour; (in Matlab) to run the commands.
Execute this line only if you are using Matlab.
getd = @(p)path(p,path);
Then you can add the toolboxes to the path.
getd('toolbox_signal/');
getd('toolbox_general/');
getd('toolbox_graph/');
Segmentation Using Geodesic Ball
It is possible to extract an object by growing a geodesic ball.
First we load an image.
n = 256;
name = 'cortex';
M = rescale( sum(load_image(name,n),3) );
Display.
clf;
imageplot(M);
Starting point of the grodesic ball.
pstart = [154;175];
Choose a metric that is minimal for value of the image close to pstart.
W = abs(M-M(pstart(1),pstart(2)));
W = rescale( max(W,0.03), 0.01,1).^2;
Compute the Fast Marching from the center.
clear options;
options.nb_iter_max = Inf;
options.end_points = [];
[D,S,Q] = perform_fast_marching(1./W, pstart, options);
Exercice 1: (check the solution) Display geodesic balls {x \ M(x)<T} for various T.
exo1;
Segmentation Using Voronoi Diagrams
It is possible to perform the segmentation by using an edge stopping metric, and Vornoi diagram for several seeds.
Magnitude of the gradient.
mu = 2;
d = sqrt( sum( grad(perform_blurring(M,mu)).^2, 3) );
d = perform_blurring(d,mu);
Edge stopping metric.
W = rescale( min(d,0.15), 0.01,1).^2;
Display the metric.
clf;
imageplot(W);
Starting points.
pstart = [[30;30] [139;86] [158;170] [128;134] [124;122]];
Perform propagation.
options.nb_iter_max = Inf;
options.end_points = [];
[D,S,Q] = perform_fast_marching(1./W, pstart, options);
Display Voronoi diagrams.
clf;
imageplot(Q);
colormap(jet(256));
Exercice 2: (check the solution) Display the level sets.
exo2;
