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	** <code>method</code>: 'Chan-Vese' (region-based) or 'edge' (gradient-based).		** <code>method</code>: 'Chan-Vese' (region-based) or 'edge' (gradient-based).
	* <code>visboundaries</code>: A helper function to overlay binary mask boundaries onto the original image for visualization.		* <code>visboundaries</code>: A helper function to overlay binary mask boundaries onto the original image for visualization.


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= Model-Based Segmentation: Active Contours =

'''Model-Based Segmentation''' is a top-down approach where a geometric model or a mathematical energy function evolves to fit the objects in an image. Unlike data-based methods (like thresholding) which look at pixels individually, model-based methods consider the connectivity and smoothness of the object's boundary.

This article explores the '''Active Contours''' (or "Snakes") algorithm, specifically using the Chan-Vese method to segment objects like coins.

__TOC__

== Theoretical Background ==

=== Active Contours (Snakes) ===
An Active Contour is a curve that moves through an image to minimize an energy function. The curve is influenced by two forces:
* '''Internal Forces:''' These keep the curve smooth and continuous (preventing it from becoming jagged or breaking).
* '''External Forces:''' These pull the curve toward image features like edges or region boundaries.

=== The Chan-Vese Method ===
The standard Active Contour relies on gradients (edges). However, the '''Chan-Vese''' model is a region-based active contour.
* It does not look for edges directly.
* Instead, it tries to separate the image into two regions (inside the curve and outside the curve) such that the pixel intensities inside are homogeneous and the pixel intensities outside are homogeneous.
* This makes it robust to noise and able to detect objects whose boundaries are not clearly defined by sharp gradients.

== MATLAB Implementation ==

The following MATLAB script demonstrates the evolution of an active contour over several iterations.

=== Code Logic ===

<syntaxhighlight lang="matlab">
% Model-Based Segmentation
% Algorithm: Active Contours
clc; clear; close all;

% 1. Load Image
% 'coins.png' is a standard MATLAB demo image
I = imread('coins.png');

% 2. Define Initial Mask
% The algorithm needs a starting point. We create a rectangle slightly
% smaller than the image border. The curve will shrink/expand from here.
mask = zeros(size(I));
mask(10:end-10, 10:end-10) = 1;

% 3. Run Active Contours
% We run the algorithm for different numbers of iterations to visualize the process.

% 100 Iterations: The curve starts shrinking but hasn't separated objects yet.
bw_100 = activecontour(I, mask, 100, 'Chan-Vese');

% 300 Iterations: The curve begins to snap around individual objects.
bw_300 = activecontour(I, mask, 300, 'Chan-Vese');

% 500 Iterations: The curve has fully tightened around the coins.
bw_500 = activecontour(I, mask, 500, 'Chan-Vese');

% 4. Visualization
figure('Name', 'Task 5: Active Contour Evolution (0-500)', ...
'NumberTitle', 'off', ...
'Position', [50, 100, 1600, 400]);

% --- Original + Initial Mask ---
subplot(1, 4, 1);
imshow(I); hold on;
visboundaries(mask, 'Color', 'b', 'LineWidth', 2);
title({'1. Start', '(Initial Blue Mask)'}, 'FontSize', 11);

% --- 100 Iterations ---
subplot(1, 4, 2);
imshow(I); hold on;
visboundaries(bw_100, 'Color', 'y', 'LineWidth', 2);
title({'2. 100 Iterations', '(Under-segmented)'}, 'FontSize', 11);

% --- 300 Iterations ---
subplot(1, 4, 3);
imshow(I); hold on;
visboundaries(bw_300, 'Color', 'r', 'LineWidth', 2);
title({'3. 300 Iterations', '(Converged)'}, 'FontSize', 11, 'FontWeight', 'bold');

% --- 500 Iterations ---
subplot(1, 4, 4);
imshow(I); hold on;
visboundaries(bw_500, 'Color', 'g', 'LineWidth', 2);
title({'4. 500 Iterations', '(Stable / Tight Fit)'}, 'FontSize', 11);
</syntaxhighlight>

== Analysis of Results ==

The active contour is an iterative process.
# '''Initialization:''' We start with a generic box (blue). This is the initial guess.
# '''Evolution:''' As iterations proceed, the box shrinks.
# '''Topology Change:''' A key feature of the level-set implementation (used in Chan-Vese) is that the curve can split. Notice how the single blue box eventually splits into multiple separate circles (red/green) to wrap around each coin individually.
# '''Convergence:''' At 500 iterations, the contours stop moving because the energy function has reached a minimum—the regions inside the circles are bright (coins) and the region outside is dark (background).

[[File:Model based segmentation.png|center|1000px]]

== Key MATLAB Functions ==

* <code>activecontour(I, mask, n, method)</code>: Evolves the segmentation.
** <code>n</code>: Number of iterations.
** <code>method</code>: 'Chan-Vese' (region-based) or 'edge' (gradient-based).
* <code>visboundaries</code>: A helper function to overlay binary mask boundaries onto the original image for visualization.

Image Processing: Model based segmentation - Versionsgeschichte

Ajay.paul@stud.hshl.de am 5. März 2026 um 13:23 Uhr