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	* <code>imsegkmeans</code>: A specialized function for image segmentation using K-Means (optimized for image data structures).		* <code>imsegkmeans</code>: A specialized function for image segmentation using K-Means (optimized for image data structures).
	* <code>imagesc</code>: Displays data as an image using the full range of the current colormap (useful for viewing label matrices).		* <code>imagesc</code>: Displays data as an image using the full range of the current colormap (useful for viewing label matrices).

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= Data-Based Segmentation: K-Means Clustering =

'''Data-Based Segmentation''' involves partitioning an image into distinct regions based purely on the statistical properties of the pixel data (such as color or intensity), without using a specific geometric model (like circles or lines).

This article explores how to segment a microscopic tissue image using the **K-Means Clustering** algorithm in the L*a*b* color space.

__TOC__

== Theoretical Background ==

=== K-Means Clustering ===
'''K-Means''' is an unsupervised machine learning algorithm used to partition data into <math>k</math> distinct clusters.
# '''Initialization:''' Select <math>k</math> random points as initial cluster centroids.
# '''Assignment:''' Assign every pixel in the image to the nearest centroid based on a distance metric (usually Euclidean distance).
# '''Update:''' Recalculate the centroids by taking the mean of all pixels assigned to each cluster.
# '''Repeat:''' Iterate steps 2 and 3 until the centroids stabilize (convergence).

=== Color Space Transformation ===
Standard RGB images mix color and lighting information, which can confuse segmentation algorithms.
* '''RGB (Red, Green, Blue):''' Not ideal for segmentation because color distance in RGB does not match human perception.
* '''L*a*b* (Lightness, a*, b*):''' A perceptually uniform color space.
** '''L*:''' Lightness (0 = Black, 100 = White).
** '''a*:''' Green to Red component.
** '''b*:''' Blue to Yellow component.
By ignoring the '''L*''' channel and clustering only on '''a*''' and '''b*''', we segment based purely on color, making the algorithm robust to lighting variations.

== MATLAB Implementation ==

The following MATLAB script demonstrates loading an image, converting color spaces, applying K-Means, and visualizing the result.

=== Code Logic ===

<syntaxhighlight lang="matlab">
% Data-Based Segmentation
% Algorithm: K-Means Clustering (imsegkmeans)
clc; clear; close all;

% 1. Load the Image
% 'hestain.png' is a standard MATLAB demo image of H&E stained tissue
I = imread('hestain.png');

% 2. Convert to L*a*b* (Feature Extraction)
% We transform RGB to L*a*b* to isolate color information.
lab_I = rgb2lab(I);

% Extract the a* and b* channels.
% These contain the color info (Red/Green/Blue/Yellow balance).
ab = lab_I(:,:,2:3);

% Convert to single precision for the K-Means algorithm calculation
ab = im2single(ab);

% 3. Run K-Means
% We choose k=3 because H&E stained images typically contain:
% 1. Purple (Nuclei)
% 2. Pink (Cytoplasm/Tissue)
% 3. White (Background)
k = 3;
pixel_labels = imsegkmeans(ab, k, 'NumAttempts', 3);

% 4. Visualization
figure('Name', 'Task 4: Segmentation Results', ...
'NumberTitle', 'off', ...
'Position', [100, 100, 1000, 500]);

% Show Original
subplot(1, 2, 1);
imshow(I);
title('Original Image');

% Show Segmentation Label Matrix
subplot(1, 2, 2);
imagesc(pixel_labels);
axis image;
colormap(gca, jet); % 'jet' gives distinct colors for 1, 2, and 3
colorbar;
title(['K-Means Clusters (k=', num2str(k), ')']);
</syntaxhighlight>

== Analysis of Results ==

The result, stored in <code>pixel_labels</code>, is a matrix of the same size as the image where every value is 1, 2, or 3.

[[Datei:Segmentation Results.png|center|600px]]

=== Interpretation ===
* '''Cluster 1:''' Typically corresponds to the white background (low a*, low b*).
* '''Cluster 2:''' Typically corresponds to the pink connective tissue (medium a*).
* '''Cluster 3:''' Typically corresponds to the purple nuclei (high a*, low b*).

Note: The specific label numbers (1, 2, 3) depend on random initialization and may swap between runs.

=== Why use 'NumAttempts'? ===
K-Means can get stuck in local minima depending on where the initial centroids are placed. By setting <code>'NumAttempts', 3</code>, MATLAB runs the algorithm 3 times with different random starting points and returns the result with the lowest total error summation.

== Key MATLAB Functions ==

* <code>rgb2lab</code>: Converts images from RGB to CIE L*a*b* color space.
* <code>imsegkmeans</code>: A specialized function for image segmentation using K-Means (optimized for image data structures).
* <code>imagesc</code>: Displays data as an image using the full range of the current colormap (useful for viewing label matrices).

Image Processing: Data based segmentation - Versionsgeschichte

Ajay.paul@stud.hshl.de am 5. März 2026 um 13:22 Uhr