Image Processing: Data based segmentation

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.

Theoretical Background

K-Means Clustering

K-Means is an unsupervised machine learning algorithm used to partition data into $k$ distinct clusters.

1. Initialization: Select $k$ random points as initial cluster centroids.
2. Assignment: Assign every pixel in the image to the nearest centroid based on a distance metric (usually Euclidean distance).
3. Update: Recalculate the centroids by taking the mean of all pixels assigned to each cluster.
4. 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

% 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), ')']);

Analysis of Results

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

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 'NumAttempts', 3, MATLAB runs the algorithm 3 times with different random starting points and returns the result with the lowest total error summation.

Key MATLAB Functions

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