SWE 423: Multimedia Systems

Project #1: Image Segmentation Using Graph Theory

A UNIFIED METHOD FOR SEGMENTATION AND EDGE

DETECTION USING GRAPH THEORY

0. J . M o r r i s

M. de J. Lee

A. G. Constantinides.Signal Processing Section,

Department o f Electrical Engineering ,

Imperial College, London SW7 2BT.

Graph Theoretic Principles for Image Analysis

• Mapping Images onto Graphs– 4-neighbourhood– 8-neighbourhood

• The Shortest [Minimal] Spanning Trees (SST)

• SST-Based Segmentation of Images

SST-based Segmentation Algorithm

Algorithm SST

Input: A gray-scale image with P pixels and number R

Output: An image segmented into R regions

1. Map the image onto a primal weighted graph.

2. Find an SST of the graph.

3. Cut the SST at the R – 1 most costly edges.

4. Assign the average tree vertex weight to each vertex in each tree in the forest

5. Map the partition onto a segmentation image

Recursive Shortest Spanning Tree Algorithm

Algorithm RSSTInput: A gray-scale image with P pixels and number ROutput: An image segmented into R regions1. Map the image onto a primal weighted graph.2. For I = P2 downto R1 do:

2.1. Find an SST of the graph.2.2. Cut the SST at the I most costly edges.2.3. Assign the average tree vertex weight to each vertex in

each tree in the forest2.4. Re-evaluate the graph edge weights

3. Map the partition back onto a segmentation image.