1. SWE 423: Multimedia Systems Project #1: Image Segmentation Using Graph Theory

2. 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.

3. 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

4. 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

5. Recursive Shortest Spanning Tree Algorithm Algorithm RSST 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. For I = P  2 downto R  1 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 forest 2.4. Re-evaluate the graph edge weights 3. Map the partition back onto a segmentation image.