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# lecture15 - Graph Theoretical Techniques for Image...

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1 Graph Theoretical Techniques for Image Segmentation Region Segmentation

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2 Region Segmentation Find sets of pixels, such that All pixels in region i satisfy some constraint of similarity. n R R R , , , 2 1 I R i i = ± = 2200 j i R R j i , Graph A graph G(V,E) is a triple consisting of a vertex set V(G) an edge set E(G) and a relation that associates with each edge two vertices called its end points.
3 Path A path is a sequence of edges e1, e2, e3, … en. Such that each (for each i>2 & i<n) edge ei is adjacent to e(i+1) and e(i-1). e1 is only adjacent to e2 and en is only adjacent to e(n-1) A graph G is connected if there is a path from every vertex to every other vertex in G . A graph G that is not connected is called disconnected graph.

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Graphs Representations a e d c b ± ² ³ ³ ³ ³ ³ ³ ´ µ 0 1 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 1 0 Adjacency Matrix: W Weighted Graphs and Their Representations a e d c b ± ² ³ ³ ³ ³ ³ ³ ´ µ 0 1
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lecture15 - Graph Theoretical Techniques for Image...

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