Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The image segmentation problem is concerned with partitioning an image into multiple regions according to some homogeneity criterion. This article is primarily concerned with graph theoretic approaches to image segmentation.The set of points in an arbitrary feature space can be represented as a weighted undirected complete graph G = (V, E), where the nodes of the graph are the points in the feature space. The weight wij of an edge (i, j) \in E is a function of the similarity between the nodes i and j. In this context, we can formulate the image segmentation problem as a graph partitioning problem that asks for a partition V_1, \cdots, V_k of the vertex set V, where, according to some measure, the vertices in any set Vi have high similarity, and the vertices in two different sets Vi,Vj have low similarity.
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