Image Segmentation by Dominant Sets

We develop a framework for the image segmentation problem based on a new graph-theoretic formulation of clustering. The approach is motivated by the analogies between the intuitive concept of a cluster and that of a dominant set of vertices, a novel notion that generalizes that of a maximal complete subgraph to edge-weighted graphs. We also establish a correspondence between dominant sets and the extrema of a quadratic form over the standard simplex, thereby allowing us the use of continuous optimization techniques such as replicator dynamics from evolutionary game theory. Such systems are attractive as can easily be implemented in a parallel network of locally interacting computational units, and offer the advantage of biological plausibility. We present experimental results on real-world images which show the effectiveness of the approach.