A new graph-theoretic approach to clustering and segmentation

Authors:
Massimiliano Pavan;Marcello Pelillo
Affiliations:
Dipartimento di Infonnatica, Universita Ca' Foscari di Venezia, Venezia Mestre, Italy;Dipartimento di Infonnatica, Universita Ca' Foscari di Venezia, Venezia Mestre, Italy
Venue:
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Year:
2003

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Abstract

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 be coded in a few lines of any high-level programming language, can easily be implemented in a parallel network of locally interacting units, and offer the advantage of biological plausibility. We present experimental results on real-world images which show the effectiveness of the proposed approach.