Grouping with Asymmetric Affinities: A Game-Theoretic Perspective

Pairwise grouping and clustering approaches have traditionally worked under the assumption that the similarities or compatibilities between the elements to be grouped are symmetric. However, asymmetric compatibilities arise naturally in many areas of computer vision and pattern recognition. Hence, there is a need for a new generic approach to clustering and grouping that can deal with asymmetries in the compatibilities. In this paper, we present a generic framework for grouping and clustering derived from a game-theoretic formalization of the competition between the hypotheses of group membership, and apply it to perceptual grouping. In the proposed approach groups correspond to evolutionary stable strategies, a classic notion in evolutionary game theory. We also provide a combinatorial characterization of the stable strategies, and, hence, of the elements that belong to a group. Experiments show that our approach outperforms both state-of-the-art clustering-based perceptual grouping approacheswith symmetric compatibilities, and other approaches explicitly designed to make use of asymmetric compatibilities.