Matching delaunay graphs

Andrew M. Finch, Richard C. Wilson, Edwin R. Hancock

Abstract: This paper describes a Bayesian framework for matching Delaunay triangulations. Relational structures of this sort are ubiquitous in intermediate level computer vision, being used to represent both Voronoi tessellations of the image plane and volumetric surface data. Our matching process is realised in terms of probabilistic relaxation. The novelty of our method stems from its use of a support function specified in terms of face-units of the graphs under match. In this way, we draw on more expressive constraints than is possible at the level of edge-units alone. In order to apply this new relaxation process to the matching of realistic imagery requires a model of the compatibility between faces of the data and model graphs. We present a particularly simple compatibility model that is entirely devoid of free parameters. It requires only knowledge of the numbers of nodes, edges and faces in the model graph. The resulting matching scheme is evaluated on radar images and compared with its edge-based counterpart. We establish the operational limits and noise sensitivity on the matching of random-dot patterns.