Graph matching with hierarchical discrete relaxation

Our aim in this paper is to develop a Bayesian framework for matching hierarchical relational models. Such models are widespread in computer vision. The framework that we adopt for this study is provided by iterative discrete re-laxation. Here the aim is to assign the discrete matches so as to optimise a global cost function that draws information concerning the consistency of match from dierent levels of the hierarchy. Our Bayesian development naturally dis-tinguishes between intra-level and inter-level constraints. This allows the impact of reassigning a match to be assessed not only at its own (or peer) level of representation, but also upon its parents and children in the hierarchy. We illustrate the eectiveness of the technique in the matching of line-segment groupings in synthetic aperture radar (SAR) images o