Probabilistic graph and hypergraph matching

We consider the problem of finding a matching between two sets of features, given complex relations among them, going beyond pairwise. Each feature set is modeled by a hypergraph where the complex relations are represented by hyper-edges. A match between the feature sets is then modeled as a hypergraph matching problem. We derive the hyper-graph matching problem in a probabilistic setting represented by a convex optimization. First, we formalize a soft matching criterion that emerges from a probabilistic interpretation of the problem input and output, as opposed to previous methods that treat soft matching as a mere relaxation of the hard matching problem. Second, the model induces an algebraic relation between the hyper-edge weight matrix and the desired vertex-to-vertex probabilistic matching. Third, the model explains some of the graph matching normalization proposed in the past on a heuristic basis such as doubly stochastic normalizations of the edge weights. A key benefit of the ...

• Type: Conference
• Year: 2008
• Where: CVPR
• Authors: Ron Zass, Amnon Shashua
• Keywords: Computer Vision, CVPR 2008, Graph Matching Normalization, Hard Matching Problem, Hyper-graph Matching Problem, Hypergraph Matching Problem, Vertex-to-vertex Probabilistic Matching