Graphical Models and Point Pattern Matching

This paper describes a novel solution to the rigid point pattern matching problem in Euclidean spaces of any dimension. Although we assume rigid motion, jitter is allowed. We present a non-iterative, polynomial time algorithm that is guaranteed to find an optimal solution for the noiseless case. First we model point pattern matching as a weighted graph matching problem, where weights correspond to Euclidean distances between nodes. We then formulate graph matching as a problem of finding a maximum probability configuration in a Graphical Model. By using graph rigidity arguments, we prove that a sparse Graphical Model yields equivalent results to the fully connected model in the noiseless case. This allows us to obtain an efficient Junction Tree algorithm that runs in polynomial time and is provably optimal for exact matching between noiseless point sets. For inexact matching, we can still apply the same algorithm to find approximately optimal solutions. Experimental results obtained b...

• Type: Journal
• Year: 2006
• Where: PAMI
• Authors: Tibério S. Caetano, Terry Caelli, Dale Schuurmans, Dante Augusto Couto Barone
• Keywords: Noiseless Case, Optimal Solutions, PAMI 2006, Polynomial Time