title: Graphical models and point pattern matching.
abstract: 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 noniterative, 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 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 by our approach show improvements in accuracy over current methods, particularly when matching patterns of different sizes.
authors.affiliation: National ICT Australia, Locked Bag 8001, Canberra ACT 2601, Australia. Tiberio.Caetano@nicta.com.au
authors.forename: Tibério S
authors.initials: TS
authors.lastname: Caetano
authors.forename: Terry
authors.initials: T
authors.lastname: Caelli
authors.forename: Dale
authors.initials: D
authors.lastname: Schuurmans
authors.forename: Dante A C
authors.initials: DA
authors.lastname: Barone
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D003196:Computer Graphics; D003198:Computer Simulation; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods; D015233:Models, Statistical; D009716:Numerical Analysis, Computer-Assisted; D010363:Pattern Recognition, Automated / Q000379:methods*; D012815:Signal Processing, Computer-Assisted; D013382:Subtraction Technique