Graphical Models and Point Pattern Matching
- Tiberio S. Caetano, National ICT Australia and the Australian National University
- Terry Caelli, National ICT Australia and the Australian National University
- Dale Schuurmans, AICML
- Dante A.C. Barone, Instituto de Informatica, Universidade Federal do Rio Grande do Sul
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 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.
Citation
T. Caetano, T. Caelli, D. Schuurmans, D. Barone. "Graphical Models and Point Pattern Matching". IEEE Transactions on Pattern Analysis and Machine Intelligence, 28(10), January 2006.| Keywords: | Point pattern matching, graph matching, graphical models, Markov random fields, Junction Tree, machine learning |
| Category: | In Journal |
BibTeX
@article{Caetano+al:IEEETransactionsPAMI06,
author = {Tiberio S. Caetano and Terry Caelli and Dale Schuurmans and Dante
A.C. Barone},
title = {Graphical Models and Point Pattern Matching},
Volume = "28",
Number = "10",
journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
year = 2006,
}Last Updated: August 16, 2007Submitted by Russ Greiner
