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Issue No. 11 - November (2008 vol. 30)
ISSN: 0162-8828
pp: 2047-2054
Julian J. McAuley , NICTA, Canberra
Tibério S. Caetano , NICTA, Canberra
Marconi S. Barbosa , NICTA, Canberra
A recent paper \cite{CaeCaeSchBar06} proposed a provably optimal, polynomial time method for performing near-isometric point pattern matching by means of exact probabilistic inference in a chordal graphical model. Its fundamental result is that the chordal graph in question is shown to be \emph{globally rigid}, implying that exact inference provides the \emph{same} matching solution as exact inference in a complete graphical model. This implies that the algorithm is optimal when there is no noise in the point patterns. In this paper, we present a new graph which is also globally rigid but has an advantage over the graph proposed in \cite{CaeCaeSchBar06}: its maximal clique size is smaller, rendering inference significantly more efficient. However, this graph is not chordal and thus standard Junction Tree algorithms cannot be directly applied. Nevertheless, we show that loopy belief propagation in such a graph converges to the optimal solution. This allows us to retain the optimality guarantee in the noiseless case, while substantially reducing both memory requirements and processing time. Our experimental results show that the accuracy of the proposed solution is indistinguishable from that of \cite{CaeCaeSchBar06} when there is noise in the point patterns.
Point pattern matching, graph matching, graphical models, belief propagation, global rigidity, chordal graphs

T. S. Caetano, J. J. McAuley and M. S. Barbosa, "Graph Rigidity, Cyclic Belief Propagation, and Point Pattern Matching," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 30, no. , pp. 2047-2054, 2008.
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