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Abstract: A recent paper \cite{CaeCaeSchBar06} proposed a provably optimal, polynomialtime method for performing near-isometric point pattern matching by means ofexact probabilistic inference in a chordal graphical model. Their fundamentalresult is that the chordal graph in question is shown to be globally rigid,implying that exact inference provides the same matching solution as exactinference in a complete graphical model. This implies that the algorithm isoptimal when there is no noise in the point patterns. In this paper, we presenta new graph which is also globally rigid but has an advantage over the graphproposed in \cite{CaeCaeSchBar06}: its maximal clique size is smaller,rendering inference significantly more efficient. However, our graph is notchordal and thus standard Junction Tree algorithms cannot be directly applied.Nevertheless, we show that loopy belief propagation in such a graph convergesto the optimal solution. This allows us to retain the optimality guarantee inthe noiseless case, while substantially reducing both memory requirements andprocessing time. Our experimental results show that the accuracy of theproposed solution is indistinguishable from that of \cite{CaeCaeSchBar06} whenthere is noise in the point patterns.



Author: Julian J. McAuley, Tiberio S. Caetano, Marconi S. Barbosa

Source: https://arxiv.org/



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