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arXiv · 1104.1204

Planar Cycle Covering Graphs

Julian Yarkony·Alexander T. Ihler·Charless C. Fowlkes
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Abstract

We describe a new variational lower-bound on the minimum energy configuration of a planar binary Markov Random Field (MRF). Our method is based on adding auxiliary nodes to every face of a planar embedding of the graph in order to capture the effect of unary potentials. A ground state of the resulting approximation can be computed efficiently by reduction to minimum-weight perfect matching. We show that optimization of variational parameters achieves the same lower-bound as dual-decomposition into the set of all cycles of the original graph. We demonstrate that our variational optimization converges quickly and provides high-quality solutions to hard combinatorial problems 10-100x faster than competing algorithms that optimize the same bound.

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Julian Yarkony, Alexander T. Ihler, Charless C. Fowlkes. 2011-04-06. Planar Cycle Covering Graphs. https://arxiv.org/abs/1104.1204

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