Beyond Trees: MRF Inference via Outer-Planar Decomposition

Maximum a posteriori (MAP) inference in Markov Random Fields (MRFs) is an NP-hard problem, and thus research has focussed on either finding efficiently solvable subclasses (e.g. trees), or approximate algorithms (e.g. Loopy Belief Propagation (BP) and Tree-reweighted (TRW) methods). This paper presents a unifying perspective of these approximate techniques called "Decomposition Methods". These are methods that decompose the given problem over a graph into tractable subproblems over subgraphs and then employ message passing over these subgraphs to merge the solutions of the subproblems into a global solution. This provides a new way of thinking about BP and TRW as successive steps in a hierarchy of decomposition methods. Using this framework, we take a principled first step towards extending this hierarchy beyond trees. We leverage a new class of graphs amenable to exact inference, called outerplanar graphs, and propose an approximate inference algorithm called Outer-Planar D...

• Type: Conference
• Year: 2010
• Where: CVPR
• Authors: Dhruv Batra, Andrew Gallagher, Devi Parikh, Tsuhan Chen
• Keywords: Approximate, Approximate Inference Algorithm, Computer Vision, CVPR 2010, Decomposition Methods