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Linear Programming, Belief Propagation and Low Level Vision
Yair Weiss
In: Emphasis Week on Learning and Inference in Low and Mid Level Vision, 23 - 25 February 2005, Berkeley, CA.
AbstractLinear Programming (LP) relaxations are a standard method in computer
science for approximately solving combinatorial optimizations. I will
briefly describe our failed attempts to apply LP relaxations to problems
in low-level vision. The number of variables and constraints is simply
too much for general purpose LP solvers. I will then describe a recent
surprising result by Wainwright, Jaakkola and Willsky (2003) that show
how to solve LP relaxations using a variant of Belief Propagation. Our
theoretical contribution is an extension of the Wainwright et al. result
for relaxation results that are partly integer and partly fractional.
Experimentally, we use our results to find the global optimum of a
widely used energy function for stereo vision. On a standard benchmark
set for which many approximation algorithms have been applied, we are
able to find the global optimum in a few minutes.
Joint work with Talya Meltzer and Chen Yanover. [Edit]
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