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Efficient Inference of Continuous Markov Random Fields with Polynomial Potentials
Shenlong Wang · Alex Schwing · Raquel Urtasun

Thu Dec 11 11:00 AM -- 03:00 PM (PST) @ Level 2, room 210D

In this paper, we prove that every multivariate polynomial with even degree can be decomposed into a sum of convex and concave polynomials. Motivated by this property, we exploit the concave-convex procedure to perform inference on continuous Markov random fields with polynomial potentials. In particular, we show that the concave-convex decomposition of polynomials can be expressed as a sum-of-squares optimization, which can be efficiently solved via semidefinite programming. We demonstrate the effectiveness of our approach in the context of 3D reconstruction, shape from shading and image denoising, and show that our approach significantly outperforms existing approaches in terms of efficiency as well as the quality of the retrieved solution.

Author Information

Shenlong Wang (University of Toronto)
Alex Schwing (University of Illinois at Urbana-Champaign)
Raquel Urtasun (University of Toronto)

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