Energy Minimization for Linear Envelope MRFs

Markov random fields with higher order potentials have emerged as a powerful model for several problems in computer vision. In order to facilitate their use, we propose a new representation for higher order potentials as upper and lower envelopes of linear functions. Our representation concisely models several commonly used higher order potentials, thereby providing a unified framework for minimizing the corresponding Gibbs energy functions. We exploit this framework by converting lower envelope potentials to standard pairwise functions with the addition of a small number of auxiliary variables. This allows us to minimize energy functions with lower envelope potentials using conventional algorithms such as BP, TRW and α-expansion. Furthermore, we show how the minimization of energy functions with upper envelope potentials leads to a difficult minmax problem. We address this difficulty by proposing a new message passing algorithm that solves a linear programming relaxation of the ...

• Type: Conference
• Year: 2010
• Where: CVPR
• Authors: Pushmeet Kohli, M. Pawan Kumar
• Keywords: Computer Vision, CVPR 2010, Envelope Potentials, Lower Envelope, Lower Envelope Potentials