Newton-type Methods for Inference in Higher-Order Markov Random Fields

Hariprasad Kannan (1, 2) , Nikos Komodakis (3, 4) , Nikos Paragios (1, 2)

1 CVN - Centre de vision numérique
2 GALEN - Organ Modeling through Extraction, Representation and Understanding of Medical Image Content
3 LIGM - Laboratoire d'Informatique Gaspard-Monge
4 ENPC - École des Ponts ParisTech

Linear programming relaxations are central to MAP inference in discrete Markov Random Fields. The ability to properly solve the Lagrangian dual is a critical component of such methods. In this paper, we study the benefit of using Newton-type methods to solve the Lagrangian dual of a smooth version of the problem. We investigate their ability to achieve superior convergence behavior and to better handle the ill-conditioned nature of the formulation, as compared to first order methods. We show that it is indeed possible to efficiently apply a trust region Newton method for a broad range of MAP inference problems. In this paper we propose a provably convergent and efficient framework that includes (i) excellent compromise between computational complexity and precision concerning the Hessian matrix construction, (ii) a damping strategy that aids efficient optimization , (iii) a truncation strategy coupled with a generic pre-conditioner for Conjugate Gradients, (iv) efficient sum-product computation for sparse clique potentials. Results for higher-order Markov Random Fields demonstrate the potential of this approach.

Mots clés: Markov Random Fields; Computer vision; MAP inference

Domaines: Vision par ordinateur et reconnaissance de formes [cs.CV]; Logiciel mathématique [cs.MS]; Analyse numérique [cs.NA]

Hariprasad Kannan, Nikos Komodakis, Nikos Paragios. Newton-type Methods for Inference in Higher-Order Markov Random Fields. IEEE International Conference on Computer Vision and Pattern Recognition, Jul 2017, Honolulu, United States. pp.7224 - 7233. ⟨hal-01580862⟩