Global Interactions in Random Field Models: A Potential Function Ensuring Connectedness

Markov random field (MRF) models, including conditional random field models, are popular in computer vision. However, in order to be computationally tractable, they are limited to incorporating only local interactions and cannot model global properties such as connectedness, which is a potentially useful high-level prior for object segmentation. In this work, we overcome this limitation by deriving a potential function that forces the output labeling to be connected and that can naturally be used in the framework of recent maximum a posteriori (MAP)-MRF linear program (LP) relaxations. Using techniques from polyhedral combinatorics, we show that a provably strong approximation to the MAP solution of the resulting MRF can still be found efficiently by solving a sequence of max-flow problems. The efficiency of the inference procedure also allows us to learn the parameters of an MRF with global connectivity potentials by means of a cutting plane algorithm. We experimentally evaluate our a...

• Type: Journal
• Year: 2010
• Where: SIAMIS
• Authors: Sebastian Nowozin, Christoph H. Lampert
• Keywords: Potential Functions, Random Field Models, Random Fields, SIAMIS 2010