Global connectivity potentials for random field models

Markov random field (MRF, CRF) models are popular in computer vision. However, in order to be computationally tractable they are limited to incorporate 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 enforces the output labeling to be connected and that can naturally be used in the framework of recent MAP-MRF LP relaxations. Using techniques from polyhedral combinatorics, we show that a provably tight 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 a MRF with global connectivity potentials by means of a cutting plane algorithm. We experimentally evaluate our algorithm on both synthetic data and on the challenging segmentation task of the PASCAL VOC 2008 data set. We show that in both cases the addition of a connectedness prior significantly reduces the segmentation error.