Global Connectivity Potentials for Random Field Models
Sebastian Nowozin and Christoph Lampert
In: IEEE Computer Vision and Pattern Recognition (CVPR), Miami, FL(2009).
Markov random eld (MRF, CRF) models are popular in
computer vision. However, in order to be computationally
tractable they are limited to incorporate only local inter-
actions and cannot model global properties, such as con-
nectedness, 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 efciently by solving
a sequence of max-ow problems. The efciency of the in-
ference 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 al-
gorithm on both synthetic data and on the challenging seg-
mentation task of the PASCAL VOC 2008 data set. We show
that in both cases the addition of a connectedness prior sig-
nicantly reduces the segmentation error.