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Abstract:
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.
