In this paper, we introduce a higher-order MRF optimization
framework. On the one hand, it is very general;
we thus use it to derive a generic optimizer that can be applied
to almost any higher-order MRF and that provably
optimizes a dual relaxation related to the input MRF problem.
On the other hand, it is also extremely flexible and
thus can be easily adapted to yield far more powerful algorithms
when dealing with subclasses of high-order MRFs.
We thus introduce a new powerful class of high-order potentials,
which are shown to offer enough expressive power
and to be useful for many vision tasks. To address them, we
derive, based on the same framework, a novel and extremely
efficient message-passing algorithm, which goes beyond the
aforementioned generic optimizer and is able to deliver almost
optimal solutions of very high quality. Experimental
results on vision problems demonstrate the extreme effectiveness
of our approach. For instance, we show that in
some cases w...