The concept of graph cuts is by now a standard method
for all sorts of low level vision problems. Its popularity is
largely due to the fact that globally or near globally optimal
solutions can be computed using efficient max flow
algorithms. On the other hand it has been observed that
this method may suffer from metrication errors. Recent
work has begun studying continuous versions of graph cuts,
which give smaller metrication errors. Another advantage
is that continuous cuts are straightforward to parallelize.
In this paper we extend the class of functionals that can
be optimized in the continuous setting to include anisotropic
TV-norms. We show that there is a so called coarea formula
for these functionals making it possible to minimize them by
solving a convex problem. We also show that the concept
of α-expansion moves can be reformulated to fit the continuous
formulation, and we derive approximation bounds in
analogy with the discrete case. A continuous version of ...
Carl Olsson, Martin Byr¨od, Niels Chr. Overgaard,