A Unified Multiscale Framework for Discrete Energy Minimization
This work addresses the computational bottleneck of discrete optimization in computer vision, offering a more efficient and application-independent solution, though it appears incremental relative to existing multiscale approaches.
The authors tackled the NP-hard problem of discrete energy minimization in computer vision by proposing a multiscale framework that constructs an energy pyramid directly from the energy itself, leading to improved results on challenging non-submodular energies compared to current methods.
Discrete energy minimization is a ubiquitous task in computer vision, yet is NP-hard in most cases. In this work we propose a multiscale framework for coping with the NP-hardness of discrete optimization. Our approach utilizes algebraic multiscale principles to efficiently explore the discrete solution space, yielding improved results on challenging, non-submodular energies for which current methods provide unsatisfactory approximations. In contrast to popular multiscale methods in computer vision, that builds an image pyramid, our framework acts directly on the energy to construct an energy pyramid. Deriving a multiscale scheme from the energy itself makes our framework application independent and widely applicable. Our framework gives rise to two complementary energy coarsening strategies: one in which coarser scales involve fewer variables, and a more revolutionary one in which the coarser scales involve fewer discrete labels. We empirically evaluated our unified framework on a variety of both non-submodular and submodular energies, including energies from Middlebury benchmark.