4 research outputs found
Sublabel-Accurate Relaxation of Nonconvex Energies
We propose a novel spatially continuous framework for convex relaxations
based on functional lifting. Our method can be interpreted as a
sublabel-accurate solution to multilabel problems. We show that previously
proposed functional lifting methods optimize an energy which is linear between
two labels and hence require (often infinitely) many labels for a faithful
approximation. In contrast, the proposed formulation is based on a piecewise
convex approximation and therefore needs far fewer labels. In comparison to
recent MRF-based approaches, our method is formulated in a spatially continuous
setting and shows less grid bias. Moreover, in a local sense, our formulation
is the tightest possible convex relaxation. It is easy to implement and allows
an efficient primal-dual optimization on GPUs. We show the effectiveness of our
approach on several computer vision problems
Submodular relaxation for inference in Markov random fields
In this paper we address the problem of finding the most probable state of a
discrete Markov random field (MRF), also known as the MRF energy minimization
problem. The task is known to be NP-hard in general and its practical
importance motivates numerous approximate algorithms. We propose a submodular
relaxation approach (SMR) based on a Lagrangian relaxation of the initial
problem. Unlike the dual decomposition approach of Komodakis et al., 2011 SMR
does not decompose the graph structure of the initial problem but constructs a
submodular energy that is minimized within the Lagrangian relaxation. Our
approach is applicable to both pairwise and high-order MRFs and allows to take
into account global potentials of certain types. We study theoretical
properties of the proposed approach and evaluate it experimentally.Comment: This paper is accepted for publication in IEEE Transactions on
Pattern Analysis and Machine Intelligenc