4 research outputs found

    Sublabel-Accurate Relaxation of Nonconvex Energies

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    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

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    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
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