Sublabel–Accurate Relaxation of Nonconvex Energies

T. Móllenhoff, E. Laude, M. Moeller, J. Lellmann, D. Cremers


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 - see Fig. 1. 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.
Original languageEnglish
Title of host publication2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
Number of pages9
Publication date01.06.2016
ISBN (Print)978-1-4673-8852-8
ISBN (Electronic)978-1-4673-8851-1
Publication statusPublished - 01.06.2016
Event2016 IEEE Conference on Computer Vision and Pattern Recognition - Las Vegas, United States
Duration: 27.06.201630.06.2016


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