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.
|Title of host publication
|2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
|Number of pages
|Published - 01.06.2016
|2016 IEEE Conference on Computer Vision and Pattern Recognition - Las Vegas, United States
Duration: 27.06.2016 → 30.06.2016