The IEEE Conference on Computer Vision and Pattern Recognition (CVPR) is one of the largest conferences in the field of computer vision and image processing, with over 3600 attendees and more than 1800 submissions.
In the paper, we introduce a method for approximating hard variational nonconvex problems using convex problems, for which efficient numerical solvers exist. This allows to use more powerful nonconvex image models, reducing the risk of only being able to find a suboptimal solution. In contrast to existing methods, our approach greatly reduces the memory and computation time required, often by a factor of 10 or more.
Abstract:
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.
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See Jan Lellmann's publication page for the full PDF and presentation.
