Sublabel-Accurate Convex Relaxation of Vectorial Multilabel Energies

Sublabel - Accurate Convex Relaxation of Vectorial Multilabel Energies – Supplementary Material –

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...

Convex Relaxation for Multilabel Problems with Product Label Spaces

Convex relaxations for continuous multilabel problems have attracted a lot of interest recently [1–5]. Unfortunately, in previous methods, the runtime and memory requirements scale linearly in the total number of labels, making them very inefficient and often unapplicable for problems with higher dimensional label spaces. In this paper, we propose a reduction technique for the case that the lab...

Convex Relaxation of Vectorial Problems with Coupled Regularization

We propose convex relaxations for nonconvex energies on vector-valued functions which are tractable yet as tight as possible. In contrast to existing relaxations, we can handle the combination of nonconvex data terms with coupled regularizers such as l-regularizers. The key idea is to consider a collection of hypersurfaces with a relaxation that takes into account the entire functional rather t...

Nonmetric Priors for Continuous Multilabel Optimization

We propose a novel convex prior for multilabel optimization which allows to impose arbitrary distances between labels. Only symmetry, d(i, j) ≥ 0 and d(i, i) = 0 are required. In contrast to previous grid based approaches for the nonmetric case, the proposed prior is formulated in the continuous setting avoiding grid artifacts. In particular, the model is easy to implement, provides a convex re...