Sublabel-Accurate Multilabeling Meets Product Label Spaces - Ye, Zhenzhang; Haefner, Bjoern; Quéau, Yvain; Möllenhoff, Thomas; Cremers, Daniel (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2021)
Functional lifting methods are a promising approach to determine optimal or near-optimal solutions to difficult nonconvex variational problems. Yet, they come with increased memory demands, limiting their practicability. To overcome this drawback, this paper presents a combination of two approaches designed to make liftings more scalable, namely product-space relaxations and sublabel-accurate discretizations. Our main contribution is a simple way to solve the resulting semi-infinite optimization problem with a sampling strategy. We show that despite its simplicity, our approach significantly outperforms baseline methods, in the sense that it finds solutions with lower energies given the same amount of memory. We demonstrate our empirical findings on the nonconvex optical flow and manifold-valued denoising problems.
CRIS-Team Scopus Importer:2023-03-08
Keywords: Convex relaxation; Global optimization; Manifold-valued problems; Variational methods