Functional Liftings of Vectorial Variational Problems with Laplacian Regularization

We propose a functional lifting-based convex relaxation of variational problems with Laplacian-based second-order regularization. The approach rests on ideas from the calibration method as well as from sublabel-accurate continuous multilabeling approaches, and makes these approaches amenable for variational problems with vectorial data and higher-order regularization, as is common in image processing applications. We motivate the approach in the function space setting and prove that, in the special case of absolute Laplacian regularization, it encompasses the discretization-first sublabel-accurate continuous multilabeling approach as a special case. We present a mathematical connection between the lifted and original functional and discuss possible interpretations of minimizers in the lifted function space. Finally, we exemplarily apply the proposed approach to 2D image registration problems.Comment: 12 pages, 3 figures; accepted at the conference "Scale Space and Variational Methods" in Hofgeismar, Germany 201

Building Scene Models by Completing and Hallucinating Depth and Semantics

Building 3D scene models has been a longstanding goal of computer vision. The great progress in depth sensors brings us one step closer to achieving this in a single shot. However, depth sensors still produce imperfect measurements that are sparse and contain holes. While depth completion aims at tackling this issue, it ignores the fact that some regions of the scene are occluded by the foreground objects. Building a scene model would therefore require to hallucinate the depth behind these objects. In contrast with existing methods that either rely on manual input, or focus on the indoor scenario, we introduce a fully-automatic method to jointly complete and hallucinate depth and semantics in challenging outdoor scenes. To this end, we develop a two-layer model representing both the visible information and the hidden one. At the heart of our approach lies a formulation based on the Mumford-Shah functional, for which we derive an effective optimization strategy. Our experiments evidence that our approach can accurately fill the large holes in the input depth maps, segment the different kinds of objects in the scene, and hallucinate the depth and semantics behind the foreground objects