Weighted Minimal Hypersurfaces and Their Applications in Computer Vision

Many interesting problems in computer vision can be formulated as a minimization problem for an {\em energy functional}. If this functional is given as an integral of a scalar-valued weight function over an unknown hypersurface, then the minimal surface we are looking for can be determined as a solution of the functional's Euler-Lagrange equation. This paper deals with a general class of weight functions that may depend on the surface point and normal. By making use of a mathematical tool called {\em the method of the moving frame}, we are able to derive the Euler-Lagrange equation in arbitrary-dimensional space and without the need for any surface parameterization. Our work generalizes existing proofs, and we demonstrate that it yields the correct evolution equations for a variety of previous computer vision techniques which can be expressed in terms of our theoretical framework. In practical applications, the surface evolution which converges to a solution of the Euler-Lagrange equation can be implemented using level set techniques. The well-known transition to a level set evolution equation, which we briefly review in this paper, works in the general case as well. That way, problems involving minimal hypersurfaces in dimensions higher than three, which were previously impossible to solve in practice, can now be introduced and handled by generalized versions of existing algorithms. As one example, we sketch a novel idea how to reconstruct temporally coherent geometry from multiple video streams

The Sixth Visual Object Tracking VOT2018 Challenge Results

The Visual Object Tracking challenge VOT2018 is the sixth annual tracker benchmarking activity organized by the VOT initiative. Results of over eighty trackers are presented; many are state-of-the-art trackers published at major computer vision conferences or in journals in the recent years. The evaluation included the standard VOT and other popular methodologies for short-term tracking analysis and a “real-time” experiment simulating a situation where a tracker processes images as if provided by a continuously running sensor. A long-term tracking subchallenge has been introduced to the set of standard VOT sub-challenges. The new subchallenge focuses on long-term tracking properties, namely coping with target disappearance and reappearance. A new dataset has been compiled and a performance evaluation methodology that focuses on long-term tracking capabilities has been adopted. The VOT toolkit has been updated to support both standard short-term and the new long-term tracking subchallenges. Performance of the tested trackers typically by far exceeds standard baselines. The source code for most of the trackers is publicly available from the VOT page. The dataset, the evaluation kit and the results are publicly available at the challenge website (http://votchallenge.net).Funding agencies: Slovenian research agencySlovenian Research Agency - Slovenia [P2-0214, P2-0094, J2-8175]; Czech Science FoundationGrant Agency of the Czech Republic [GACR P103/12/G084]; WASP; VR (EMC2); SSF (SymbiCloud); SNIC; AIT Strategic Research Programme 2017 Visua</p