Subdivision Directional Fields

We present a novel linear subdivision scheme for face-based tangent directional fields on triangle meshes. Our subdivision scheme is based on a novel coordinate-free representation of directional fields as halfedge-based scalar quantities, bridging the finite-element representation with discrete exterior calculus. By commuting with differential operators, our subdivision is structure-preserving: it reproduces curl-free fields precisely, and reproduces divergence-free fields in the weak sense. Moreover, our subdivision scheme directly extends to directional fields with several vectors per face by working on the branched covering space. Finally, we demonstrate how our scheme can be applied to directional-field design, advection, and robust earth mover's distance computation, for efficient and robust computation

Disparity and Optical Flow Partitioning Using Extended Potts Priors

This paper addresses the problems of disparity and optical flow partitioning based on the brightness invariance assumption. We investigate new variational approaches to these problems with Potts priors and possibly box constraints. For the optical flow partitioning, our model includes vector-valued data and an adapted Potts regularizer. Using the notation of asymptotically level stable functions we prove the existence of global minimizers of our functionals. We propose a modified alternating direction method of minimizers. This iterative algorithm requires the computation of global minimizers of classical univariate Potts problems which can be done efficiently by dynamic programming. We prove that the algorithm converges both for the constrained and unconstrained problems. Numerical examples demonstrate the very good performance of our partitioning method

Beyond Correlation Filters: Learning Continuous Convolution Operators for Visual Tracking

Discriminative Correlation Filters (DCF) have demonstrated excellent performance for visual object tracking. The key to their success is the ability to efficiently exploit available negative data by including all shifted versions of a training sample. However, the underlying DCF formulation is restricted to single-resolution feature maps, significantly limiting its potential. In this paper, we go beyond the conventional DCF framework and introduce a novel formulation for training continuous convolution filters. We employ an implicit interpolation model to pose the learning problem in the continuous spatial domain. Our proposed formulation enables efficient integration of multi-resolution deep feature maps, leading to superior results on three object tracking benchmarks: OTB-2015 (+5.1% in mean OP), Temple-Color (+4.6% in mean OP), and VOT2015 (20% relative reduction in failure rate). Additionally, our approach is capable of sub-pixel localization, crucial for the task of accurate feature point tracking. We also demonstrate the effectiveness of our learning formulation in extensive feature point tracking experiments. Code and supplementary material are available at http://www.cvl.isy.liu.se/research/objrec/visualtracking/conttrack/index.html.Comment: Accepted at ECCV 201

Quantum Algorithm for SAT Problem and Quantum Mutual Entropy

It is von Neumann who opened the window for today's Information epoch. He defined quantum entropy including Shannon's information more than 20 years ahead of Shannon, and he introduced a concept what computation means mathematically. In this paper I will report two works that we have recently done, one of which is on quantum algorithum in generalized sense solving the SAT problem (one of NP complete problems) and another is on quantum mutual entropy properly describing quantum communication processes.Comment: 19 pages, Proceedings of the von Neumann Centennial Conference: Linear Operators and Foundations of Quantum Mechanics, Budapest, Hungary, 15-20 October, 200