Local uniqueness of vortices for 2D steady Euler flow

We study the steady planar Euler flow in a bounded simply connected domain, where the vortex function is $f=t_+^p$ with $p>0$ and the vorticity strength is prescribed. By studying the location and local uniqueness of vortices, we prove that the vorticity method and the stream function method actually give the same solution. We also show that if the vorticity of flow is located near an isolated minimum point and non-degenerate critical point of the Kirchhoff-Routh function, it must be stable in the nonlinear sense.Comment: 47 pages. arXiv admin note: text overlap with arXiv:1703.0986

End-to-end Flow Correlation Tracking with Spatial-temporal Attention

Discriminative correlation filters (DCF) with deep convolutional features have achieved favorable performance in recent tracking benchmarks. However, most of existing DCF trackers only consider appearance features of current frame, and hardly benefit from motion and inter-frame information. The lack of temporal information degrades the tracking performance during challenges such as partial occlusion and deformation. In this work, we focus on making use of the rich flow information in consecutive frames to improve the feature representation and the tracking accuracy. Firstly, individual components, including optical flow estimation, feature extraction, aggregation and correlation filter tracking are formulated as special layers in network. To the best of our knowledge, this is the first work to jointly train flow and tracking task in a deep learning framework. Then the historical feature maps at predefined intervals are warped and aggregated with current ones by the guiding of flow. For adaptive aggregation, we propose a novel spatial-temporal attention mechanism. Extensive experiments are performed on four challenging tracking datasets: OTB2013, OTB2015, VOT2015 and VOT2016, and the proposed method achieves superior results on these benchmarks.Comment: Accepted in CVPR 201