On regularity properties of a surface growth model

We show local higher integrability of derivative of a suitable weak solution to the surface growth model, provided a scale-invariant quantity is locally bounded. If additionally our scale-invariant quantity is small, we prove local smoothness of solutions.

Clustering driving styles via image processing

It has become of key interest in the insurance industry to understand and extract information from telematics car driving data. Telematics car driving data of individual car drivers can be summarised in so-called speed–acceleration heatmaps. The aim of this study is to cluster such speed–acceleration heatmaps to different categories by analysing similarities and differences in these heatmaps. Making use of local smoothness properties, we propose to process these heatmaps as RGB images. Clustering can then be achieved by involving supervised information via a transfer learning approach using the pre-trained AlexNet to extract discriminative features. The K-means algorithm is then applied on these extracted discriminative features for clustering. The experiment results in an improvement of heatmap clustering compared to classical approaches.

Multi People Tracking using Related Motion Patterns Based on Particles

Many state-of-the-art approaches to people tracking rely on detecting them in each frame independently, grouping detections into short but reliable trajectory segments, and then further grouping them into full trajectories. This grouping typically relies on imposing local smoothness constraints but almost never on enforcing more global constraints on the trajectories. In this paper, we propose an approach to imposing global consistency by first inferring behavioral patterns from the ground truth and then using them to guide the tracking algorithm. When used in conjunction with severalstate-of-the-art algorithms, this further increases their already good performance. Furthermore, we propose an unsupervised scheme that yields almost similar improvements without the need for ground truth

Adaptive isogeometric boundary element methods with local smoothness control

In the frame of isogeometric analysis, we consider a Galerkin boundary element discretization of the hyper-singular integral equation associated with the 2D Laplacian. We propose and analyze an adaptive algorithm which locally refines the boundary partition and, moreover, steers the smoothness of the NURBS ansatz functions across elements. In particular and unlike prior work, the algorithm can increase and decrease the local smoothness properties and hence exploits the full potential of isogeometric analysis. We prove that the new adaptive strategy leads to linear convergence with optimal algebraic rates. Numerical experiments confirm the theoretical results. A short appendix comments on analogous results for the weakly-singular integral equation.

Local Smoothness of Graph Signals

Analysis of vertex-varying spectral content of signals on graphs challenges the assumption of vertex invariance and requires the introduction of vertex-frequency representations as a new tool for graph signal analysis. Local smoothness, an important parameter of vertex-varying graph signals, is introduced and defined in this paper. Basic properties of this parameter are given. By using the local smoothness, an ideal vertex-frequency distribution is introduced. The local smoothness estimation is performed based on several forms of the vertex-frequency distributions, including the graph spectrogram, the graph Rihaczek distribution, and a vertex-frequency distribution with reduced interferences. The presented theory is illustrated through numerical examples.