Research on target tracking algorithm based on mean shift with adaptive bandwidth

The traditional mean shift algorithm used fixed kernels or symmetric kernel function, which will cause the target tracking lost or failure. The target tracking algorithm based on mean shift with adaptive bandwidth was proposed. Firstly, the signed distance constraint function was introduced to produce the anisotropic kernel function based on signed distance kernel function. This anisotropic kernel function satisfies that the value of the region function outside the target is zero, which provides accurate tracking window for the target tracking. Secondly, calculate the mean shift window center of anisotropic kernel function template, the theory basis is the sum of vector weights from the sample point in the tracking window to the center point is zero. Thirdly, anisotropic kernel function templates adaptive update implementation by similarity threshold to limit the change of the template between two sequential pictures, so as to realize real-time precise tracking. Finally, the contrast experimental results show that our algorithm has good accuracy and high real time.

An Experimental Study on the Actuator Line Method with Anisotropic Regularization Kernel

Nowadays, actuator line method (ALM) has become the most potential method in wind turbine simulations, especially in wind farm simulations and fluid-structure interaction simulations. The regularization kernel, which was originally introduced to ALM to avoid numerical singularity, has been found to have great influence on rotor torque predictions and wake simulations. This study focuses on the effect of each parameter used in the standard kernel and the anisotropic kernel. To validate the simulation, the torque and the wake characteristics of a model wind turbine were measured. The result shows that the Gaussian width ϵ (for standard kernel) and the parameter in chord length direction ϵc (for anisotropic kernel) mainly affect the normal velocity of each blade element when using ALM but have little effect on the tangential velocity calculation. Therefore, these parameters have great influence on the attack angle and rotor torque prediction. The thickness parameter ϵ t is the main difference between the standard kernel and the anisotropic kernel and it has a strong effect on the wind turbine wakes simulation. When using the anisotropic kernel, the wake structure is clearer and less likely to disperse, which is more consistent with the experimental results. Based on the studies above, a non-uniform mesh is recommended when using the anisotropic regularization kernel. Using a mesh refined in the main flow direction, ALM with anisotropic kernel can predict torque and wake characteristics better while maintaining low computational costs.

Two-sample statistics based on anisotropic kernels

The paper introduces a new kernel-based Maximum Mean Discrepancy (MMD) statistic for measuring the distance between two distributions given finitely many multivariate samples. When the distributions are locally low-dimensional, the proposed test can be made more powerful to distinguish certain alternatives by incorporating local covariance matrices and constructing an anisotropic kernel. The kernel matrix is asymmetric; it computes the affinity between $n$ data points and a set of $n_R$ reference points, where $n_R$ can be drastically smaller than $n$. While the proposed statistic can be viewed as a special class of Reproducing Kernel Hilbert Space MMD, the consistency of the test is proved, under mild assumptions of the kernel, as long as $\|p-q\| \sqrt{n} \to \infty $, and a finite-sample lower bound of the testing power is obtained. Applications to flow cytometry and diffusion MRI datasets are demonstrated, which motivate the proposed approach to compare distributions.

Global entropy weak solutions for general non-local traffic flow models with anisotropic kernel

We prove the well-posedness of entropy weak solutions for a class of scalar conservation laws with non-local flux arising in traffic modeling. We approximate the problem by a Lax-Friedrichs scheme and we provide L∞ and BV estimates for the sequence of approximate solutions. Stability with respect to the initial data is obtained from the entropy condition through the doubling of variable technique. The limit model as the kernel support tends to infinity is also studied.

Adaptive density estimator for galaxy surveys

Galaxy number or luminosity density serves as a basis for many structure classification algorithms. Several methods are used to estimate this density. Among them kernel methods have probably the best statistical properties and allow also to estimate the local sample errors of the estimate. We introduce a kernel density estimator with an adaptive data-driven anisotropic kernel, describe its properties and demonstrate the wealth of additional information it gives us about the local properties of the galaxy distribution.