论文标题
Hypersphere的Gegenbauer内核过滤
Gegenbauer kernel filtration on the unit hypersphere
论文作者
论文摘要
通过在Riemannian歧管上平滑内核来实现可视化的量化对象是一项持续的研究，这是一项持续的研究。但是，使用针对具有非欧盟拓扑的歧管上的线性域创建的常见过滤器可以产生误导性结果。虽然在较低的歧管上使用平滑内核进行量化函数的卷积进行了许多正在进行的研究，但较高维度的问题尤其是挑战。较低尺寸紧凑的riemannian歧管的一个重要概括是单位超球。在本文中，我们得出了在单位过球表面上的gegenbauer内核过滤的明确形式的卷积公式。我们证明Gegebauer过滤是超球传球谐波谐波的一系列有限线性组合的限制，以及其他结果。
Filtration of quantifiable objects by smoothing kernels on Riemannian manifolds for visualisation is an ongoing research. However, using common filters created for linear domains on manifolds with non-Euclidean topologies can yield misleading results. While there is a lot of ongoing research on convolution of quantifiable functions with smoothing kernels on the lower dimensional manifolds, higher-dimensional problems particularly pose a challenge. One important generalization of lower dimensional compact Riemannian manifolds is the unit hypersphere. In this paper, we derive explicit forms of convolution formulae for Gegenbauer kernel filtration on the surface of unit hypersphere. We prove that the Gegebauer filtration is the limit of a sequence of finite linear combinations of the hyperspherical Legendre harmonics, among other results.
