Convergence analysis of subdivision processes on the sphere
Convergence analysis of subdivision processes on the sphere
复制标题
球面细分过程的收敛性分析
DOI：
--
复制
发表时间：
2020
影响因子：
2.1
通讯作者：
J. Wallner
中科院分区：
文献类型：
--
作者：
Svenja Hüning;J. Wallner
我们分析了作用于球面上数据的线性细分过程的非线性黎曼类比的收敛性。我们展示了如何对曲线细分规则，如果输入数据的密度低于阈值，我们可以推导出保证收敛的界限。以前的结果只产生几个数量级较小的阈值，因此对收敛性的先验检查无用。这是第一次在具有正曲率的几何和不享受任何特殊性质（如插值或非负掩模）的细分规则中显示出这样的结果。
We analyse the convergence of nonlinear Riemannian analogues of linear subdivision processes operating on data in the sphere. We show how for curve subdivision rules we can derive bounds guaranteeing convergence if the density of input data is below that threshold. Previous results only yield thresholds that are several magnitudes smaller and are thus useless for a priori checking of convergence. It is the first time that such a result has been shown for a geometry with positive curvature and for subdivision rules not enjoying any special properties like being interpolatory or having non-negative mask.