论文标题
通过盖子的参数化越野河流过滤
Parameterized Vietoris-Rips Filtrations via Covers
论文作者
论文摘要
计算拓扑的一个挑战是处理由点云数据（例如越野杆）过滤构建的大型过滤几何复合物。这导致了用于并行计算和压缩方案的开发，这些方案限制了简单在数据封面中的开放集中。我们将无环载体的方法扩展到持久同源性的设置，以详细介绍越过越过覆盖物和完整构造的越野河流过滤之间的关系。我们展示了如何使用这些复合物在基本空间上研究数据，并使用我们的结果来指导数据封面的选择。我们在各种封面上演示了这些技术，并在研究了高维图像贴片模型的高阶同源性时表明了这种结构的实用性。
A challenge in computational topology is to deal with large filtered geometric complexes built from point cloud data such as Vietoris-Rips filtrations. This has led to the development of schemes for parallel computation and compression which restrict simplices to lie in open sets in a cover of the data. We extend the method of acyclic carriers to the setting of persistent homology to give detailed bounds on the relationship between Vietoris-Rips filtrations restricted to covers and the full construction. We show how these complexes can be used to study data over a base space and use our results to guide the selection of covers of data. We demonstrate these techniques on a variety of covers, and show the utility of this construction in investigating higher-order homology of a model of high-dimensional image patches.
