水平集和层间集的同调性和鲁棒性
Homology and Robustness of Level and Interlevel Sets
摘要：
给定拓扑空间上的一个函数$f: \Xspace \to \Rspace$，我们考虑区间的原像及其同调群，并展示如何从$f$的扩展持久图中读取这些群的秩。此外，我们量化的鲁棒性的扰动下的$f$使用井组的同源类，我们展示了如何读取这些组的行列从相同的扩展持久性图。特殊情况$\Xspace = \Rspace^3$在医学成像和科学可视化领域具有分支。
英文摘要：
Given a function $f: \Xspace \to \Rspace$ on a topological space, we consider the preimages of intervals and their homology groups and show how to read the ranks of these groups from the extended persistence diagram of $f$. In addition, we quantify the robustness of the homology classes under perturbations of $f$ using well groups, and we show how to read the ranks of these groups from the same extended persistence diagram. The special case $\Xspace = \Rspace^3$ has ramifications in the fields of medical imaging and scientific visualization.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
