Abstract
The kinetic data structure (KDS) framework is a powerful tool for maintaining various geometric configurations of continuously moving objects. In this work, we introduce the kinetic hourglass, a novel KDS implementation designed to compute the bottleneck distance for geometric matching problems. We detail the events and updates required for handling general graphs, accompanied by a complexity analysis. Furthermore, we demonstrate the utility of the kinetic hourglass by applying it to compute the bottleneck distance between two persistent homology transforms (PHTs) derived from shapes in R2, which are topological summaries obtained by computing persistent homology from every direction in S1.
Elena Xinyi Wang
Postdoc Researcher
My research interests include topological data analysis(TDA), computational topology and geometry, and machine learning.