157 citations · 242 across the 16 of their papers we have counts for
7 papers · 1 filter
Fast Merge Tree Computation via SYCL
Arnur Nigmetov, Dmitriy Morozov
A merge tree is a topological descriptor of a real-valued function. Merge trees are used in visualization and topological data analysis, either directly or as a means to another en…
Topological Optimization with Big Steps
Arnur Nigmetov, Dmitriy Morozov
Using persistent homology to guide optimization has emerged as a novel application of topological data analysis. Existing methods treat persistence calculation as a black box and b…
Output-sensitive Computation of Generalized Persistence Diagrams for 2-filtrations
Dmitriy Morozov, Amit Patel
When persistence diagrams are formalized as the Mobius inversion of the birth-death function, they naturally generalize to the multi-parameter setting and enjoy many of the key pro…
Geometry Helps to Compare Persistence Diagrams
Michael Kerber, Dmitriy Morozov, Arnur Nigmetov
Exploiting geometric structure to improve the asymptotic complexity of discrete assignment problems is a well-studied subject. In contrast, the practical advantages of using geomet…
Witnessed k-Distance
Leonidas J. Guibas, Quentin Mérigot, Dmitriy Morozov
Distance function to a compact set plays a central role in several areas of computational geometry. Methods that rely on it are robust to the perturbations of the data by the Hausd…
Homology and Robustness of Level and Interlevel Sets
Paul Bendich, Herbert Edelsbrunner, Dmitriy Morozov +1
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 fr…