76 citations · 213 across the 18 of their papers we have counts for
4 papers · 1 filter
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…
Categorified Reeb Graphs
Vin de Silva, Elizabeth Munch, Amit Patel
The Reeb graph is a construction which originated in Morse theory to study a real valued function defined on a topological space. More recently, it has been used in various applica…
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…
Quantifying Transversality by Measuring the Robustness of Intersections
Herbert Edelsbrunner, Dmitriy Morozov, Amit Patel
By definition, transverse intersections are stable under infinitesimal perturbations. Using persistent homology, we extend this notion to a measure. Given a space of perturbations,…