13 citations · 77 across the 21 of their papers we have counts for
27 papers
Comparing Morse Complexes Using Optimal Transport: An Experimental Study
Mingzhe Li, Carson Storm, Austin Yang Li +2
Morse complexes and Morse-Smale complexes are topological descriptors popular in topology-based visualization. Comparing these complexes plays an important role in their applicatio…
Topologically Attributed Graphs for Shape Discrimination
Justin Curry, Washington Mio, Tom Needham +2
In this paper we introduce a novel family of attributed graphs for the purpose of shape discrimination. Our graphs typically arise from variations on the Mapper graph construction,…
Convergence of Leray Cosheaves for Decorated Mapper Graphs
Justin Curry, Washington Mio, Tom Needham +2
We introduce decorated mapper graphs as a generalization of mapper graphs capable of capturing more topological information of a data set. A decorated mapper graph can be viewed as…
Flexible and Probabilistic Topology Tracking with Partial Optimal Transport
Mingzhe Li, Xinyuan Yan, Lin Yan +2
In this paper, we present a flexible and probabilistic framework for tracking topological features in time-varying scalar fields using merge trees and partial optimal transport. Me…
Comparison Results for Gromov-Wasserstein and Gromov-Monge Distances
Facundo Mémoli, Tom Needham
Inspired by the Kantorovich formulation of optimal transport distance between probability measures on a metric space, Gromov-Wasserstein (GW) distances comprise a family of metrics…
Statistical Shape Analysis of Shape Graphs with Applications to Retinal Blood-Vessel Networks
Aditi Basu Bal, Xiaoyang Guo, Tom Needham +1
This paper provides theoretical and computational developments in statistical shape analysis of shape graphs, and demonstrates them using analysis of complex data from retinal bloo…