• Publications
  • Influence
Proximity of persistence modules and their diagrams
TLDR
We extend the definition of persistence diagram to a larger setting, introduce the notions of discretization of a persistence module and associated pixelization map, and show how to interpolate between persistence modules, thereby lending a more analytic character to this otherwise algebraic setting. Expand
  • 331
  • 27
  • PDF
The Structure and Stability of Persistence Modules
TLDR
This book is a comprehensive treatment of the theory of persistence modules over the real line. Expand
  • 270
  • 14
  • PDF
Metric Graph Reconstruction from noisy Data
TLDR
We present a novel algorithm that takes as an input a data set, and outputs a metric graph that is homeomorphic to the underlying metric graph and has bounded distortion of distances. Expand
  • 39
  • 7
The Gudhi Library: Simplicial Complexes and Persistent Homology
TLDR
We present the main algorithmic and design choices that have been made to represent complexes and compute persistent homology in the Gudhi library. Expand
  • 76
  • 6
  • PDF
Lines and Free Line Segments Tangent to Arbitrary Three-Dimensional Convex Polyhedra
TLDR
We prove that the set of lines tangent to four possibly intersecting convex polyhedra in $\mathbb{R}^3$ with a total of $n$ edges consists of $\Theta(n^2k^2)$ connected components in the worst case. Expand
  • 31
  • 5
  • PDF
Convergence rates for persistence diagram estimation in topological data analysis
TLDR
We establish convergence rates of persistence diagrams associated to data randomly sampled from any compact metric space to a well defined limit diagram encoding the topological features of the support of the measure. Expand
  • 57
  • 4
  • PDF
Metric graph reconstruction from noisy data
TLDR
We present a novel algorithm that takes as an input such a data set, and outputs the underlying metric graph with guarantees. Expand
  • 35
  • 4
  • PDF
Farthest-Polygon Voronoi Diagrams
TLDR
Given a family of k disjoint connected polygonal sites of total complexity n, we consider the farthest-site Voronoi diagram of these sites, and give an O(n log3 n) time algorithm to compute it. Expand
  • 15
  • 4
The monotonicity of f-vectors of random polytopes
TLDR
We show that for planar convex sets, the number of facets of the convex hull of $n$ points chosen uniformly and independently in a convex body is asymptotically increasing. Expand
  • 10
  • 3
  • PDF
Farthest-polygon Voronoi diagrams
TLDR
We consider the farthest-site Voronoi diagram of k disjoint connected polygonal sites in general position and of total complexity n, and give an O(nlog^3n) time algorithm to compute it. Expand
  • 30
  • 2
  • PDF