This system paper presents the Topology ToolKit (TTK), a software platform designed for the
topological analysis of scalar data in scientific visualization. While topological data analysis …

Geometric and topological inference deals with the retrieval of information about a geometric
object using only a finite set of possibly noisy sample points. It has connections to manifold …

In this article, we extend the notions of dominated vertex and strong collapse of a simplicial
complex as introduced by J. Barmak and E. Miniam. We say that a simplex (of any …

We introduce a fast and memory efficient approach to compute the persistent homology (PH)
of a sequence of simplicial complexes. The basic idea is to simplify the complexes of the …

This article considers the question of how to succinctly approximate a multidimensional
convex body by a polytope. Given a convex body K of unit diameter in Euclidean d …

It has been observed since a long time that data are often carrying interesting topological
and geometric structures. Characterizing such structures and providing efficient tools to infer …

This paper is a continuation of the research reported in [7] on the usage of strong collapses
to accelerate the computation of persistent homology (PH). We show that further decisive …

Topological Data Analysis (TDA) is an emergent field that aims to discover topological
information hidden in a dataset. TDA tools have been commonly used to create filters and …

We introduce the Stellar decomposition, a model for efficient topological data structures over
a broad range of simplicial and cell complexes. A Stellar decomposition of a complex is a …

A filtration over a simplicial complex K is an ordering of the simplices of K such that all
prefixes in the ordering are subcomplexes of K. Filtrations are at the core of Persistent …