11 citations · 55 across the 33 of their papers we have counts for
12 papers · 1 filter
Persistent Homology and Equivariance in Data Analysis: A Topological Introduction
Patrizio Frosini, Ulderico Fugacci, Nicola Quercioli +1
This new book is intended as a first elementary introduction to Topological Data Analysis for mathematics students seeking a rigorous account of the foundations of persistent homol…
The Convex Matching Distance in Multiparameter Persistence
Francesco Conti, Patrizio Frosini, Ulderico Fugacci +4
We introduce the convex matching distance, a novel metric for comparing functions with values in the real plane. This metric measures the maximal bottleneck distance between the pe…
Matching distance via the extended Pareto grid
Patrizio Frosini, Eloy Mósig García, Nicola Quercioli +1
One of the most animated themes of multidimensional persistence is the comparison between invariants. The matching distance between persistent Betti numbers functions (or rank inva…
Geometry of the matching distance for 2D filtering functions
Marc Ethier, Patrizio Frosini, Nicola Quercioli +1
In this paper we exploit the concept of extended Pareto grid to study the geometric properties of the matching distance for -valued regular functions defined on a Rie…
On the geometrical properties of the coherent matching distance in 2D persistent homology
Andrea Cerri, Marc Ethier, Patrizio Frosini
In this paper we study a new metric for comparing Betti numbers functions in bidimensional persistent homology, based on coherent matchings, i.e. families of matchings that vary in…
Combining persistent homology and invariance groups for shape comparison
Patrizio Frosini, Grzegorz Jablonski
In many applications concerning the comparison of data expressed by -valued functions defined on a topological space , the invariance with respect to a given group…
G-invariant Persistent Homology
Patrizio Frosini
Classical persistent homology is a powerful mathematical tool for shape comparison. Unfortunately, it is not tailored to study the action of transformation groups that are differen…
Uniqueness of models in persistent homology: the case of curves
Patrizio Frosini, Claudia Landi
We consider generic curves in R^2, i.e. generic C^1 functions f from S^1 to R^2. We analyze these curves through the persistent homology groups of a filtration induced on S^1 by f.…
Stable comparison of multidimensional persistent homology groups with torsion
Patrizio Frosini
The present lack of a stable method to compare persistent homology groups with torsion is a relevant problem in current research about Persistent Homology and its applications in P…
Invariance properties of the multidimensional matching distance in Persistent Topology and Homology
Andrea Cerri, Patrizio Frosini
Persistent Topology studies topological features of shapes by analyzing the lower level sets of suitable functions, called filtering functions, and encoding the arising information…
Stability of multidimensional persistent homology with respect to domain perturbations
Patrizio Frosini, Claudia Landi
Motivated by the problem of dealing with incomplete or imprecise acquisition of data in computer vision and computer graphics, we extend results concerning the stability of persist…
Multidimensional persistent homology is stable
Andrea Cerri, Barbara Di Fabio, Massimo Ferri +2
Multidimensional persistence studies topological features of shapes by analyzing the lower level sets of vector-valued functions. The rank invariant completely determines the multi…