11 citations · 55 across the 33 of their papers we have counts for
9 papers · 1 filter
A probabilistic result on impulsive noise reduction in Topological Data Analysis through Group Equivariant Non-Expansive Operators
Patrizio Frosini, Ivan Gridelli, Andrea Pascucci
In recent years, group equivariant non-expansive operators (GENEOs) have attracted attention in the fields of Topological Data Analysis and Machine Learning. In this paper we show…
The Persistent Homotopy Type Distance
Patrizio Frosini, Claudia Landi, Facundo Memoli
We introduce the persistent homotopy type distance dHT to compare real valued functions defined on possibly different homotopy equivalent topological spaces. The underlying idea in…
The coherent matching distance in 2D persistent homology
Andrea Cerri, Marc Ethier, Patrizio Frosini
Comparison between multidimensional persistent Betti numbers is often based on the multidimensional matching distance. While this metric is rather simple to define and compute by c…
Position paper: Towards an observer-oriented theory of shape comparison
Patrizio Frosini
In this position paper we suggest a possible metric approach to shape comparison that is based on a mathematical formalization of the concept of observer, seen as a collection of s…
Comparison of Persistent Homologies for Vector Functions: from continuous to discrete and back
Niccolò Cavazza, Marc Ethier, Patrizio Frosini +2
The theory of multidimensional persistent homology was initially developed in the discrete setting, and involved the study of simplicial complexes filtered through an ordering of t…
No embedding of the automorphisms of a topological space into a compact metric space endows them with a composition that passes to the limit
Patrizio Frosini, Claudia Landi
The Hausdorff distance, the Gromov-Hausdorff, the Fréchet and the natural pseudo-distances are instances of dissimilarity measures widely used in shape comparison. We show that the…
Necessary Conditions for Discontinuities of Multidimensional Size Functions
Andrea Cerri, Patrizio Frosini
Some new results about multidimensional Topological Persistence are presented, proving that the discontinuity points of a k-dimensional size function are necessarily related to the…
Natural pseudo-distance and optimal matching between reduced size functions
M. d'Amico, P. Frosini, C. Landi
This paper studies the properties of a new lower bound for the natural pseudo-distance. The natural pseudo-distance is a dissimilarity measure between shapes, where a shape is view…
Stability in multidimensional Size Theory
Andrea Cerri, Patrizio Frosini, Claudia Landi
This paper proves that in Size Theory the comparison of multidimensional size functions can be reduced to the 1-dimensional case by a suitable change of variables. Indeed, we show…