In topological data analysis (TDA), one often studies the shape of data by constructing a
filtered topological space, whose structure is then examined using persistent homology …

Differential topology, and specifically Morse theory, provide a suitable setting for formalizing
and solving several problems related to shape analysis. The fundamental idea behind …

Topological persistence has proven to be a key concept for the study of real-valued
functions defined over topological spaces. Its validity relies on the fundamental property that …

In 2009, Chazal et al. introduced ϵ ϵ-interleavings of persistence modules. ϵ ϵ-
interleavings induce a pseudometric d_ I d I on (isomorphism classes of) persistence …

We consider the question of defining interleaving metrics on generalized persistence
modules over arbitrary preordered sets. Our constructions are functorial, which implies a …

The recent introduction of 3D shape analysis frameworks able to quantify the deformation of
a shape into another in terms of the variation of real functions yields a new interpretation of …

Multidimensional persistence mostly studies topological features of shapes by analyzing the
lower level sets of vector‐valued functions, called filtering functions. As is well known, in the …

In this paper we present an efficient framework for computation of persistent homology of
cubical data in arbitrary dimensions. An existing algorithm using simplicial complexes is …

In this paper we present a methodology of classifying hepatic (liver) lesions using
multidimensional persistent homology, the matching metric (also called the bottleneck …

The notion of generalized rank in the context of multiparameter persistence has become an
important ingredient for defining interesting homological structures such as generalized …