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

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 …

Size Theory has proven to be a useful framework for shape analysis in the context of pattern
recognition. Its main tool is a shape descriptor called size function. Size Theory has been …

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 …

Natural data offer a hard challenge to data analysis. One set of tools is being developed by
several teams to face this difficult task: Persistent topology. After a brief introduction to this …

Size Theory has proven to be a useful geometrical/topological approach to shape
comparison. Originally introduced by considering 1-dimensional properties of shapes …

Persistent homology has proven itself quite efficient in the topological and qualitative
comparison of filtered topological spaces, when invariance with respect to every …

Shape similarity is an acute issue in Computer Vision and Computer Graphics that involves
many aspects of human perception of the real world, including judged and perceived …

The persistence diagram of Cohen-Steiner, Edelsbrunner, and Harer was recently
generalized by Patel to the case of constructible persistence modules with values in a …