Generalized second fundamental form for varifolds: an application to point clouds

10 July 2019
Versione stampabile

Venue: Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Sala Seminari "-1"
At: 2 p.m.


  • Simon Vialaret (ENS Paris-Saclay – Internship Program)


Metric properties of approximations of manifolds have been widely studied in computational geometry. Recently, a new general framework relying on geometric measure theory has been proposed by Buet, Leonardi and Masnou. It is based on the so-called notion of varifold, a weak notion of embedded manifold allowing to consider a large category of unsmooth and unstructured geometric data. A theory of generalized curvature has been developed, and provides extended definitions for mean curvature and second fundamental form, which are consistent with the smooth case. However, while a natural varifold can be associated to any submanifold in the Euclidean n-space, it is not clear how to construct, in practical applications, a varifold corresponding to some given discrete dataset. We will then deal with the question of choosing a mass distribution for a point cloud, such that the corresponding weak second fundamental form satisfies classical structural properties.

Contact person: Gian Paolo Leonardi