Year: 2025
Type: preprint
Abstract: We investigate the inference of varifold structures in a statistical framework: assuming that we have access to i.i.d. samples in $\mathbb{R}^n$ obtained from an underlying $d$--dimensional shape $S$ endowed with a possibly non uniform density $θ$, we propose and analyse an estimator of the varifold structure associated to $S$. The shape $S$ is assumed to be piecewise $C^{1,a}$ in a sense that allows for a singular set whose small enlargements are of small $d$--dimensional measure. The estimators are kernel--based both for infering the density and the tangent spaces and the convergence result holds for the bounded Lipschitz distance between varifolds, in expectation and in a noiseless model. The mean convergence rate involves the dimension $d$ of $S$, its regularity through $a \in (0, 1]$ and the regularity of the density $θ$.
Source: arXiv (Cornell University)
Authors: Boricaud, Charly, Buet, Blanche
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Agence Nationale de la Recherche
OpenAlex ID: W4406930627