Convergence rate for the $\lambda$-Medial-Axis estimation under regularity conditions

Catherine Aaron (1, 2)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 UCA [2017-2020] - Université Clermont Auvergne [2017-2020]

Let $\mathcal{X}=\{X_1,\ldots X_n\}\subset \mathbb{R}^d$ be a random sample of observations drawn with a probability distribution supported on $S$ satisfying that both $S$ and $\overline{S^c}$ are $r_0$-convex ($r_0>0$). In this paper we propose an estimator of the medial axis of $S$ based on the $\lambda$-medial axis and the $r$-convex hull. Its convergence rate is derived. An heuristic to tune the parameters of the estimator is given and a small simulation study is performed.

Mots clés: r 0 -convexity; Manifold Learning; Skeleton; Geometric Inference; Medial-Axis

Domaines: Statistiques [math.ST]

Catherine Aaron. Convergence rate for the $\lambda$-Medial-Axis estimation under regularity conditions. Electronic Journal of Statistics , 2019, ⟨10.1214/19-EJS1581⟩. ⟨hal-01558392v3⟩