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

Abstract : 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.
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Submitted on : Thursday, July 4, 2019 - 1:38:04 PM
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Catherine Aaron. Convergence rate for the $\lambda$-Medial-Axis estimation under regularity conditions. 2019. ⟨hal-01558392v3⟩

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