Computable Bounds for the Reach and r-Convexity of Subsets of $${{\mathbb {R}}}^d$$

Cotsakis, Ryan

doi:10.1007/s00454-023-00624-8

Discrete Comput Geom

2024

DOI: 10.1007/s00454-023-00624-8

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Computable Bounds for the Reach and r-Convexity of Subsets of $${{\mathbb {R}}}^d$$

Ryan Cotsakis

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Cited by 2 publications

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Estimating the Convex Hull of the Image of a Set with Smooth Boundary: Error Bounds and Applications

Lew,

Bonalli,

Janson

et al. 2024

Discrete Comput Geom

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Estimating the Convex Hull of the Image of a Set with Smooth Boundary: Error Bounds and Applications

Lew,

Bonalli,

Janson

et al. 2024

Discrete Comput Geom

View full text Add to dashboard Cite

On the perimeter estimation of pixelated excursion sets of two‐dimensional anisotropic random fields

Cotsakis,

Di Bernardino,

Opitz

2023

Scandinavian J Statistics

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We are interested in creating statistical methods to provide informative summaries of random fields through the geometry of their excursion sets. To this end, we introduce an estimator for the length of the perimeter of excursion sets of random fields on ℝ2 observed over regular square tilings. The proposed estimator acts on the empirically accessible binary digital images of the excursion regions and computes the length of a piecewise linear approximation of the excursion boundary. The estimator is shown to be consistent as the pixel size decreases, without the need of any normalization constant, and with neither assumption of Gaussianity nor isotropy imposed on the underlying random field. In this general framework, even when the domain grows to cover ℝ2, the estimation error is shown to be of smaller order than the side length of the domain. For affine, strongly mixing random fields, this translates to a multivariate Central Limit Theorem for our estimator when multiple levels are considered simultaneously. Finally, we conduct several numerical studies to investigate statistical properties of the proposed estimator in the finite‐sample data setting.This article is protected by copyright. All rights reserved.

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Computable Bounds for the Reach and r-Convexity of Subsets of $${{\mathbb {R}}}^d$$

Cited by 2 publications

References 44 publications

Estimating the Convex Hull of the Image of a Set with Smooth Boundary: Error Bounds and Applications

Estimating the Convex Hull of the Image of a Set with Smooth Boundary: Error Bounds and Applications

On the perimeter estimation of pixelated excursion sets of two‐dimensional anisotropic random fields

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