A nonparametric approach to the estimation of lengths and surface areas

By Antonio Cuevas, Ricardo Fraiman, A. Rodr'iguez-Casal. 2007

60 citations recorded by the source corpus.

The Minkowski content L 0 (G) of a body G ⊂R d represents the boundary length (for d = 2) or the surface area (for d = 3) of G. A method for estimating L 0 (G) is proposed. It relies on a nonparametric estimator based on the information provided by a random sample (taken on a rectangle containing G) in which we are able to identify whether every point is inside or outside G. Some theoretical properties concerning strong consistency, L 1 -error and convergence rates are obtained. A practical application to a problem of image analysis in cardiology is discussed in some detail. A brief simulation study is provided.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/54d008bd9f97a1b3e682df6fc349f56c1e0e7ec7

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In Applied Mathematics

In Computer Vision and Pattern Recognition

In Geometry and Topology

Citations in the corpus

Estimating the reach of a manifold (2017, methodology): “It is used in [15] as a regularity parameter in the estimation of the Minkowski boundary lengths and surface areas.”
A weighted k-nearest neighbor density estimate for geometric inference (2011, background): “Cuevas, Fraiman, and Rodr´ıguez-Casal [14] provide a consistent estimate of the Minkowski content that turns out to also provide an estimate of the boundary of the studied object.”
On Statistical Properties of Sets Fulfilling Rolling-Type Conditions (2011, background): “Under these assumptions, these authors improved the convergence rates for the Minkowski content L0(S) obtained in [10].”