The Minkowski content L0(G) of a body G⊂ℝd represents the boundary length (for d=2) or the surface area (for d=3) of G. A method for estimating L0(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, L1-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.
Publié le : 2007-07-14
Classification:
Minkowski content,
nonparametric set estimation,
length estimation,
statistical image analysis,
62G07,
62G20
@article{1185303997,
author = {Cuevas, Antonio and Fraiman, Ricardo and Rodr\'\i guez-Casal, Alberto},
title = {A nonparametric approach to the estimation of lengths and surface areas},
journal = {Ann. Statist.},
volume = {35},
number = {1},
year = {2007},
pages = { 1031-1051},
language = {en},
url = {http://dml.mathdoc.fr/item/1185303997}
}
Cuevas, Antonio; Fraiman, Ricardo; Rodríguez-Casal, Alberto. A nonparametric approach to the estimation of lengths and surface areas. Ann. Statist., Tome 35 (2007) no. 1, pp. 1031-1051. http://gdmltest.u-ga.fr/item/1185303997/