In this paper optimal rates of convergence are derived for estimates of sets in $N$-dimensional "black and white" pictures under smoothness conditions. It is assumed that the boundaries of the "black" regions have a smooth parameterisation, that is, that the boundaries are given by smooth functions from the sphere $S^{N-1}$ into $\mathbb{R}^N$. Furthermore, classes of convex regions are considered. Two models are studied: edge estimation models motivated by image segmentation problems and density support estimation.
Publié le : 1995-04-14
Classification:
Boundary estimation,
binary pictures,
density support estimation,
optimal rates of convergence,
$\varepsilon$-entropy,
62G05,
62G20
@article{1176324533,
author = {Mammen, E. and Tsybakov, A. B.},
title = {Asymptotical Minimax Recovery of Sets with Smooth Boundaries},
journal = {Ann. Statist.},
volume = {23},
number = {6},
year = {1995},
pages = { 502-524},
language = {en},
url = {http://dml.mathdoc.fr/item/1176324533}
}
Mammen, E.; Tsybakov, A. B. Asymptotical Minimax Recovery of Sets with Smooth Boundaries. Ann. Statist., Tome 23 (1995) no. 6, pp. 502-524. http://gdmltest.u-ga.fr/item/1176324533/