The Annals of Statistics

Asymptotical Minimax Recovery of Sets with Smooth Boundaries

E. Mammen and A. B. Tsybakov

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 23, Number 2 (1995), 502-524.

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176324533

Digital Object Identifier
doi:10.1214/aos/1176324533

Mathematical Reviews number (MathSciNet)
MR1332579

Zentralblatt MATH identifier
0834.62038

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62G20: Asymptotic properties

Keywords
Boundary estimation binary pictures density support estimation optimal rates of convergence $\varepsilon$-entropy

Citation

Mammen, E.; Tsybakov, A. B. Asymptotical Minimax Recovery of Sets with Smooth Boundaries. Ann. Statist. 23 (1995), no. 2, 502--524. doi:10.1214/aos/1176324533. https://projecteuclid.org/euclid.aos/1176324533


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