Open Access
April, 1995 Asymptotical Minimax Recovery of Sets with Smooth Boundaries
E. Mammen, A. B. Tsybakov
Ann. Statist. 23(2): 502-524 (April, 1995). DOI: 10.1214/aos/1176324533


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.


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E. Mammen. A. B. Tsybakov. "Asymptotical Minimax Recovery of Sets with Smooth Boundaries." Ann. Statist. 23 (2) 502 - 524, April, 1995.


Published: April, 1995
First available in Project Euclid: 11 April 2007

zbMATH: 0834.62038
MathSciNet: MR1332579
Digital Object Identifier: 10.1214/aos/1176324533

Primary: 62G05
Secondary: 62G20

Keywords: $\varepsilon$-entropy , binary pictures , boundary estimation , density support estimation , Optimal rates of convergence

Rights: Copyright © 1995 Institute of Mathematical Statistics

Vol.23 • No. 2 • April, 1995
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