Asymptotical minimax recovery of sets with smooth boundaries
In this paper optimal rates of convergence are derived for estimates of sets in NNN-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...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
1995
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| In: |
The annals of statistics
Year: 1995, Volume: 23, Issue: 2, Pages: 502-524 |
| ISSN: | 2168-8966 |
| DOI: | 10.1214/aos/1176324533 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1214/aos/1176324533 Verlag, Volltext: https://projecteuclid.org/euclid.aos/1176324533 Verlag, Volltext: https://projecteuclid.org/download/pdf_1/euclid.aos/1176324533 
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| Author Notes: | E. Mammen, A.B. Tsybakov |
| Summary: | In this paper optimal rates of convergence are derived for estimates of sets in NNN-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 SN−1SN−1S^{N-1} into RNRN\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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| Item Description: | First available in Project Euclid: 11 April 2007 Gesehen am 26.02.2018 |
| Physical Description: | Online Resource |
| ISSN: | 2168-8966 |
| DOI: | 10.1214/aos/1176324533 |