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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| Hauptverfasser: | , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
1995
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| In: |
The annals of statistics
Year: 1995, Jahrgang: 23, Heft: 2, Pages: 502-524 |
| ISSN: | 2168-8966 |
| DOI: | 10.1214/aos/1176324533 |
| Online-Zugang: | 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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| Verfasserangaben: | E. Mammen, A.B. Tsybakov |
MARC
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| 245 | 1 | 0 | |a Asymptotical minimax recovery of sets with smooth boundaries |c E. Mammen, A.B. Tsybakov |
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| 520 | |a 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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| 650 | 4 | |a binary pictures | |
| 650 | 4 | |a Boundary estimation | |
| 650 | 4 | |a density support estimation | |
| 650 | 4 | |a optimal rates of convergence | |
| 700 | 1 | |a Cybakov, Aleksandr B. |e VerfasserIn |0 (DE-588)111180600 |0 (DE-627)691107572 |0 (DE-576)339827947 |4 aut | |
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