Asymptotical minimax recovery of sets with smooth boundaries

• Verfasst von: Mammen, Enno [VerfasserIn]
• Verfasst von: Cybakov, Aleksandr B. [VerfasserIn]
• Titel: Asymptotical minimax recovery of sets with smooth boundaries
• Verf.angabe: E. Mammen, A.B. Tsybakov
• Jahr: 1995
• Umfang: 23 S.
• Fussnoten: First available in Project Euclid: 11 April 2007 ; Gesehen am 26.02.2018
• Titel Quelle: Enthalten in: The annals of statistics
• Ort Quelle: Hayward, Calif. : IMS Business Off., 1973
• Jahr Quelle: 1995
• Band/Heft Quelle: 23(1995), 2, Seite 502-524
• ISSN Quelle: 2168-8966
• DOI: doi:10.1214/aos/1176324533
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: $\varepsilon$-entropy
• Sach-SW: binary pictures
• Sach-SW: Boundary estimation
• Sach-SW: density support estimation
• Sach-SW: optimal rates of convergence
• K10plus-PPN: 1570183414

Abstract

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.