ASYMPTOTICAL MINIMAX RECOVERY OF SETS WITH SMOOTH BOUNDARIES

• 成果类型: Article
• 署名作者: MAMMEN, E; TSYBAKOV, AB
• 署名单位: Sorbonne Universite
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176324533
• 发表日期: 1995
• 页码: 502-524
• 关键词: Nonparametric regression; Convex set; approximation; edge

摘要

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 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.