Asymptotical minimax recovery of sets with smooth boundaries - Mammen, Enno; Cybakov, Aleksandr B. (The annals of statistics, 1995)
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.