Abstract
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 $\mathbb{R}^N$. Furthermore, classes of convex regions are considered. Two models are studied: edge estimation models motivated by image segmentation problems and density support estimation.
Citation
E. Mammen. A. B. Tsybakov. "Asymptotical Minimax Recovery of Sets with Smooth Boundaries." Ann. Statist. 23 (2) 502 - 524, April, 1995. https://doi.org/10.1214/aos/1176324533
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