ASYMPTOTICAL MINIMAX RECOVERY OF SETS WITH SMOOTH BOUNDARIES

In this paper optimal rates of convergence are derived for estimates o f 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 give n by smooth functions from the sphere S-N-1 into R(N). Furthermore, cl asses of convex regions are considered. Two models are studied: edge e stimation models motivated by image segmentation problems and density support estimation.