Image Processing for Plane Domains: Change-Point Problems for the Domain's Area

Image models are considered for growing domains observed in Gaussian white noise. The “jump” and “kink” change-point problems are studied for the domain's area. When noise is small the minimax rates of convergence are found for Markov stopping rules in different classes of growing domains. The peculiarity of the problem is this: the domain's shape is unknown and plays the role of an infinite-dimensional “nuisance parameter” which strongly influences the precision of the estimators.