A set-indexed process in a two-region image

We investigate the problem of edge estimation in a two-region image in the setting of a fixed design regression model. The edge estimation problem is equivalent to estimating one of the plateau sets where the regression function is constant, and we define a global set-valued estimator by finding the partition which maximizes a weighted distance measure. An investigation of the weak convergence of the random sets generated by this estimator shows that a properly scaled stochastic process in symmetric differences between estimated and true partitions converges in the limit to a set-indexed Brownian motion with drift in d.