APPROXIMATING THE DISTRIBUTION OF MAXIMUM-LIKELIHOOD CONTOUR ESTIMATORS IN 2-REGION IMAGES

We consider two types of two-region image models with a univariate bou ndary representation and independent lattice observations. A non-param etric histogram-like contour estimator with an increasing number of su bintervals is studied when also the number of observations tends to in finity, and the difference between the region grey level distributions tends to zero. The asymptotic distribution is expressed in terms of l ocations of maxima of two-sided Brownian motions with negative drift, in particular triangular drift and a mixture of triangular and parabol ic drift. Examples with simulated and real data are provided to illust rate the results.