This paper introduces global confidence region techniques for analyzing and visualizing the performance of parametric surface estimators. Computation of the probability that the entire surface estimate lies within the confidence region is a challenging problem, because the surface estimate is a non-stationary random field. We derive lower bounds on this probability using exceedence probability of Gaussian random fields. These asymptotic global confidence regions conveniently display the uncertainty in various geometric parameters such as shape, size, orientation, and position of the estimated object, and facilitate geometric inferences.
Numerical simulations suggest that the new bounds are quite tight.