Global Confidence Regions for Parametric Surface Estimation

by Jong Chul Ye, Yoram Bresler and Pierre Moulin

This paper introduces global confidence region techniques for
analyzing and visualizing the performance of parametric surface
estimators.  Assuming a statistical model for the measurement data and
an asymptotically normal and efficient estimator for the surface
parameters, Cram\'{e}r-Rao bounds are used to define an asymptotic
confidence region, centered around the true surface.  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.