Many problems in computer vision require estimation of both model parameters and boundaries, which limits the usefulness of standard estimation techniques from statistics. Example problems include surface reconstruction from range data, estimation of parametric motion models, fitting circular or elliptic arcs to edgel data, and many others. This paper introduces a new estimation technique, called the "Domain Bounding M-Estimator", which is a generalization of ordinary M-estimators combining error measures on model parameters and boundaries in a joint, robust objective function. Minimization of the objective function given a rough initialization yields simultaneous estimates of parameters and boundaries. The DBM-Estimator has been applied to estimating line segments, surfaces, and the symmetry transformation between two edgel chains. It is unaffected by outliers and prevents boundary estimates from crossing even small magnitude discontinuities.

The problem of model selection is relevant to many areas of computer vision. Model selection criteria have been used in the vision literature and many more have been proposed in statistics, but the relative strengths of these criteria have not been analyzed in vision. More importantly, suitable extensions to these criteria must be made to solve problems unique to computer vision. Using the problem of surface reconstruction as our context, we analyze existing criteria using simulations and sensor data, introduce new criteria from statistics, develop novel criteria capable of handling unknown error distributions and outliers, and extend model selection criteria to apply to the surface merging problem. The new surface merging rules improve upon previous results, and work well even at small step heights (h=3/spl sigma/) and crease discontinuities. Our results show that a Bayesian criteria and its bootstrapped variant perform the best, although for time-sensitive applications, a variant of the Akaike criterion may be a better choice. Unfortunately, none of the criteria work reliably for small region sizes, implying that model selection and surface merging should be avoided unless the region size is sufficiently large.