Estimating model parameters and boundaries by minimizing a joint, robust objective function

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.