Trans . on Pattern Analysis and Machine IntelligenceEstimation of Model Parameters and BoundariesBy Minimizing a Joint , Robust ObjectiveFunctionCharles

This paper introduces a new robust technique that simultaneously estimates model parameters and the domain over which the model applies. It removes the implicit assumption of an innnite domain in standard estimation techniques, and is useful in several computer vision problems. Examples include curve tting, image segmentation, and estimating image-to-image transforms. This new technique , called the \Domain Bounding M-Estimator" (DBM-Estimator) is a generalization of ordinary M-Estimators deened in the statistics literature. The DBM-Estimator objective function combines two error measures on each data point: one is the usual population model t residual and the other is a \do-main distance" residual. Minimizing the objective function yields simultaneous estimates of population model parameters and region (domain) boundary parameters. Representations are developed for boundaries of one-dimensional and two-dimensional domains. The latter is similar to active contour models. The DBM-Estimator has been applied to estimating line segments, surfaces, and the symmetry transformation between two edgel chains. The DBM-Estimator is un-aaected by outliers and prevents boundary estimates from crossing all but the smallest magnitude discontinuities.