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Describes how to estimate 3D surface models from dense sets of noisy range data taken from different points of view, i.e., multiple range maps. The proposed method uses a sensor model to develop an expression for the likelihood of a 3D surface, conditional on a set of noisy range measurements. Optimizing this likelihood with respect to the model parameters provides an unbiased and efficient estimator. The proposed numerical algorithms make this estimation computationally practical for a wide variety of circumstances. The results from this method compare favorably with state-of-the-art approaches that rely on the closest-point or perpendicular distance metric, a convenient heuristic that produces biased solutions and fails completely when surfaces are not sufficiently smooth, as in the case of complex scenes or noisy range measurements. Empirical results on both simulated and real ladar data demonstrate the effectiveness of the proposed method for several different types of problems. Furthermore, the proposed method offers a general framework that can accommodate extensions to include surface priors, more sophisticated noise models, and other sensing modalities, such as sonar or synthetic aperture radar.