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Several existing algorithms for reconstructing 3D models from range data first approximate the object's 3D distance field to provide an implicit representation of the scanned object and then construct a surface model of the object using this distance field. In these existing approaches, computing and storing 3D distance values from range data contribute significantly to the computational and storage requirements. This paper presents an efficient method for estimating the 3D Euclidean distance field from 2D range images that can be used by any of these algorithms. The proposed method uses Adaptively Sampled Distance Fields to minimize the number of distance evaluations and significantly reduce storage requirements of the sampled distance field. The method is fast because much of the computation required to convert the line-of-sight range distances to Euclidean distances can be done during a pre-processing step in the 2D coordinate space of each range image.