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This paper addresses a common problem in the segmentation of range images. We present methods for the least-squares fitting of spheres, cylinders, cones, and tori to 3D point data, and their application within a segmentation framework. Least-squares fitting of surfaces other than planes, even of simple geometric type, has rarely been studied. Our main application areas of this research are reverse engineering of solid models from depth-maps and automated 3D inspection where reliable extraction of these surfaces is essential. Our fitting method has the particular advantage of being robust in the presence of geometric degeneracy, i.e., as the principal curvatures of the surfaces being fitted decrease, the results returned naturally become closer and closer to those surfaces of "simpler type", i.e., planes, cylinders, cones, or spheres, which best describe the data. Many other methods diverge because, in such cases …