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<p><b>Abstract</b>—This paper addresses a common problem in the segmentation of range images. We would like to identify and fit surfaces of known type wherever these are a good fit. This paper presents 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 been rarely 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 (or become more equal), 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, various parameters or their combination become infinite.</p>
Nonlinear least squares, geometric distance, cylinder, cone, sphere, torus, surface fitting, segmentation.

G. Lukacs, R. Martin and D. Marshall, "Robust Segmentation of Primitives from Range Data in the Presence of Geometric Degeneracy," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 23, no. , pp. 304-314, 2001.
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