IEEE Transactions on Pattern Analysis and Machine Intelligence
Direct least-squares fitting of algebraic surfaces
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Surfaces in range image understanding
Surfaces in range image understanding
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IEEE Transactions on Pattern Analysis and Machine Intelligence
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IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
A note on the least squares fitting of ellipses
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Pattern Recognition Letters
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IEEE Transactions on Pattern Analysis and Machine Intelligence
Faithful Least-Squares Fitting of Spheres, Cylinders, Cones and Tori for Reliable Segmentation
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Direct Least Squares Fitting of Ellipses
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Faithful recovering of quadric surfaces from 3D range data
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IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
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Surface mesh segmentation and smooth surface extraction through region growing
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Pattern Recognition Letters
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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 驴simpler type,驴 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.