IEEE Transactions on Pattern Analysis and Machine Intelligence
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A theory and low computational cost linear algorithm is presentedfor estimating algebraic surfaces of second degree for representingan object in 3D, based on fitting in the dual space (space oftangent planes) computed from images taken by a calibrated camerain a number of positions. The approach and algorithm are designedto handle implicit quadric surfaces, which are regular or singular,in a uniform way without distinguishing the two cases. Asignificance of these quadric surface estimation results is, asillustrated in the paper, the estimation of complex 3D free formshapes in a computationally simple way in terms of quadric patches.The paper explains how singular quadrics cause instabilities in the3D surface fitting and representation, and presents regularization,based on this understanding, to produce accurate stable surfacerepresentations.