A Unified Linear Fitting Approach for Singular and Non-Singular 3D Quadrics from Occluding Contours
Abstract
A theory and low computational cost linear algorithm is
presented for estimating algebraic surfaces of second degree for
representing an object in 3D, based on fitting in the dual space
(space of tangent planes) computed from images taken by a
calibrated camera in a number of positions. The approach and
algorithm are designed to handle implicit quadric surfaces, which
are regular or singular, in a uniform way without distinguishing
the two cases. A significance of these quadric surface estimation
results is, as illustrated in the paper, the estimation of complex
3D free form shapes in a computationally simple way in terms of
quadric patches. The paper explains how singular quadrics cause
instabilities in the 3D surface fitting and representation, and
presents regularization, based on this understanding, to produce
accurate stable surface representations.
Reference
@inproceedings{jpt-hlk03,
author = {Kang, K. and Tarel, J.-P. and Cooper, D. B.},
title = {A Unified Linear Fitting Approach for Singular and Non-Singular 3D Quadrics from Occluding Contours},
booktitle = {IEEE International Workshop on Higher-level Knowledge in 3D Modeling and Motion (HLK'2003)},
date = {October 17},
address = {Nice, France},
pages = {48-57},
year = {2003},
note = {http://perso.lcpc.fr/tarel.jean-philippe/publis/hlk03.html}
}
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