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A symbolic approach to polyhedral scene analysis by parametric calotte propagation*

Published online by Cambridge University Press:  01 July 2008

Hongbo Li ,
Lina Zhao  and
Ying Chen
Hongbo Li*
Affiliation:
Mathematics Mechanization Research Center, AMSS, Chinese Academy of Sciences, Beijing 100080, P. R. China
Lina Zhao
Affiliation:
Department of Mathematics and Computer Science, School of Science, Beijing University of Chemical Technology, Beijing 100080, P. R. China
Ying Chen
Affiliation:
Department of Basic Sciences, Beijing Electronic Science and Technology Institute, Beijing 100080, P. R. China
*
*Corresponding author. E-mail: hli@mmrc.iss.ac.cn
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Summary

Polyhedral scene analysis studies whether a 2D line drawing of a 3D polyhedron is realizable in space, and if so, it gives the results of parameterizing the space of all possible realizations. For generic 2D data, symbolic computation with Grassmann–Cayley algebra is needed in the analysis. In this paper, we propose a method called parametric calotte propagation to solve the realization and parameterization problems for general polyhedral scenes at the same time. In algebraic manipulation, parametric propagation is more efficient than elimination. In applications, it can lead to linear construction sequences for nonspherical polyhedra whose resolvable sequences do not exist.

Keywords

Structure geometryPolyhedral scene analysisGrassmann–Cayley algebraBracket algebraConstraint satisfaction
Type
Article
Information
Robotica , Volume 26 , Special Issue 4: Geometry in Robotics: Sensing , July 2008 , pp. 483 - 501
Copyright
Copyright © Cambridge University Press 2007

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Footnotes

*

Supported partially by NSFC 10471143 and NKBRSF 2004CB318001.

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