Discrete conformal shape representation and reconstruction of 3d mesh objects

Authors:
Hongdong Li;Richard Hartley;Hans Burkhardt
Affiliations:
Research School of Information Sciences and Engineering, The Australian National University;Research School of Information Sciences and Engineering, The Australian National University;Computer Science Department, University of Freiburg, Freiburg, Germany
Venue:
ICIAP'05 Proceedings of the 13th international conference on Image Analysis and Processing
Year:
2005

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Abstract

This paper studies shape representation of general 3D objects. In particular, it proposes a conformal representation for genus-zero mesh objects, by using the discrete conformal mapping technique. It also proposes a new method to reconstruct the original shape from its conformal representation. In order to simplify and robustify the computation, we made several improvements to the above two procedures. The modifications include planar graph drawing initialization, Moebius factorization and spring-embedding-based reconstruction, etc. Though being mostly incremental, these modifications do provide significant improvements on previous methods. Possible applications include 3D geometry compression and object classification/recognition, etc.