Conformal spherical representation of 3D genus-zero meshes

Authors:
Hongdong Li;Richard Hartley
Affiliations:
Research School of Information Sciences and Engineering, The Australian National University, Canberra Research Labs, National ICT Australia Ltd., Australia;Research School of Information Sciences and Engineering, The Australian National University, Canberra Research Labs, National ICT Australia Ltd., Australia
Venue:
Pattern Recognition
Year:
2007

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Abstract

This paper describes an approach of representing 3D shape by using a set of invariant spherical harmonic (SH) coefficients after conformal mapping. Specifically, a genus-zero 3D mesh object is first conformally mapped onto the unit sphere by using a modified discrete conformal mapping, where the modification is based on Mobius factorization and aims at obtaining a canonical conformal mapping. Then a SH analysis is applied to the resulting conformal spherical mesh. The obtained SH coefficients are further made invariant to translation and rotation, while at the same time retain the completeness, thanks to which the original shape information has been faithfully preserved.