ConformalBased Surface Morphing and MultiScale Representation
Abstract
:1. Introduction
2. Previous Work
3. Mathematical Background
3.1. Conformal Factor and Curvature of a Riemann Surface
3.2. $(\lambda ,H)$ Representation for Surface
4. Methodology
4.1. MultiScale Representation of Surfaces
Algorithm 1: Multiscale representation of a surface. 

4.2. Surface Morphing
Algorithm 2: Morphing of surfaces. 

5. Numerical Algorithms
5.1. Numerical Implementation of the $(\lambda ,H)$ Representation and Surface Reconstruction
5.2. Numerical Implementation of the MultiScale Representation of a Surface
5.3. Numerical Implementation of Surface Morphing
6. Experimental Results
6.1. Surface Reconstruction
Surface  Max L^{2} error  Mean L^{2} error  Max (L^{2}/$\sqrt{\mathbf{Area}}$) error 

Human face  3.0033  1.0771  0.0167 
Human face 2  2.5706  0.7239  0.0150 
Cortical surface  2.2157  0.5967  0.0114 
Teeth surface  0.1189  0.0329  0.0098 
Buddha surface  8.7897  2.1967  0.0183 
6.2. MultiScale Representation of Surfaces
6.3. Surface Morphing
7. Conclusions
Acknowledgments
Conflicts of Interest
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Lam, K.C.; Wen, C.; Lui, L.M. ConformalBased Surface Morphing and MultiScale Representation. Axioms 2014, 3, 222243. https://doi.org/10.3390/axioms3020222
Lam KC, Wen C, Lui LM. ConformalBased Surface Morphing and MultiScale Representation. Axioms. 2014; 3(2):222243. https://doi.org/10.3390/axioms3020222
Chicago/Turabian StyleLam, Ka Chun, Chengfeng Wen, and Lok Ming Lui. 2014. "ConformalBased Surface Morphing and MultiScale Representation" Axioms 3, no. 2: 222243. https://doi.org/10.3390/axioms3020222