Conformal-Based Surface Morphing and Multi-Scale Representation

Axioms

Ka Chun Lam¹  Chengfeng Wen¹ 

[1] Department of Mathematics, The Chinese University of Hong Kong, Room 220 Lady Shaw Building, CUHK, Shatin, Hong-Kong, China;

关键词: surface morphing;    multi-scale representation;    conformal parameterization;    conformal factor;    mean curvature;   

DOI  :  10.3390/axioms3020222

来源: mdpi

【 摘 要 】

This paper presents two algorithms, based on conformal geometry, for the multi-scale representations of geometric shapes and surface morphing. A multi-scale surface representation aims to describe a 3D shape at different levels of geometric detail, which allows analyzing or editing surfaces at the global or local scales effectively. Surface morphing refers to the process of interpolating between two geometric shapes, which has been widely applied to estimate or analyze deformations in computer graphics, computer vision and medical imaging. In this work, we propose two geometric models for surface morphing and multi-scale representation for 3D surfaces. The basic idea is to represent a 3D surface by its mean curvature function, H, and conformal factor function λ, which uniquely determine the geometry of the surface according to Riemann surface theory. Once we have theparameters. We test the proposed algorithms on 3D human face data and MRI-derived brain surfaces. Experimental results show that our proposed methods can effectively obtain multi-scale surface representations and give natural surface morphing results.

【 授权许可】

CC BY   
© 2014 by the authors; licensee MDPI, Basel, Switzerland.