Next Article in Journal
Classical Probability and Quantum Outcomes
Next Article in Special Issue
A Comparative Study of Several Classical, Discrete Differential and Isogeometric Methods for Solving Poisson’s Equation on the Disk
Previous Article in Journal / Special Issue
Characteristic Number: Theory and Its Application to Shape Analysis
Axioms 2014, 3(2), 222-243; doi:10.3390/axioms3020222
Article

Conformal-Based Surface Morphing and Multi-Scale Representation

,
 and
*
Received: 11 February 2014 / Revised: 9 April 2014 / Accepted: 23 April 2014 / Published: 20 May 2014
Download PDF [19270 KB, uploaded 20 May 2014]

Abstract

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 the (λ, H) parameterization of the surface, post-processing of the surface can be done directly on the conformal parameter domain. In particular, the problem of multi-scale representations of shapes can be reduced to the signal filtering on the λ and H parameters. On the other hand, the surface morphing problem can be transformed to an interpolation process of two sets of (λ, H) parameters. 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.
Keywords: surface morphing; multi-scale representation; conformal parameterization; conformal factor; mean curvature surface morphing; multi-scale representation; conformal parameterization; conformal factor; mean curvature
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Share & Cite This Article

Further Mendeley | CiteULike
Export to BibTeX |
EndNote
MDPI and ACS Style

Lam, K.C.; Wen, C.; Lui, L.M. Conformal-Based Surface Morphing and Multi-Scale Representation. Axioms 2014, 3, 222-243.

View more citation formats

Article Metrics

Comments

Citing Articles

[Return to top]
Axioms EISSN 2075-1680 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert