DMCA
Computational Conformal Geometry and Its Applications (2007)
BibTeX
@MISC{Zeng07computationalconformal,
author = {Wei Zeng and Co-advisor Xianfeng Gu},
title = {Computational Conformal Geometry and Its Applications},
year = {2007}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
Conformal geometry has deep roots in pure mathematics. It is the intersection of complex analysis, Riemann surface theory, algebraic geometry, differential geometry and algebraic topology. Computational conformal geometry plays an important role in digital geometry processing. Recently, theory of discrete conformal geometry and algorithms of computational conformal geometry have been developed. A series of practical algorithms are presented to compute conformal mapping, which has been broadly applied in a lot of practical fields, including computer graphics, computer vision, medical imaging, visualization, and so on. The thesis focuses on computational conformal geometry and its applications on computer graphics and visualization, including surface conformal spherical parameterization, 3D shape space descriptor, quasiconformal mapping, surface remeshing, and consistent matching. Practical conformal parameterization methods are generated for specified popular applications, like human face expressions matching, and colon flattening. The initial experimental results are very promising.
Keyphrases
computational conformal geometry computer graphic important role colon flattening conformal mapping quasiconformal mapping shape space descriptor pure mathematics complex analysis riemann surface theory consistent matching computer vision practical field differential geometry discrete conformal geometry initial experimental result surface conformal spherical parameterization algebraic geometry medical imaging practical algorithm specified popular application deep root conformal geometry practical conformal parameterization method digital geometry processing surface remeshing algebraic topology human face expression
