Generation of 3D objects using Lie algebra models based on curvature analysis and comparison with B-spline fitting

Author

Jinhui Chao ; Ura, Kouichi ; Honma, Go

Author_Institution

Dept. of Electr. & Electron. Eng., Chuo Univ., Tokyo, Japan

Volume

4

fYear

1999

fDate

1999

Firstpage

366

Abstract

This paper discusses 3D free object synthesis using models of linear and Hamiltonian Lie algebra, which can represent a wide class of non-algebra and compact shapes and recover the objects uniquely using their invariants with respect to Euclidean or affine transformations. A curvature analysis of the surfaces represented by these Lie algebra models is shown, based on which an efficient algorithm of shape generation is proposed. Then the description power of these Lie algebra object models is evaluated by comparing them with the B-splines model

Keywords

Lie algebras; computational geometry; image processing; splines (mathematics); 3D free object synthesis; 3D objects generation; B-spline fitting; B-splines model; Euclidean transformations; Hamiltonian Lie algebra; Lie algebra models; affine transformations; curvature analysis; invariants; shape generation; Algebra; Algorithm design and analysis; Curve fitting; Data mining; Graphics; IP networks; Power generation; Shape; Spline; Visualization;

fLanguage

English

Publisher

ieee

Conference_Titel

Image Processing, 1999. ICIP 99. Proceedings. 1999 International Conference on

Conference_Location

Kobe

Print_ISBN

0-7803-5467-2

Type

conf

DOI

10.1109/ICIP.1999.819615

Filename

819615