SIAM Journal on Computing
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Efficient computation of geodesic shortest paths
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Topology matching for fully automatic similarity estimation of 3D shapes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Optimal System of Loops on an Orientable Surface
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Global conformal surface parameterization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Matching 3D Models with Shape Distributions
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Surface Classification Using Conformal Structures
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Optimal Global Conformal Surface Parameterization
VIS '04 Proceedings of the conference on Visualization '04
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Laplace-spectra as fingerprints for shape matching
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Fast exact and approximate geodesics on meshes
ACM SIGGRAPH 2005 Papers
Computing surface hyperbolic structure and real projective structure
Proceedings of the 2006 ACM symposium on Solid and physical modeling
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Discrete Curvature Flows for Surfaces and 3-Manifolds
Emerging Trends in Visual Computing
Characterizing shape using conformal factors
EG 3DOR'08 Proceedings of the 1st Eurographics conference on 3D Object Retrieval
Deformation similarity measurement in quasi-conformal shape space
Graphical Models
| Hi-index | 0.00 |
Surface classification is one of the most fundamental problems in geometric modeling. Surfaces can be classified according to their conformal structures. In general, each topological equivalent class has infinite conformally equivalent classes. This paper introduces a novel method to classify surfaces by their conformal structures. Surfaces in the same conformal class share the same uniformization metric, which induces constant Gaussian curvature everywhere on the surface. Under the uniformization metric, each homotopy class of a closed curves on the surface has a unique geodesic. The lengths of all closed geodesics form the geodesic spectrum. The map from the fundamental group to the geodesic spectrum completely determines the conformal structure of the surface. We first compute the uniformization metric using discrete Ricci flow method, then compute the Fuchsian group generators, finally deduce the geodesic spectra from the generators in a closed form. The method is rigorous and practical. Geodesic spectra is applied as the signature of surfaces for shape comparison and classification.