Packing circles and spheres on surfaces
ACM SIGGRAPH Asia 2009 papers
Generalized Koebe's method for conformal mapping multiply connected domains
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Comparative analysis of quasi-conformal deformations in shape space
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part III
Shape analysis of vestibular systems in adolescent idiopathic scoliosis using geodesic spectra
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part III
Computing Extremal Quasiconformal Maps
Computer Graphics Forum
Hyperbolic ricci flow and its application in studying lateral ventricle morphometry
MBIA'12 Proceedings of the Second international conference on Multimodal Brain Image Analysis
Surface- and volume-based techniques for shape modeling and analysis
SIGGRAPH Asia 2013 Courses
Deformation similarity measurement in quasi-conformal shape space
Graphical Models
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Shape indexing, classification, and retrieval are fundamental problems in computer graphics. This work introduces a novel method for surface indexing and classification based on Teichmuller theory. The Teichmuller space for surfaces with the same topology is a finite dimensional manifold, where each point represents a conformal equivalence class, a curve represents a deformation process from one class to the other. We apply Teichmuller space coordinates as shape descriptors, which are succinct, discriminating and intrinsic; invariant under the rigid motions and scalings, insensitive to resolutions. Furthermore, the method has solid theoretic foundation, and the computation of Teichmuller coordinates is practical, stable and efficient. This work focuses on the surfaces with negative Euler numbers, which have a unique conformal Riemannian metric with -1 Gaussian curvature. The coordinates which we will compute are the lengths of a special set of geodesics under this special metric. The metric can be obtained by the curvature flow algorithm, the geodesics can be calculated using algebraic topological method. We tested our method extensively for indexing and comparison of about one hundred of surfaces with various topologies, geometries and resolutions. The experimental results show the efficacy and efficiency of the length coordinate of the Teichmuller space.