Resilient routing for sensor networks using hyperbolic embedding of universal covering space
INFOCOM'10 Proceedings of the 29th conference on Information communications
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
Conformal geometry based supine and prone colon registration
MICCAI'10 Proceedings of the Second international conference on Virtual Colonoscopy and Abdominal Imaging: computational challenges and clinical opportunities
The hitchhiker's guide to the galaxy of mathematical tools for shape analysis
ACM SIGGRAPH 2012 Courses
Hyperbolic ricci flow and its application in studying lateral ventricle morphometry
MBIA'12 Proceedings of the Second international conference on Multimodal Brain Image Analysis
Prone to supine CT colonography registration using a landmark and intensity composite method
MICCAI'12 Proceedings of the 4th international conference on Abdominal Imaging: computational and clinical applications
Efficient topological cleaning for visual colon surface flattening
MICCAI'12 Proceedings of the 4th international conference on Abdominal Imaging: computational and clinical applications
Ricci flow-based spherical parameterization and surface registration
Computer Vision and Image Understanding
Hyperbolic harmonic brain surface registration with curvature-based landmark matching
IPMI'13 Proceedings of the 23rd international conference on Information Processing in Medical Imaging
Surface- and volume-based techniques for shape modeling and analysis
SIGGRAPH Asia 2013 Courses
Teichmüller Shape Descriptor and Its Application to Alzheimer's Disease Study
International Journal of Computer Vision
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Ricci flow is a powerful curvature flow method, which is invariant to rigid motion, scaling, isometric, and conformal deformations. We present the first application of surface Ricci flow in computer vision. Previous methods based on conformal geometry, which only handle 3D shapes with simple topology, are subsumed by the Ricci flow-based method, which handles surfaces with arbitrary topology. We present a general framework for the computation of Ricci flow, which can design any Riemannian metric by user-defined curvature. The solution to Ricci flow is unique and robust to noise. We provide implementation details for Ricci flow on discrete surfaces of either euclidean or hyperbolic background geometry. Our Ricci flow-based method can convert all 3D problems into 2D domains and offers a general framework for 3D shape analysis. We demonstrate the applicability of this intrinsic shape representation through standard shape analysis problems, such as 3D shape matching and registration, and shape indexing. Surfaces with large nonrigid anisotropic deformations can be registered using Ricci flow with constraints of feature points and curves. We show how conformal equivalence can be used to index shapes in a 3D surface shape space with the use of Teichmüller space coordinates. Experimental results are shown on 3D face data sets with large expression deformations and on dynamic heart data.