Ricci Curvature Flow for General Shape Registration and Geometric Analysis

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Venue:OE 134

Ricci Curvature Flow for General Shape Registration and Geometric Analysis

Prof. Wei Zeng

School of Computing and Information Sciences, Florida International University

Abstract:

Ricci flow has been successfully applied in the proof of Poincare’s conjecture, which deforms the Riemannian metric proportionally to the curvature, such that the curvature evolves according to a heat diffusion process. Ricci flow offers a powerful tool for shape registration and geometric analysis, which plays fundamental roles in a broad range of applications in engineering and medicine. This talk focuses on the theory of discrete surface Ricci flow, the computational algorithms and their applications in practice. Ricci flow has unique merits: (a) by Ricci flow, all shapes in real life can be unified to one of three canonical shapes, the sphere, the plane or the hyperbolic disk; (b) therefore, most 3D geometric problems can be converted to 2D image problems; (c) furthermore, this conversion preserves original geometric information. Ricci flow has been used to tackle the following fundamental problems in engineering and biomedicine: 3D human face registration and deformable surface tracking in computer vision; global surface parameterization in computer graphics; conformal brain mapping and virtual colonoscopy in medical imaging; homotopy detection in computational topology; delivery guaranteed greedy routing and load balancing in wireless sensor network, and so on. The future task is to explore Ricci curvature flow on volumetric geometric data and its efficiency for real-time geometric processing tasks.

Short Bio:

Dr. Wei Zeng is an assistant professor of the School of Computing and Information Sciences at Florida International University. Supervised by Harry Shum from Microsoft Research Asia and David Gu at Stony Brook, Dr. Zeng finished her Ph.D. thesis on “Computational Conformal Geometry Based Shape Analysis”. Her research interests include Computational Conformal Geometry, Computational Quasiconformal geometry, discrete differential geometry, discrete Ricci flow, geometric analysis, and their applications to surface matching, registration, tracking, recognition, and shape analysis. Her research areas span over medical imaging, computer vision, computer graphics and visualization, wireless sensor network, geometric modeling and computational topology. More information can be found at: http:/www.cis.fiu.edu~wzeng