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3D dynamic surface tracking is an important research problem and plays a vital role in many computer vision and medical imaging applications. However, it is still challenging to efficiently register surface sequences which has large deformations and strong noise. In this paper, we propose a novel automatic method for non-rigid 3D dynamic surface tracking with surface Ricci flow and Teichmiiller map...
In brain mapping research, parameterized 3-D surface models are of great interest for statistical comparisons of anatomy, surface-based registration, and signal processing. Here, we introduce the theories of continuous and discrete surface Ricci flow, which can create Riemannian metrics on surfaces with arbitrary topologies with user-defined Gaussian curvatures. The resulting conformal parameterizations...
In this paper, we propose multivariate tensor-based surface morphometry, a new method for surface analysis, using holomorphic differentials; we also apply it to study brain anatomy. Differential forms provide a natural way to parameterize 3D surfaces, but the multivariate statistics of the resulting surface metrics have not previously been investigated. We computed new statistics from the Riemannian...
Two surfaces are conformally equivalent if there exists a bijective angle-preserving map between them. The Teichmüller space for surfaces with the same topology is a finite-dimensional manifold, where each point represents a conformal equivalence class, and the conformal map is homotopic to the identity map. In this paper, we propose a novel method to apply conformal equivalence based shape index...
We apply multivariate tensor-based morphometry to study lateral ventricular surface abnormalities associated with HIV/AIDS. We use holomorphic one-forms to obtain a conformal parameterization of ventricular geometry, and to register lateral ventricular surfaces across subjects. In a new development, we computed new statistics on the Riemannian surface metric tensors that encode the full information...
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