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Current CT techniques are able to produce isotropic high resolution CT images (0.5mm). Recent research has revealed that the interior of the left ventricle has complex structures and topology, which has potentially valuable information. However, this makes the matching between models much more challenging. In this paper, we propose a novel method to match two models with non-trivial topology. 3D mesh...
Surface remeshing plays a fundamental role in digital geometry processing. In this paper, we present a novel framework for global surface remeshing based on symmetric Delaunay triangulations on the uniformization spaces. Surfaces with arbitrary topologies can be uniformized to one of three canonical uniformization spaces: the sphere, the Euclidean plane and the hyperbolic plane. The uniformization...
Teichmuller shape space is a finite dimensional Riemannian manifold, where each point represents a class of surfaces, which are conformally equivalent, and a path represents a deformation process from one shape to the other. Two surfaces in the real world correspond to the same point in the Teichmuller space, only if they can be conformally mapped to each other. Teichmuller shape space can be used...
Homotopy group plays a role in computational topology with a fundamental importance. Each homotopy equivalence class contains an infinite number of loops. Finding a canonical representative within a homotopy class will simplify many computational tasks in computational topology, such as loop homotopy detection, pants decomposition. Furthermore, the canonical representative can be used as the shape...
Faulty components in a network need to be localized and repaired to sustain the health of the network. In this paper, we propose a novel approach that carefully combines active and passive measurements to localize faults in wireless sensor networks. More specifically, we formulate a problem of optimal sequential testing guided by end-to-end data. This problem determines an optimal testing sequence...
3D surface matching is fundamental for shape analysis. As a powerful method in geometric analysis, Ricci flow can flexibly design metrics by prescribed target curvature. In this paper we describe a novel approach for matching surfaces with complicated topologies based on hyperbolic Ricci flow. For surfaces with negative Euler characteristics, such as a human face with holes (eye contours), the canonical...
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