3D surface classification is a fundamental problem in computer vision and computational geometry. Surfaces can be classified by different transformation groups. Traditional classification methods mainly use topological transformation groups and Euclidean transformation groups. We introduce a novel method to classify surfaces by conformal transformation groups. Conformal equivalent class is refiner than topological equivalent class and coarser than isometric equivalent class, making it suitable for practical classification purposes. For general surfaces, the gradient fields of conformal maps form a vector space, which has a natural structure invariant under conformal transformations. We present an algorithm to compute this conformal structure, which can be represented as matrices, and use it to classify surfaces. The result is intrinsic to the geometry, invariant to triangulation and insensitive to resolution. To the best

We discuss conjectures following from the attractor mechanism in type II string theory about the possible Chern classes of stable holomorphic vector bundles on Calabi-Yau threefolds. In particular, we give sufficient conditions for Chern classes to correspond to stable bundles.

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A structured light system for three-dimensional shape measurement with single camera has the shortcoming of camera occlusion. To alleviate this problem, this paper introduces a structured light system with dual cameras for three-dimensional shape measurement. We discuss (1) system description, (2) system calibration, (3) three-dimensional data registration using the iterative closest-point (ICP) algorithm, and (4) three-dimensional data merging using holoimage. The principle of the system is introduced, and experiments are presented to verify its performance.

This paper develops a novel computational technique to define and construct manifold splines with only one singular point by employing the rigorous mathematical theory of Ricci flow. The central idea and new computational paradigm of manifold splines are to systematically extend the algorithmic pipeline of spline surface construction from any planar domain to an arbitrary topology. As a result, manifold splines can unify planar spline representations as their special cases. Despite its earlier success, the existing manifold spline framework is plagued by the topology-dependent, large number of singular points (ie,| 2 g 2| for any genus-g surface), where the analysis of surface behaviors such as continuity remains extremely difficult. The unique theoretical contribution of this paper is that we devise new mathematical tools so that manifold splines can now be constructed with only one singular point, reaching their