题目: Geometric Methods for Analyzing Unorganized Data in 3D and Higher

报告人：Rongjie Lai（Rensselaer Polytechnic Institute）

时间: 2014年12月29日, 周一   下午15:00-16:30

地点：管理楼1611

摘要: Point clouds are the simplest and most basic forms for data representation in 3D and higher. Examples include those used in 3D modeling, image science, the Internet and many others. Analyzing and inferring the underlying structure from the point clouds are crucial in many applications. However, these raw data or primitive representations in Rn are lack of global parameterization and far from intrinsic, which obstruct further intrinsic and global analysis for given data. On the other hand, point clouds from practical problems are usually with certain coherent structures which allow us to model them as points sampled from lower dimensional Riemmannian manifolds in a high dimensional space. In this talk, I will discuss our work on solving PDEs on point clouds. It can be applied to manifolds with arbitrary dimensions and co-dimensions. This approach enables us to propose geometric methods for analyzing and understanding point clouds through solutions of PDEs on point clouds. As applications, I will demonstrate our methods to intrinsic geometric quantities extraction, comparison and registration for point clouds based on solutions of certain geometric PDEs. (Joint work with Hongkai Zhao)

主办单位：365英国上市官网  

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