Professor Hong-Kai Zhao (赵宏凯 教授) Department of Mathematics, University of California, Irvine

Abstract: I will present a general framework for solving partial differential equations on manifolds represented by meshless points, i.e., point clouds, without parameterization or connection information. Our method is based on a local approximation of the manifold, such as using least squares, in a local intrinsic coordinate system constructed by local principal component analysis (PCA) using K-nearest neighbors (KNN). Once the local reconstruction is available, differential operators on the manifold can be approximated discretely. The framework extends to manifolds of any dimension. The complexity of our method scales well with the total number of points and the true dimension of the manifold (not the embedded dimension). Applications to point cloud analysis and manifold learning will be discussed.

About the Speaker: Hongkai Zhao is Professor in the Department of Mathematics and the Department of Computer Science at UC Irvine. He got his BS from Peking University in 1990 and his Ph.D from UCLA in 1996. He was Gabor Szego Assistant Professor at Stanford before joining UC Irvine. He was the Chair of the Mathematics Department at UC Irvine 2010-2013. Hongkai Zhao was awarded the Sloan Foundation Fellowship in 2002 and Feng Kang Prize in 2007. He was Changjiang Guest Professor at Peking University and Distinguished Professor in Beijing International Center for Mathematical Research.  His research areas include level set methods, multiphase and moving interface problems, inverse problems and imaging, image processing and computer vision, and the fast sweeping method for Hamilton-Jacobi equations.

Date&Time: July 22, 2013 (Monday), 15:00-16:00
Location: 606 Conference Room, No.3 Heqing Road, Haidian District