George Kamberov
Department of Computer Science
Stevens Institute of Technology
"Topology and Geometry of Unorganized Point Clouds"
Thursday February 17th, 12:20-1:10, Lind 409

Abstract
The reliable extraction of quantitative geometric information from a discrete cloud of points sampled from a surface is an important task in computer vision and computer graphics. There is a massive amount of excellent research attempting to deal with this challenging task.

The dominant paradigm is to fit a smooth parameterized or implicit surface, or a polygonal mesh to the point cloud, and then to apply the standard differential geometric formulae on the smooth surface or one of the numerous methods for estimating curvature and curvature lines on a polygonal surface. These approaches generally perform badly and far from real-time on sparse, noisy, non-organized data and on scenes involving multiple objects, occlusions, and partial views.

We present a new method for defining neighborhoods, and assigning principal curvature frames, and mean and Gauss curvatures to the points of an unorganized oriented point-cloud. The neighborhoods are estimated by measuring implicitly the surface distance between points. The 3D shape recovery is based on conformal geometry, works directly on the cloud, and does not rely on the generation of polygonal or smooth models.

Bio
George Kamberov is the head of the Computer Visualization and Graphics Laboratory and an Associate Professor in Computer Science at Stevens Institute of Technology. Before joining Stevens he was G. C. Evans Instructor at Rice University and a William Chauvenet Assistant professor at Washington University at St. Louis. He has held visiting professor positions at the University of Massachusetts, Amherst, and at the University of North Carolina, Chapel Hill. His research interests and publications are in computer vision, real-time computer graphics, shape representation, differential geometry, stochastic systems, differential equations, and high energy physics. His recent and ongoing work is on developing and implementing new methods for analysis, and shape representation and visualization and apply them to problems arising in medical imaging, in the analysis of high energy plasma, in the development and deployment of situation awareness tools for monitoring and control of large sensor networks, and in point based rendering.

George Kamberov received a Ph.D. in Mathematics from the University of Pennsylvania in 1990. He is publishing research papers in mathematics, physics, and computer science. In 1992 he coauthored a research monograph "Quaternions, Spinors, and Surfaces" published by the American Mathematical Society.

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