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GRASP Lab Seminar 2003-2004
December 12, 2:00 PM, Levine Hall 315, hosted by Kostas Daniildis.
Gerda Kamberova
Hofstra University, NY
Surface Shape from Discrete Point Clouds
Abstract: Given an oriented 3D cloud of points (i.e., points with normals) , we address the problem of computing the shape invariants of the underlying unknown surface from which the cloud was sampled. In this talk we will overview the conformal method for assigning curvatures and principal curvature frames to an unorganized oriented point-cloud. The method is based on conformal geometry. We have tested the method on data from stereo, laser range finders, and medical data. For the purpose of evaluation, we demonstrate the performance of our method on publicly available synthetic data -- and show that we do comparably or better than other methods commonly employed in the field. A second line of research that relates to the problem, is the extraction of the cloud topology, prior to recovering its geometry. Recently we have defined a new measure of "closeness" on the cloud that account for surface distance (not only Euclidean distance). Thus we have a machine for extracting locally the shape of the surface from the unorganized oriented point cloud. Discrete clouds of points and their differential invariants are more and more appropriate for high performance computer graphics systems. From a point of view of computer vision, such models are attractive because they do not impose a'priori artificial assumption on the surfaces, and do not use global polyhedral approximations. The conformal method that we are developing does not require global surface parameterization, global polyhedral approximation, or fitting of model surfaces to the data.
Biography: PhD in Computer Science, University of Pennsylvania, Philadelphia, Dec 1992 Area: Decision making under uncertainty (in particular, applications to computer vision, robotics, and multi sensor fusion) MS in Mathematics, Sofia State University, Bulgaria, 1982 Area: Topological algebra Previous Teaching/Research experience: Rice University, University of Pennsylvania, Washington University in St. Louis
