Professor Keenan Crane (Carnegie Mellon University): “Compressed Shape Representations for Geometric Computing & Learning”

Speaker: Professor Keenan Crane (Carnegie Mellon)

Title: “Compressed Shape Representations for Geometric Computing & Learning”

Video:

Abstract:  Digital encodings of shape have major implications for the way we acquire, transmit, analyze, and learn information about the natural world.  This talk explores how encodings of shape via integer normal coordinates, little-known outside geometric topology, can be enriched and generalized to meet the needs of applied geometric computing.  The basic observation is that shapes can be “compressed” by counting the number of times they intersect a fixed background grid—leveraging the logarithmic compression inherent in place-value number encodings.  We will begin in 2D, and show how this perspective leads to quality guarantees and robust data structures for surface mesh processing (e.g., surface mapping, or solving numerical PDEs).  We will then share ongoing work on 3D encodings, leading to a subgrid marching tetrahedra algorithm that overcomes fundamental challenges with classic marching cubes (e.g., capturing thin sheets), and leads to new representations for 3D generative models.

Bio: Keenan Crane is the Michael B. Donohue Associate Professor of Computer Science and Robotics at Carnegie Mellon University, and a member of the Center for Nonlinear Analysis.  He is a Packard Fellow and recipient of the NSF CAREER Award, was a Google PhD Fellow in the Department of Computing and Mathematical Sciences at Caltech, and was an NSF Mathematical Postdoctoral Research Fellow (MSPRF) at Columbia University.  Crane’s work applies insights from differential geometry to build fundamental representations and algorithms for processing, designing, and analyzing geometric data.  This work has been featured in venues such as Notices of the AMS and Communications of the ACM, as well as in the popular press through outlets such as WIRED, Popular Mechanics, National Public Radio, The New York Times, and Scientific American.