Sunday, July 13, 1997
Stanford University, Stanford, California
James Sethian, University of California, Berkeley, and Lawrence Berkeley National Laboratory
Manufacturing microchips, locating heart walls in MRI scans, sharpening noisy images, tracking flames in turbulent flows and locating geodesics on surfaces all share a common concern, namely tracking moving interfaces. This is an introductory course in level set techniques, which are a class of computational methods for tracking moving interfaces. These techniques are currently in use in a wide collection of theoretical engineering, and industrial applications, including the geometry of moving surfaces, medical imaging, the manufacture of semiconductor devices, and fluid mechanics.
This course is an equal blend of theory, algorithms, and applications. It will highlight robust and efficient algorithms for the above applications, as well as many others. Along the way, we will introduce and cover a variety of related topics necessary to build these algorithms, including approximation of viscosity solutions to partial differential equations, the numerical technology from hyperbolic conservation laws, and fast heapsort algorithms for special cases arising from stationary Hamilton-Jacobi equations.
The course is aimed at a general introductory level. The intended audience is mathematicians, applied scientists, practicing engineers, computer graphic artists, and anyone interested in the evolution of boundaries and interfaces.
There are no formal prerequisites; this course is a condensation of a one-semester course at Berkeley on level set methods that is attended by people from across the range of sciences and engineering disciplines. Some emphasis will be placed on real algorithms, hence a basic familiarity with numerical analysis is helpful, but not required.
James Sethian is Professor of Mathematics at the University of California at Berkeley, and Department Head of the Mathematics Department at the Lawrence Berkeley National Laboratory.
8:45-9:00 Welcome Remarks: James A. Sethian
9:00-10:00 Overview of Level Set Methods. How to Track a Moving Front: Theory and Algorithms
10:30-12:00 Fast Techniques: Computational Adaptivity and Fast Marching Methods
1:30-3:00 Applications I: The Geometry of Moving Curves and Surfaces, Geodesics on Surfaces, Sharpening Noisy Images, and Locating Structures in Medical Imaging
3:30-5:00 Applications II: Making Microchips, Following Rising Bubbles, Tracking Flames, and Computing Robotic Paths
5:00-5:30 Open Discussion
5:30 Course adjourns
Seats are limited. We urge attendees to register early to take advantage of the advance rates. To register, please complete the Preregistration Form and send it, with your payment, to reach SIAM on or before June 30, 1997.
Registration fees include a recently published book on level set methods by James Sethian, coffee breaks, and lunch.
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