Short Courses

A Short Course on Level Set Methods and Applications
Saturday, July 22, 2006
Hyatt Regency Century Plaza Hotel

Instructors

Stanley Osher (UCLA)
Eran Guendelman (Stanford University)
Joseph Teran (NYU)

Course Description

Level set methods have seen tremendously expanded applications over the past 15 years spanning fields including image/video processing, computer vision, graphics, computational physics, biomechanics and the entertainment industry.  This has been made possible by the flexibility of the level set formulation in dealing with topology changes of curves and surfaces, and by the mathematical theory and numerical tools developed in the last 15 years in studying these methods.
In this short course, we will cover many of the wide-ranging applications of level set methods in numerical simulation of fluid and solids mechanics.  Examples include free surface and multiphase flows for fire and liquids with the material interface represented as level sets, fracture dynamics with the crack tip represented as the intersection of two level sets and path (front propagation velocity) determined via gradient descent, as well as solid/fluid coupling and FEM simulation of elastic solids like biological tissues and cloth.  We will also discuss applications in image processing including denoising, image segmentation and restoration as well as inverse problems and optimal design.  In particular, an optimal design strategy for the structure of photonic crystals will be examined.  Photonic crystals are dielectric structures and optimally have piecewise constant dielectric distribution, a level set is used to model the interface between materials with different dielectric constants and the front is propagated via gradient descent.

Course Outline

1. Introduction to Level Set Methods and Numerical Tools (Osher)
2. Simulating Fluids with Levelset Methods (Guendelman)
3. A Variational Crack Propagation Model Using Level Set Methods and the Virtual Node Algorithm (Teran)
4. Inverse Problems and Image Science (Osher)
5. Solid Fluid Coupling (Guendelman)
6. Quasistatic Invertible Finite Elements for Finite Strain Elasticity (Teran)

Dr. Stanley Osher is Professor of Mathematics, and Director of Special Projects at the Institute for Pure and Applied Mathematics (IPAM) at the University of California, Los Angeles.  Dr. Osher is the co-inventor and principal developer of widely used state-of-the-art high resolution schemes for approximating conservation laws and Hamilton-Jacobi equations; level set methods for computing moving fronts involving topology changes; total variation and other partial differential equations based image processing techniques.  His many innovations have had enormous impact across disciplinary boundaries in image processing, control, flow simulation, as well as many other fields and have enabled him to co-found three companies.  Dr. Osher has recently been elected to the National Academy of Sciences and has been a Fulbright Fellow, an Alfred P. Sloan Fellow, a SERC Fellow and a US – Israeli Binational Fellow.  He has also received many awards including the SIAM Kleinman Prize for his many contributions to the analysis and computation and applications in science and engineering, the 2003 ICIAM Pioneer Prize, the Japan Society of Mechanical Engineers, Computational Mechanics Award 2002 and the NASA Public Service Group Achievement Award 1992. Dr. Osher has also been an invited speaker at the International Congress of Mathematicians.

Eran Guendelman is currently completing his Ph.D. at Stanford University (expected June, 2006) under the supervision of Ronald Fedkiw. His research interests include physically-based simulation, computational solid and fluid mechanics, and computer graphics. He has developed algorithms for rigid body simulation as well as for solid-fluid coupling problems involving thin deformable shells interacting with free-surface water. He has also spent time at Industrial Light + Magic, helping to develop simulation techniques for solids and fluids, and integrating these into the visual effects production pipeline.

Dr. Joseph Teran recently completed his Ph.D. at Stanford University as an NSF Graduate Research Fellow under the supervision of Ronald Fedkiw.  He is currently a National Science Foundation Mathematical Sciences Postdoctoral Fellow at the Courant Institute working with Dr. Charles Peskin and Dr. Michael Shelley.  At Stanford University his work was centered on developing algorithms for simulating elastic solids with particular emphasis on improving computational cost and robustness.  Skeletal muscle simulation was used as an application area for evaluating the relevance of the algorithmic developments.  At Courant, his focus is on algorithm development for simulations that couple solids and fluids as well as on applications in liquid crystal elastomer dynamics.  While in graduate school, Dr. Teran worked with Honda Research in an effort to develop realistic musculature models of the lower extremity for device testing.  He also spent time with Sony Pictures Imageworks applying his algorithms to realistic character flesh dynamics for digital doubles in movies.