CVPR 2001 Short Course

 

Level-set Methods and Partial Differential Equations in Computer Vision and Image Processing

 

Instructors: Stanley Osher (UCLA), Guillermo Sapiro (University of Minnesota), and Ron Fedkiw (Stanford University)

 

Duration: 3.5 hours

 

 

SUMMARY

 

Level-set methods and partial differential equations are receiving an increasing amount of attention from the computer vision and image processing communities. These techniques provide a fundamental framework for addressing many problems in these areas. In this course we will discuss the underlying concepts, equations, and numerical methods for this technique. A large number of applications will be discussed.

 

TOPICS

 

Fundamentals (1.5 hours):

      Derivation of level-set equations

      Basic numerical implementation

      Variational level sets

      Fast numerical implementations

      Constructing the embedding function

      PDE's on surfaces

 

Applications (1.5 hours):

      Image segmentation

      Image interpolation

      Image enhancement

      Object tracking

      Pattern generation

      Vector field denoising and visualization

      Image inpainting

      Natural phenomena simulation

      Stereo

 

Discussion and the future (.5 hours)

 

 

COURSE MATERIAL

 

G. Sapiro, Geometric Partial Differential Equations and Image Analysis, Cambridge University Press, January 2001

 

S. Osher and R. Fedkiw, Level set methods: An overview and some recent result, UCLA CAM Report 00-08, to appear, J. Comp. Physics

 

 

BIOGRAPHIES

 

Stanley Osher was born in Brooklyn, New York on April 24, 1942. He received his B.S from Brooklyn College in 1962, M.S. and Phd. from the Courant Institute of Mathematical Sciences, New York University in 1964 and 1966 respectively. He has been a Professor of Mathematics at UCLA since 1977. Before that he was at SUNY, Stony Brook, UC Berkeley and Brookhaven National Laboratory. He is the coinventor of: (1) The Level Set Method, (2)Total Variation Based Image Restoration and (3) High order ENO and WENO schemes for computing flows with steep gradients. His research interests include: computer vision, image/video processing, graphics, scientific computing, numerical analysis and applied partial differential equations. He has over 110 research papers in refereed journals, is the associate editor of four major journals, and has over 25 former Ph.D. students.

 

S. Osher has been a Fulbright, Alfred P. Sloan, SERC (England) and U. S.-Israel Fellow, has shared the NASA Public Service Group Achievement Award, was an invited speaker at the International Congress of Mathematicians.

 

His work has been cited frequently by the national and international media, most recently in Science News, v155, April 1999, "Computing at the Edge", and Die Zeit, v16, Sept. 1999, "Flutwellen aus dem Computer"

 

From 1988-1995 he was Co-Founder, Co-CEO of Cognitech, Inc, CA. This company has been recognized professionally and by the media for its innovative and successful nonlinear partial differential based approach to image and video processing. From 1998-present, Founder, CEO of Level Set Systems, Inc., Pacific Palisades, CA.

 

 

Guillermo Sapiro was born in Montevideo, Uruguay, on April 3, 1966. He received his B.Sc. (summa cum laude), M.Sc., and Ph.D. from the Department of Electrical Engineering at the Technion, Israel Institute of Technology, in 1989, 1991, and 1993 respectively. After post-doctoral research at MIT, Dr. Sapiro became Member of Technical Staff at the research facilities of HP Labs in Palo Alto, California. He is currently with the Department of Electrical and Computer Engineering at the University of Minnesota.

 

G. Sapiro works on differential geometry and geometric partial differential equations, both in theory and applications in computer vision, computer graphics, medical imaging, and image analysis. He recently co-edited a special issue of IEEE Image Processing in this topic and a second one in the Journal of Visual Communication and Image Representation.

 

G. Sapiro was awarded the Gutwirth Scholarship for Special Excellence in Graduate Studies in 1991, the Ollendorff Fellowship for Excellence in Vision and Image Understanding Work in 1992, the Rothschild Fellowship for Post-Doctoral Studies in 1993, the Office of Naval Research Young Investigator Award in 1998, the Presidential Early Career Awards for Scientist and Engineers (PECASE) in 1988, and the National Science Foundation Career Award in 1999. He has published about 100 peer-reviewed papers and one recent book.

 

G. Sapiro is a member of IEEE.

 

Ron Fedkiw received his B.S. and M.S. in Pure Mathematics from the State University of New York at Buffalo, and his Ph.D. in Applied Mathematics from UCLA in 1996. He did postdoctoral studies in Applied Mathematics at UCLA and in Aeronautics at Caltech before becoming an Assistant Professor of Computer Science at Stanford University where he concentrates on Scientific Computing and Computer Graphics.

 

R. Fedkiw spent two years consulting with Arete Entertainment developing award winning software used to simulate nature effects for television and film. He spent one year consulting at Centropolis Effects working on computer graphics simulation of smoke for "The Patriot" starring Mel Gibson. Currently he consults with Industrial Light and Magic where he has worked on the recent blockbusters "The Mummy Returns" and "Jurassic Park III". His most recent Siggraph paper addresses visual simulations of liquids and includes images of "Shrek" taking a bath in mud.

 

R. Fedkiw is the author of over 25 (mostly journal) publications and has given about 50 invited talks. He is the recipient of numerous awards for both scholarship and teaching including the Office of Naval Research Young Investigator Award (ONR YIP) in 2001.

 

 

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