10: Level Set and PDE Methods for Computer Graphics



Sunday, Full Day
8:30 am – 5:15 pm
Room 206

The underlying concepts, equations, and numerical methods for level set and partial differential equation (PDE) methods, and how they may be used in a variety of graphics applications, including image inpainting, pattern formation, 3D curve computation, 3D shape reconstruction, surface editing, image and shape morphing, and fire and water simulation.

Prerequisites
Knowledge of calculus, linear algebra, and computer graphics, including geometric modeling and computer animation. Some familiarity with differential geometry, differential equations, numerical computing, and image processing is strongly recommended but not required.

Topics
Fundamentals (level set and PDE concepts, derivation of level set equations and other PDEs, numerical methods). Practical considerations (building a level set library, importing conventional geometry). Applications (image inpainting, pattern formation, curve computation, image and volume processing, shape reconstruction, image and volume segmentation, image and shape morphing, surface editing, dynamic visibility, anistropic diffusion, and natural phenomena simulation).

References
S. Osher and R.P. Fedkiw, The Level Set Method and Dynamic Implicit Surfaces, Springer-Verlag, New York, 2002.

S. Osher and N. Paragios (eds.), Geometric Level Set Methods in Imaging, Vision and Graphics, Springer Verlag, 2002.

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

VISPack: A C++ object-oriented library for processing volumes, images, and level-set surface models.

Organizers
David Breen
California Institute of Technology

Guillermo Sapiro
University of Minnesota


Lecturers
David Breen
California Institute of Technology

Ron Fedkiw
Stanford University

Stanley Osher
University of California, Los Angeles

Guillermo Sapiro
University of Minnesota

Ross Whitaker
University of Utah


8:30 Welcome
Breen
8:40 Introduction to PDEs and Solution Methods
Sapiro
9:30 Introduction to Level Set Methods and Technology
Osher
10:15 Break
10:30 Fast Surface Reconstruction Using the Level Set Method: Dynamic Visibility in an Implicit Visibility in an Implicit Framework
Osher
11:15 3D Scan Conversion of Geometric Models; Level Set 3D Model Morphing; Level Set Surface Editing
Breen
12:15 Lunch
1:30 Image Inpainting; Computing Geodesics and Generalized Geodesics for Computer Graphics; A Geodesic Framework for Segmentation; Edge Tracing in 2D/3D; Shape and Color Preserving Representation of High Dynamic Range Images; Pattern Formation in 3D; Surface Fairing
Sapiro
2:45 VISPACK
Whitaker
3:15 Break
3:30 Direct Sinogram Reconstruction; Image/Shape Blending; Antialiasing Binary Volumes
Whitaker
4:15 Animation and Rendering of Complex Water Surfaces; Physically Based Modeling and Animation of Fire
Fedkiw




Additional information from SIGGRAPH 2002 Courses is available in the Course Notes
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