


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,
SpringerVerlag, 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++ objectoriented library for processing volumes,
images, and levelset 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 


