Abstract:

Level set methods, an important class of partial differential equation
(PDE) methods, define dynamic surfaces implicitly as the level set (isosurface)
of a sampled, evolving nD function. The course begins with
preparatory material that introduces the concept of using partial
differential equations to solve problems in computer graphics, geometric
modeling and computer vision. This will include the structure and
behavior of several different types of differential equations, e.g. the level
set equation and the heat equation, as well as a general approach to
developing PDE-based applications. The second stage of the course will
describe the numerical methods and algorithms needed to actually
implement the mathematics and methods presented in the first stage.
The course closes with detailed presentations on several level set/PDE
applications, including image/video inpainting, pattern formation,
image/volume processing, 3D shape reconstruction, image/volume
segmentation, image/shape morphing, geometric modeling, anisotropic
diffusion, and natural phenomena simulation.

Last modified on September 8, 2004.