Hongkai Zhao

Department of Mathematics

Stanford University

**Abstract:**
In this talk I am going to address a fundamental problem in
computer visualization: how to find and represent the shape of a set
of scattered points, where only the positions of these points are known.
The key idea is the implicit representation of the shape as a particular
level set of a level set function. The final shape is interpreted as
an "elastic membrane" attached to these points. A variational formulation
is used. Numerically we dynamically follow the gradient decent
direction of the energy functional using level set method on fixed
Cartesian grids. Complicated geometries, topological changes and
singularities can be handled naturally.