Department of Mathematics
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.