CSE Distinguished Seminar | Justin Solomon

Abstract

Two contrasting viewpoints can be used to understand the geometry of a 3D shape. On the one hand, the outer surface of a shape can be thought of as a two-dimensional curved object embedded in space; on the other hand, we might view the outer surface as enclosing a three-dimensional volume of interest. These perspectives are not the same: For example, the top and bottom of a long, flat rectangle are close volumetrically but far apart along the outer surface.

Most algorithms for 3D shape analysis and understanding take the surface-based perspective. This is amenable to efficient computation but fails to capture realistic properties of surfaces encountered in computer vision and graphics applications, which often bound volumetric objects. In this talk, I will describe efforts jointly with students in the MIT Geometric Data Processing Group and collaborators elsewhere to overcome the computational challenges of incorporating volumetric information into 3D shape analysis. Along the way, we will introduce relevant tools from discrete/smooth differential geometry, meshing, and the boundary element method (BEM) that will provide theoretical and algorithmic insight into this challenging problem.