Centroidal Voronoi tessellations: algorithms and applications

Dr. Max Gunzburger

Department of Mathematics
School of Computational Science and Information Technology
Florida State University

February 13, 2004
McDonnell-Douglas Auditorium
Room 100, Material Science Building
1:45 PM

Abstract

Centroidal Voronoi tessellations (CVTs) are special Voronoi diagrams for which the generators of the diagrams are also the centers of mass (with respect to a given density function) of the Voronoi cells. CVTs have many uses and applications, several of which we discuss. These may include data compression, image segmentation, clustering, cell biology, territorial behavior of animals, resource allocation, grid generation in volumes and on surfaces, meshless computing, hypercube sampling, and reduced-order modeling. We then discuss deterministic and probabilistic methods for determining CVTs, including some new probabilistic methods that are amenable to parallel processing.