title: Simplification of three-dimensional density maps.
abstract: We consider scientific data sets that describe density functions over three-dimensional geometric domains. Such data sets are often large and coarsened representations are needed for visualization and analysis. Assuming a tetrahedral mesh representation, we construct such representations with a simplification algorithm that combines three goals: the approximation of the function, the preservation of the mesh topology, and the improvement of the mesh quality. The third goal is achieved with a novel extension of the well-known quadric error metric. We perform a number of computational experiments to understand the effect of mesh quality improvement on the density map approximation. In addition, we study the effect of geometric simplification on the topological features of the function by monitoring its critical points.
authors.affiliation: Department of Computer Science, Duke University, Durham, NC 27708, USA. vijay@cs.duke.edu
authors.forename: Vijay
authors.initials: V
authors.lastname: Natarajan
authors.forename: Herbert
authors.initials: H
authors.lastname: Edelsbrunner
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D003196:Computer Graphics; D016208:Databases, Factual; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods*; D015233:Models, Statistical; D009716:Numerical Analysis, Computer-Assisted; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted; D016008:Statistical Distributions; D014584:User-Computer Interface