2010

Differential Methods for MultiDimensional Visual Data Analysis
Handbook of Mathematical Methods in Imaging, Springer, 2010
Abstract
Images in scientific visualization are the endproduct of the data processing. Starting from higherdimensional datasets, such as scalar, vector, tensor fields given on 2D, 3D, 4D domains, the objective is to reduce this complexity to twodimensional images comprehensible to the human visual system. Various mathematical fields such as in particular differential geometry, topology (theory of discretized manifolds), differential topology, linear algebra, geometric algebra, vectorfield and tensor analysis, and partial differential equations contribute to the data filtering and transformation algorithms used in scientific visualization. The application of differential methods is core to all these fields. The following chapter will provide examples from current research on the application of these mathematical domains to scientific visualization and ultimately generating of images for analysis of multidimensional datasets.