Benger et al: Differential Methods for Multidimensional Visual Data Analysis


by Werner Benger, René Heinzl, Dietmar Hildenbrand, Tino Weinkauf, Holger Theisel and David Tschumperlé
Handbook of Mathematical Methods in Imaging, DOI 10.1007/978-3-642-27795-5_35-5, © Springer Science+Business Media New York 2014,

Article URL: http://link.springer.com/referenceworkentry/10.1007/978-0-387-92920-0_35

Abstract
Images in scientific visualization are the end product of data processing. Starting from higherdimensional data sets such as scalar, vector, and tensor fields given on 2D, 3D, and 4D domains, the objective is to reduce this complexity to two-dimensional 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, vector field 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. Ultimately the use of these methods allows for a systematic approach for image generation resulting from the analysis of multidimensional datasets.

Source: Email by W. Benger, werner_AT_cct.lsu.edu, Thursday, July 16, 2015 11:49:11 AM; SpringerReference, springer_AT_sci.scientific-direct.net

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