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2015 | OriginalPaper | Buchkapitel

Fiber Orientation Distribution Functions and Orientation Tensors for Different Material Symmetries

verfasst von : Maher Moakher, Peter J. Basser

Erschienen in: Visualization and Processing of Higher Order Descriptors for Multi-Valued Data

Verlag: Springer International Publishing

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Abstract

In this paper we give closed-form expressions of the orientation tensors up to the order four associated with some axially-symmetric orientation distribution functions (ODF), including the well-known von Mises-Fisher, Watson, and de la Vallée Poussin ODFs. Each is characterized by a mean direction and a concentration parameter. Then, we use these elementary ODFs as building blocks to construct new ones with a specified material symmetry and derive the corresponding orientation tensors. For a general ODF we present a systematic way of calculating the corresponding orientation tensors from certain coefficients of the expansion of the ODF in spherical harmonics.

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Vorheriges Kapitel Finslerian Diffusion and the Bloch–Torrey Equation

Nächstes Kapitel Topology of 3D Linear Symmetric Tensor Fields

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Titel: Fiber Orientation Distribution Functions and Orientation Tensors for Different Material Symmetries
verfasst von: Maher Moakher
Peter J. Basser
Verlag: Springer International Publishing
Buch: Visualization and Processing of Higher Order Descriptors for Multi-Valued Data
Print ISBN: 978-3-319-15089-5

Electronic ISBN: 978-3-319-15090-1

Copyright-Jahr: 2015
DOI: https://doi.org/10.1007/978-3-319-15090-1_3

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