The Bingham Distribution of Quaternions and Its Spherical Radon Transform in Texture Analysis |
| |
| Authors: | Karsten Kunze and Helmut Schaeben |
| |
| Institution: | (1) Department of Earth Sciences, ETH Zurich, CH-8092 Zurich, Switzerland;(2) Geoscience Mathematics and Informatics, University of Mining and Technology, D-09596 Freiberg, Germany |
| |
| Abstract: | Spherical geometry of quaternions is employed to characterize the Bingham distribution on the 3-dimensional sphere
as being uniquely composed of a bipolar, a circular and a spherical component. A new parametrization of its dispersion parameters provides a classification of patterns of crystallographic preferred orientations (CPO, or textures). It is shown that the Bingham distribution can represent most types of ideal CPO patterns; in particular single component, fiber and surface textures are represented by rotationally invariant bipolar, circular and spherical distributions, respectively. Pole figures of given crystal directions are derived by the spherical Radon transform of the Bingham probability density function of rotations, which are displayed for general and special cases. |
| |
| Keywords: | rotations crystallographic preferred orientations texture components fiber textures pole figures spherical statistics |
| 本文献已被 SpringerLink 等数据库收录！ |
|
