, Volume 44, Issue 11, pp 4891-4905
Date: 22 Feb 2013

Unsupervised Learning for Efficient Texture Estimation From Limited Discrete Orientation Data

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The estimation of orientation distribution functions (ODFs) from discrete orientation data, as produced by electron backscatter diffraction or crystal plasticity micromechanical simulations, is typically achieved via techniques such as the Williams–Imhof–Matthies–Vinel (WIMV) algorithm or generalized spherical harmonic expansions, which were originally developed for computing an ODF from pole figures measured by X-ray or neutron diffraction. These techniques rely on ad-hoc methods for choosing parameters, such as smoothing half-width and bandwidth, and for enforcing positivity constraints and appropriate normalization. In general, such approaches provide little or no information-theoretic guarantees as to their optimality in describing the given dataset. In the current study, an unsupervised learning algorithm is proposed which uses a finite mixture of Bingham distributions for the estimation of ODFs from discrete orientation data. The Bingham distribution is an antipodally-symmetric, max-entropy distribution on the unit quaternion hypersphere. The proposed algorithm also introduces a minimum message length criterion, a common tool in information theory for balancing data likelihood with model complexity, to determine the number of components in the Bingham mixture. This criterion leads to ODFs which are less likely to overfit (or underfit) the data, eliminating the need for a priori parameter choices.

Manuscript submitted December 31, 2012.