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A Dictionary Approach to Electron Backscatter Diffraction Indexing*

Published online by Cambridge University Press:  09 June 2015

Yu H. Chen ,
Se Un Park ,
Dennis Wei ,
Greg Newstadt ,
Michael A. Jackson ,
Jeff P. Simmons ,
Marc De Graef  and
Alfred O. Hero
Yu H. Chen
Affiliation:
Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109, USA
Se Un Park
Affiliation:
Schlumberger Research, Cambridge, MA 02139, USA
Dennis Wei
Affiliation:
Thomas J. Watson Research Center, IBM Research, Yorktown Heights, NY 10598, USA
Greg Newstadt
Affiliation:
Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109, USA
Michael A. Jackson
Affiliation:
BlueQuartz Software, Dayton, OH 45066, USA
Jeff P. Simmons
Affiliation:
Materials and Manufacturing Directorate, AFRL/MLLMD, Wright-Patterson AFB, OH 45433, USA
Marc De Graef*
Affiliation:
Department of Materials Science and Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA
Alfred O. Hero
Affiliation:
Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109, USA
*
*Corresponding author. degraef@cmu.edu
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Abstract

We propose a framework for indexing of grain and subgrain structures in electron backscatter diffraction patterns of polycrystalline materials. We discretize the domain of a dynamical forward model onto a dense grid of orientations, producing a dictionary of patterns. For each measured pattern, we identify the most similar patterns in the dictionary, and identify boundaries, detect anomalies, and index crystal orientations. The statistical distribution of these closest matches is used in an unsupervised binary decision tree (DT) classifier to identify grain boundaries and anomalous regions. The DT classifies a pattern as an anomaly if it has an abnormally low similarity to any pattern in the dictionary. It classifies a pixel as being near a grain boundary if the highly ranked patterns in the dictionary differ significantly over the pixel’s neighborhood. Indexing is accomplished by computing the mean orientation of the closest matches to each pattern. The mean orientation is estimated using a maximum likelihood approach that models the orientation distribution as a mixture of Von Mises–Fisher distributions over the quaternionic three sphere. The proposed dictionary matching approach permits segmentation, anomaly detection, and indexing to be performed in a unified manner with the additional benefit of uncertainty quantification.

Keywords

electron backscatter diffraction patternEBSDdynamical electron scatteringdictionary matchingmaximum likelihood orientation estimatesVon Mises–Fisher mixture distribution
Type
Techniques and Equipment Development
Information
Microscopy and Microanalysis , Volume 21 , Issue 3 , June 2015 , pp. 739 - 752
Copyright
© Microscopy Society of America 2015 

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Footnotes

*

Part of this work was reported in the Proceedings of the IEEE International Conference on Image Processing (ICIP), Melbourne, Australia, September 2013.

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