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Stereological Estimation of Orientation Distribution of Generalized Cylinders from a Unique 2D Slice

Published online by Cambridge University Press:  24 October 2013

Jean-Pierre Da Costa ,
Stefan Oprean ,
Pierre Baylou  and
Christian Germain
Jean-Pierre Da Costa*
Affiliation:
Univ. Bordeaux, IMS, UMR 5218, F-33400 Talence, France CNRS, IMS, UMR 5218, F-33400 Talence, France
Stefan Oprean
Affiliation:
CNRS, IMS, UMR 5218, F-33400 Talence, France
Pierre Baylou
Affiliation:
Univ. Bordeaux, IMS, UMR 5218, F-33400 Talence, France CNRS, IMS, UMR 5218, F-33400 Talence, France
Christian Germain
Affiliation:
Univ. Bordeaux, IMS, UMR 5218, F-33400 Talence, France CNRS, IMS, UMR 5218, F-33400 Talence, France
*
*Corresponding author. E-mail: [email protected]
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Abstract

Though three-dimensional (3D) imaging gives deep insight into the inner structure of complex materials, the stereological analysis of 2D snapshots of material sections is still necessary for large-scale industrial applications for reasons related to time and cost constraints. In this paper, we propose an original framework to estimate the orientation distribution of generalized cylindrical structures from a single 2D section. Contrary to existing approaches, knowledge of the cylinder cross-section shape is not necessary. The only requirement is to know the area distribution of the cross-sections. The approach relies on minimization of a least squares criterion under linear equality and inequality constraints that can be solved with standard optimization solvers. It is evaluated on synthetic data, including simulated images, and is applied to experimental microscopy images of fibrous composite structures. The results show the relevance and capabilities of the approach though some limitations have been identified regarding sensitivity to deviations from the assumed model.

Keywords

stereologycylinderorientationfibrous structuresmaterial science
Type
Techniques and Instrumentation Development
Information
Microscopy and Microanalysis , Volume 19 , Issue 6 , December 2013 , pp. 1678 - 1687
Copyright
Copyright © Microscopy Society of America 2013 

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