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Directional analysis of digitized planar sets by configuration counts
1Laboratory for Computational Stochastics and MaPhySto, Department of Mathematical Sciences, University of Aarhus, Ny Munkegade, DK-8000 Aarhus C, Denmark. eva@imf.au.dk
Journal of Microscopy
|November 25, 2003
Summary
Quantify material anisotropy using the oriented rose of normal directions. This method analyzes pixel images by counting informative configurations in n x n pixel squares, offering an efficient anisotropy estimation technique.
Area of Science:
- Materials Science
- Image Analysis
- Geostatistics
Background:
- Quantifying anisotropy in random sets is crucial for understanding material properties.
- The oriented rose of normal directions is a key descriptor for material anisotropy.
- Estimating anisotropy from digital images requires robust methods.
Purpose of the Study:
- To present a novel method for estimating the oriented rose of normal directions from digitized random sets (pixel images).
- To develop an efficient algorithm for identifying informative configurations within pixel images.
- To derive estimators for anisotropy based on observed configurations.
Main Methods:
- Local image analysis using n x n pixel squares.
- Identification and counting of 'informative configurations'.
- Development of an algorithm to find these configurations.
- Derivation of estimators for the oriented rose.
Main Results:
- The number of informative configurations grows polynomially with n, ensuring computational feasibility.
- An algorithm for efficiently finding informative configurations is presented.
- Estimators for the oriented rose were derived and validated.
Conclusions:
- The proposed method provides an effective way to quantify anisotropy from pixelized data.
- The focus on informative configurations enhances the efficiency of anisotropy estimation.
- The technique is applicable to both simulated data and real-world microscopic images.