Stereological estimation of integral mixed curvature with application |
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Authors: | V. Bene &dagger ,M. Hlawiczková ,& K. Volení k&Dagger |
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Affiliation: | Department of Probability and Statistics, Charles University, Sokolovská83,;86 75 Prague 8, Czech Republic;Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Pod vodárenskou věží4, 18208 Prague 8, Czech Republic;National Research Institute for the Protection of Materials, 19011 Prague 9-Běchovice, Czech Republic |
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Abstract: | This article addresses a bounded system of compact smooth surfaces in three-dimensional space. Recently, an unbiased estimator of the integral mixed curvature of the given system based on a vertical sampling design has been proposed. The aims of the present paper are: (i) to show that the proposed estimator may have an infinite variance; (ii) to suggest a modification that has better statistical properties; (iii) to extend the point estimator to a function that monitors the curvature along the gradient microstructures; (iv) to present an application of the method to real microscopic images. |
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Keywords: | Integral mixed curvature surface system systematic geometric sampling |
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