Tensorial Minkowski functionals and anisotropy measures for planar patterns
Summary Quantitative measures for anisotropic characteristics of spatial structure are needed when relating the morphology of microstructured heterogeneous materials to tensorial physical properties such as elasticity, permeability and conductance. Tensor‐valued Minkowski functionals, defined in the...
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crwiley:10.1111/j.1365-2818.2009.03331.x 2024-06-02T07:56:01+00:00 Tensorial Minkowski functionals and anisotropy measures for planar patterns SCHRÖDER‐TURK, G.E. KAPFER, S. BREIDENBACH, B. BEISBART, C. MECKE, K. 2010 http://dx.doi.org/10.1111/j.1365-2818.2009.03331.x https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1111%2Fj.1365-2818.2009.03331.x https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1365-2818.2009.03331.x en eng Wiley http://onlinelibrary.wiley.com/termsAndConditions#vor Journal of Microscopy volume 238, issue 1, page 57-74 ISSN 0022-2720 1365-2818 journal-article 2010 crwiley https://doi.org/10.1111/j.1365-2818.2009.03331.x 2024-05-03T11:11:56Z Summary Quantitative measures for anisotropic characteristics of spatial structure are needed when relating the morphology of microstructured heterogeneous materials to tensorial physical properties such as elasticity, permeability and conductance. Tensor‐valued Minkowski functionals, defined in the framework of integral geometry, provide a concise set of descriptors of anisotropic morphology. In this article, we describe the robust computation of these measures for microscopy images and polygonal shapes. We demonstrate their relevance for shape description, their versatility and their robustness by applying them to experimental data sets, specifically microscopy data sets of non‐equilibrium stationary Turing patterns and the shapes of ice grains from Antarctic cores. Article in Journal/Newspaper Antarc* Antarctic Wiley Online Library Antarctic Journal of Microscopy 238 1 57 74 |
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Wiley Online Library |
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language |
English |
description |
Summary Quantitative measures for anisotropic characteristics of spatial structure are needed when relating the morphology of microstructured heterogeneous materials to tensorial physical properties such as elasticity, permeability and conductance. Tensor‐valued Minkowski functionals, defined in the framework of integral geometry, provide a concise set of descriptors of anisotropic morphology. In this article, we describe the robust computation of these measures for microscopy images and polygonal shapes. We demonstrate their relevance for shape description, their versatility and their robustness by applying them to experimental data sets, specifically microscopy data sets of non‐equilibrium stationary Turing patterns and the shapes of ice grains from Antarctic cores. |
format |
Article in Journal/Newspaper |
author |
SCHRÖDER‐TURK, G.E. KAPFER, S. BREIDENBACH, B. BEISBART, C. MECKE, K. |
spellingShingle |
SCHRÖDER‐TURK, G.E. KAPFER, S. BREIDENBACH, B. BEISBART, C. MECKE, K. Tensorial Minkowski functionals and anisotropy measures for planar patterns |
author_facet |
SCHRÖDER‐TURK, G.E. KAPFER, S. BREIDENBACH, B. BEISBART, C. MECKE, K. |
author_sort |
SCHRÖDER‐TURK, G.E. |
title |
Tensorial Minkowski functionals and anisotropy measures for planar patterns |
title_short |
Tensorial Minkowski functionals and anisotropy measures for planar patterns |
title_full |
Tensorial Minkowski functionals and anisotropy measures for planar patterns |
title_fullStr |
Tensorial Minkowski functionals and anisotropy measures for planar patterns |
title_full_unstemmed |
Tensorial Minkowski functionals and anisotropy measures for planar patterns |
title_sort |
tensorial minkowski functionals and anisotropy measures for planar patterns |
publisher |
Wiley |
publishDate |
2010 |
url |
http://dx.doi.org/10.1111/j.1365-2818.2009.03331.x https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1111%2Fj.1365-2818.2009.03331.x https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1365-2818.2009.03331.x |
geographic |
Antarctic |
geographic_facet |
Antarctic |
genre |
Antarc* Antarctic |
genre_facet |
Antarc* Antarctic |
op_source |
Journal of Microscopy volume 238, issue 1, page 57-74 ISSN 0022-2720 1365-2818 |
op_rights |
http://onlinelibrary.wiley.com/termsAndConditions#vor |
op_doi |
https://doi.org/10.1111/j.1365-2818.2009.03331.x |
container_title |
Journal of Microscopy |
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238 |
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1 |
container_start_page |
57 |
op_container_end_page |
74 |
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1800752846240481280 |