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Comparison of two global digital algorithms for Minkowski tensor estimation

By Sabrina Tang Christensen and Markus Kiderlen
CSGB Research Reports
No. 10, July 2016

The geometry of real world objects can be described by Minkowski tensors. Algorithms have been suggested to approximate Minkowski tensors if only a binary image of the object is available. This paper presents implementations of two such algorithms. The theoretical convergence properties are confirmed by simulations on test sets, and recommendations for input arguments of the algorithms are given. For increasing resolutions, we obtain more accurate estimators for the Minkowski tensors. Digitisations of more complicated objects are shown to require higher resolutions.

Keywords: Minkowski tensor; digital algorithm; set with positive reach; digitisation

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