Discrete & Computational Geometry

, Volume 57, Issue 3, pp 545–570

Voronoi-Based Estimation of Minkowski Tensors from Finite Point Samples

Article

Abstract

Intrinsic volumes and Minkowski tensors have been used to describe the geometry of real world objects. This paper presents an estimator that allows approximation of these quantities from digital images. It is based on a generalized Steiner formula for Minkowski tensors of sets of positive reach. When the resolution goes to infinity, the estimator converges to the true value if the underlying object is a set of positive reach. The underlying algorithm is based on a simple expression in terms of the cells of a Voronoi decomposition associated with the image.

Keywords

Minkowski tensor Digital algorithm Set of positive reach Digitization 

Mathematics Subject Classification

52A38 28A75 52A20 94A08 68U10 62H35 

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Daniel Hug
    • 1
  • Markus Kiderlen
    • 2
  • Anne Marie Svane
    • 2
  1. 1.Department of MathematicsKarlsruhe Institute of TechnologyKarlsruheGermany
  2. 2.Department of MathematicsAarhus UniversityAarhus CDenmark

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