Measuring intrinsic volumes in digital 3d images

  • Authors:
  • Katja Schladitz;Joachim Ohser;Werner Nagel

  • Affiliations:
  • Fraunhofer-Institut für Techno- und Wirtschaftsmathematik, Kaiserslautern, Germany;Fachhochschule Darmstadt, Darmstadt, Germany;Fakultät für Mathematik und Informatik, Friedrich-Schiller-Universität, Jena, Germany

  • Venue:
  • DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
  • Year:
  • 2006

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Abstract

The intrinsic volumes – in 3d up to constants volume, surface area, integral of mean curvature, and Euler number – are a very useful set of geometric characteristics Combining integral and digital geometry we develop a method for efficient simultanous calculation of the intrinsic volumes of sets observed in binary images In order to achieve consistency in the derived intrinsic volumes for both foreground and background, suitable pairs of discrete connectivities have to be used To make this rigorous, the concepts discretization w.r.t an adjacency system and complementarity of adjacency systems are introduced.