Measuring Intrinsic Volumes in Digital 3d Images

  • Katja Schladitz
  • Joachim Ohser
  • Werner Nagel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4245)


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.


Euler Number Section Lattice Neighborhood Graph Congruence Class Intrinsic Volume 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Katja Schladitz
    • 1
  • Joachim Ohser
    • 2
  • Werner Nagel
    • 3
  1. 1.Fraunhofer-Institut für Techno- und WirtschaftsmathematikKaiserslauternGermany
  2. 2.Fachhochschule DarmstadtDarmstadtGermany
  3. 3.Fakultät für Mathematik und InformatikFriedrich-Schiller-UniversitätJenaGermany

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