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Measuring intrinsic volumes in digital 3d images

: Schladitz, K.; Ohser, J.; Nagel, W.


Kuba, A.:
Discrete geometry for computer imagery. 13th international conference, DGCI 2006 : Szeged, Hungary, October 25 - 27, 2006; Proceedings
Berlin: Springer, 2006 (Lecture Notes in Computer Science 4245)
ISBN: 3-540-47651-2
ISBN: 978-3-540-47651-1
International Conference on Discrete Geometry for Computer Imagery (DGCI) <13, 2006, Szeged>
Fraunhofer ITWM ()

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.