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.
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Schladitz, K., Ohser, J., Nagel, W. (2006). Measuring Intrinsic Volumes in Digital 3d Images. In: Kuba, A., Nyúl, L.G., Palágyi, K. (eds) Discrete Geometry for Computer Imagery. DGCI 2006. Lecture Notes in Computer Science, vol 4245. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11907350_21
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DOI: https://doi.org/10.1007/11907350_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-47651-1
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