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Topology Preserving Digitization with FCC and BCC Grids

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Combinatorial Image Analysis (IWCIA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 4040))

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Abstract

In digitizing 3D objects one wants as much as possible object properties to be preserved in its digital reconstruction. One of the most fundamental properties is topology. Only recently a sampling theorem for cubic grids could be proved which guarantees topology preservation [1]. The drawback of this theorem is that it requires more complicated reconstruction methods than the direct representation with voxels. In this paper we show that face centered cubic (fcc) and body centered cubic (bcc) grids can be used as an alternative. The fcc and bcc voxel representations can directly be used for a topologically correct reconstruction. Moreover this is possible with coarser grid resolutions than in the case of a cubic grid. The new sampling theorems for fcc and bcc grids also give absolute bounds for the geometric error.

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Author information

Authors and Affiliations

  1. Cognitive Systems Group, University of Hamburg, Vogt-Köln-Str. 30, D-22527, Hamburg, Germany

    Peer Stelldinger

  2. Centre for Image Analysis, Uppsala University, Lägerhyddsvägen 3, SE-75237, Uppsala, Sweden

    Robin Strand

Authors
  1. Peer Stelldinger
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  2. Robin Strand
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Editor information

Editors and Affiliations

  1. Institute for Transport Research, German-Aerospace Center (DLR), Rutherfordstr. 2, 12489, Berlin, Germany

    Ralf Reulke

  2. Fachbereich Mathematik, Universität Hamburg, Bundesstr. 55, 20146, Hamburg

    Ulrich Eckardt

  3. Dresden University of Technology,  

    Boris Flach

  4. Institut für Informatik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany

    Uwe Knauer

  5. FU Berlin, Arnimallee 3, 14195, Berlin, Germany

    Konrad Polthier

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© 2006 Springer-Verlag Berlin Heidelberg

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Stelldinger, P., Strand, R. (2006). Topology Preserving Digitization with FCC and BCC Grids. In: Reulke, R., Eckardt, U., Flach, B., Knauer, U., Polthier, K. (eds) Combinatorial Image Analysis. IWCIA 2006. Lecture Notes in Computer Science, vol 4040. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11774938_18

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  • DOI: https://doi.org/10.1007/11774938_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35153-5

  • Online ISBN: 978-3-540-35154-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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