Combinatorial Image Analysis

Volume 4040 of the series Lecture Notes in Computer Science pp 226-240

Topology Preserving Digitization with FCC and BCC Grids

  • Peer StelldingerAffiliated withCognitive Systems Group, University of Hamburg
  • , Robin StrandAffiliated withCentre for Image Analysis, Uppsala University

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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.