Topology Preserving Digitization with FCC and BCC Grids
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 . 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.
KeywordsSampling Point Direct Path Jordan Curve Surface Patch Sampling Theorem
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- 1.Stelldinger, P., Latecki, L.J.: 3D Object Digitization with Topological and Geometric Guarantees. In University Hamburg, Computer Science Department, Technical Report FBI-HH-M-334/05 (2005)Google Scholar
- 2.Theußl, T., Möller, T., Gröller, M.E.: Optimal regular volume sampling. In: VIS 2001: Proceedings of the conference on Visualization 2001, pp. 91–98. IEEE Computer Society, Washington (2001)Google Scholar
- 3.Ibanez, L., Hamitouche, C., Roux, C.: Determination of discrete sampling grids with optimal topological and spectral properties. In: Proceedings of 6th Conference on Discrete Geometry for Computer Imagery, Lyon, France, pp. 181–192 (1996)Google Scholar
- 5.Dornhofer, A.: A discrete fourier transform pair for arbitrary sampling geometries with applications to frequency domain volume rendering on the body-centered cubic lattice. Master’s thesis, Vienna University of Technology (2003)Google Scholar
- 6.Carr, H., Theuβl, T., Möller, T.: Isosurfaces on optimal regular samples. In: VISSYM 2003: Proceedings of the symposium on Data visualisation 2003, pp. 39–48. Eurographics Association (2003)Google Scholar
- 9.Pavlidis, T.: Algorithms for Graphics and Image Processing. Computer Science Press (1982)Google Scholar
- 11.Stelldinger, P., Köthe, U.: Towards a General Sampling Theory for Shape Preservation. Image and Vision Computing Journal, Special Issue on Discrete Geometry for Computer Imagery 23(2), 237–248 (2005)Google Scholar
- 12.Stelldinger, P.: Digitization of Non-regular Shapes in Arbitrary Dimensions (submitted)Google Scholar