Preserving Topology by a Digitization Process
Journal of Mathematical Imaging and Vision
Algorithms for Graphics and Imag
Algorithms for Graphics and Imag
Optimal regular volume sampling
Proceedings of the conference on Visualization '01
Multiseeded Fuzzy Segmentation on the Face Centered Cubic Grid
ICAPR '01 Proceedings of the Second International Conference on Advances in Pattern Recognition
Determination of discrete sampling grids with optimal topological and spectral properties
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
Isosurfaces on optimal regular samples
VISSYM '03 Proceedings of the symposium on Data visualisation 2003
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Distance transforms for three-dimensional grids with non-cubic voxels
Computer Vision and Image Understanding
Towards a general sampling theory for shape preservation
Image and Vision Computing
Resolution pyramids on the FCC and BCC grids
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
Quasi-interpolation by quadratic C1-splines on truncated octahedral partitions
Computer Aided Geometric Design
Digital distance functions on three-dimensional grids
Theoretical Computer Science
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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.