Multiresolution sphere packing tree: a hierarchical multiresolution 3D data structure

Sphere packing arrangements are frequently found in nature, exhibiting efficient space-filling and energy minimization properties. Close sphere packings provide a tight, uniform, and highly symmetric spatial sampling at a single resolution. We introduce the Multiresolution Sphere Packing Tree (MSP-tree): a hierarchical spatial data structure based on sphere packing arrangements suitable for 3D space representation and selective refinement. Compared to the commonly used octree, MSP-tree offers three advantages: a lower fanout (a factor of four compared to eight), denser packing (about 24% denser), and persistence (sphere centers at coarse resolutions persist at finer resolutions). We present MSP-tree both as a region-based approach that describes the refinement mechanism succintly and intuitively, and as a lattice-based approach better suited for implementation. The MSP-tree offers a robust, highly symmetric tessellation of 3D space with favorable image processing properties.

[1]  Jon Louis Bentley,et al.  Multidimensional binary search trees used for associative searching , 1975, CACM.

[2]  Wim Sweldens,et al.  Lifting scheme: a new philosophy in biorthogonal wavelet constructions , 1995, Optics + Photonics.

[3]  Joseph M. Maubach,et al.  Local bisection refinement for $n$-simplicial grids generated by reflection , 2017 .

[4]  Jovan Popovic,et al.  Progressive simplicial complexes , 1997, SIGGRAPH.

[5]  K. Sahr,et al.  Discrete Global Grid Systems , 1998 .

[6]  Markus H. Gross,et al.  Progressive tetrahedralizations , 1998, Proceedings Visualization '98 (Cat. No.98CB36276).

[7]  Leif Kobbelt,et al.  √3-subdivision , 2000, SIGGRAPH.

[8]  Günther Greiner,et al.  Hierarchical tetrahedral-octahedral subdivision for volume visualization , 2000, The Visual Computer.

[9]  Bernd Hamann,et al.  Wavelet-Based Multiresolution with , 2003, Computing.

[10]  K. Sahr,et al.  Geodesic Discrete Global Grid Systems , 2003 .

[11]  Bernd Hamann,et al.  Wavelet-based multiresolution with n-th-root-of-2 Subdivision , 2004 .

[12]  Thierry Blu,et al.  On the multidimensional extension of the quincunx subsampling matrix , 2005, IEEE Signal Processing Letters.

[13]  J. Bey,et al.  Tetrahedral grid refinement , 1995, Computing.

[14]  L. Kobbelt,et al.  A Survey on Data Structures for Level-of-Detail Models , 2005, Advances in Multiresolution for Geometric Modelling.

[15]  Alireza Entezari,et al.  A Granular Three Dimensional Multiresolution Transform , 2006, EuroVis.