Fast capacity constrained Voronoi tessellation

Capacity constrained Voronoi tessellation (CCVT) [Balzer et al. 2009] addresses a crucial quality issue of Lloyd relaxation but at the expense of slower computation, which could hinder its potential wide adoption. We present a fast capacity constrained Voronoi tessellation algorithm which is orders of magnitude faster than the original method proposed by Balzer et al. [2009] (and 10x faster than a previous accelerated implementation of the same technique) while maintaining excellent distribution quality and scaling very well as the number of points increase.

[1]  V. Ostromoukhov.  Sampling with polyominoes , 2007, SIGGRAPH 2007.

[2]  S. A. Lloyd.  An optimization approach to relaxation labelling algorithms , 1983, Image Vis. Comput..

[3]  Yan Fu,et al.  Direct sampling on surfaces for high quality remeshing , 2009, Comput. Aided Geom. Des..

[4]  Thouis R. Jones.  Efficient Generation of Poisson-Disk Sampling Patterns , 2006, J. Graph. Tools.

[5]  Robert Bridson,et al.  Fast Poisson disk sampling in arbitrary dimensions , 2007, SIGGRAPH '07.

[6]  K.B. White,et al.  Poisson Disk Point Sets by Hierarchical Dart Throwing , 2007, 2007 IEEE Symposium on Interactive Ray Tracing.

[7]  Victor Ostromoukhov,et al.  Fast hierarchical importance sampling with blue noise properties , 2004, ACM Trans. Graph..

[8]  O. Deussen,et al.  Capacity-constrained point distributions: a variant of Lloyd's method , 2009, SIGGRAPH 2009.

[9]  Stefan Jeschke,et al.  Dart Throwing on Surfaces , 2009, Comput. Graph. Forum.

[10]  Allen Gersho,et al.  Vector quantization and signal compression , 1991, The Kluwer international series in engineering and computer science.

[11]  Ares Lagae,et al.  A Comparison of Methods for Generating Poisson Disk Distributions , 2008, Comput. Graph. Forum.

[12]  Greg Humphreys,et al.  A spatial data structure for fast Poisson-disk sample generation , 2006, SIGGRAPH 2006.

[13]  Eugene Fiume,et al.  Hierarchical Poisson disk sampling distributions , 1992 .

[14]  Don P. Mitchell,et al.  Generating antialiased images at low sampling densities , 1987, SIGGRAPH.

[15]  Robert L. Cook,et al.  Stochastic sampling in computer graphics , 1988, TOGS.

[16]  J. Yellott.  Spectral consequences of photoreceptor sampling in the rhesus retina. , 1983, Science.

[17]  Dani Lischinski,et al.  Recursive Wang tiles for real-time blue noise , 2006, ACM Trans. Graph..

[18]  Li-Yi Wei.  Parallel Poisson disk sampling , 2008, SIGGRAPH 2008.

[19]  Tiow Seng Tan,et al.  Jump flooding in GPU with applications to Voronoi diagram and distance transform , 2006, I3D '06.

[20]  S. P. Lloyd,et al.  Least squares quantization in PCM , 1982, IEEE Trans. Inf. Theory.

[21]  Dinesh Manocha,et al.  Fast computation of generalized Voronoi diagrams using graphics hardware , 1999, SIGGRAPH.