The design and analysis of spatial data structures
The design and analysis of spatial data structures
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
An optimal algorithm for approximate nearest neighbor searching fixed dimensions
Journal of the ACM (JACM)
Multidimensional binary search trees used for associative searching
Communications of the ACM
Clustering Algorithms
MPI: The Complete Reference
Grid generation and optimization based on centroidal Voronoi tessellations
Applied Mathematics and Computation
Grid generation and optimization based on centroidal Voronoi tessellations
Applied Mathematics and Computation
Centroidal Voronoi Tessellation Based Algorithms for Vector Fields Visualization and Segmentation
VIS '04 Proceedings of the conference on Visualization '04
Journal of Mathematical Imaging and Vision
Recent progress in robust and quality Delaunay mesh generation
Journal of Computational and Applied Mathematics - Special issue: The international symposium on computing and information (ISCI2004)
Optimal dynamic actuator location in distributed feedback control of a diffusion process
International Journal of Sensor Networks
On centroidal voronoi tessellation—energy smoothness and fast computation
ACM Transactions on Graphics (TOG)
An edge-weighted centroidal Voronoi tessellation model for image segmentation
IEEE Transactions on Image Processing
Computers & Mathematics with Applications
Adaptive node sampling method for probabilistic roadmap planners
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
Subsampling strategies to improve learning-based retina vessel segmentation
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Centroidal Voronoi tessellation in universal covering space of manifold surfaces
Computer Aided Geometric Design
Spatial graphs for intra-cranial vascular network characterization, generation, and discrimination
MICCAI'05 Proceedings of the 8th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
Reduced-Order modeling of complex systems with multiple system parameters
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
Original article: Mesh generation for FEM based on centroidal Voronoi tessellations
Mathematics and Computers in Simulation
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Centroidal Voronoi tessellations (CVTs) are Voronoi tessellations of a region such that the generating points of the tessellations are also the centroids of the corresponding Voronoi cells. In this paper, some probabilistic methods for determining CVTs and their parallel implementations on distributed memory systems are presented. By using multi-sampling in a new probabilistic algorithm we introduce, more accurate and efficient approximations of CVTs are obtained without the need to explicit construct Voronoi diagrams. The new algorithm lends itself well to parallelization, i.e., near prefect linear speed up in the number of processors is achieved. The results of computational experiments performed on a CRAY T3E-600 system are provided which illustrate the superior sequential and parallel performance of the new algorithm when compared to existing algorithms. In particular, for the same amount of work, the new algorithms produce significantly more accurate CVTs.