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)
A geometric approach to non-parametric density estimation
Pattern Recognition
Direct sampling on surfaces for high quality remeshing
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Constrained CVT meshes and a comparison of triangular mesh generators
Computational Geometry: Theory and Applications
Facility Location Problems: A Parameterized View
AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
Direct sampling on surfaces for high quality remeshing
Computer Aided Geometric Design
On centroidal voronoi tessellation—energy smoothness and fast computation
ACM Transactions on Graphics (TOG)
Filtering relocations on a Delaunay triangulation
SGP '09 Proceedings of the Symposium on Geometry Processing
ReALE: A reconnection-based arbitrary-Lagrangian-Eulerian method
Journal of Computational Physics
Hyperbolic centroidal Voronoi tessellation
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Design and analysis of optimal noisy channel quantization with random index assignment
IEEE Transactions on Information Theory
Geodesic Methods in Computer Vision and Graphics
Foundations and Trends® in Computer Graphics and Vision
SIAM Journal on Scientific Computing
Facility location problems: A parameterized view
Discrete Applied Mathematics
Tetrahedral meshing of volumetric medical images respecting image edges
CAIP'11 Proceedings of the 14th international conference on Computer analysis of images and patterns - Volume Part I
A Spatial Regularization Approach for Vector Quantization
Journal of Mathematical Imaging and Vision
Centroidal Voronoi tessellation in universal covering space of manifold surfaces
Computer Aided Geometric Design
Dithering by Differences of Convex Functions
SIAM Journal on Imaging Sciences
PolyMesher: a general-purpose mesh generator for polygonal elements written in Matlab
Structural and Multidisciplinary Optimization
Gossip Coverage Control for Robotic Networks: Dynamical Systems on the Space of Partitions
SIAM Journal on Control and Optimization
Generalized edge-weighted centroidal Voronoi tessellations for geometry processing
Computers & Mathematics with Applications
iDiary: from GPS signals to a text-searchable diary
Proceedings of the 11th ACM Conference on Embedded Networked Sensor Systems
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Centroidal Voronoi tessellations (CVTs) are Voronoi tessellations of a bounded geometric domain such that the generating points of the tessellations are also the centroids (mass centers) of the corresponding Voronoi regions with respect to a given density function. Centroidal Voronoi tessellations may also be defined in more abstract and more general settings. Due to the natural optimization properties enjoyed by CVTs, they have many applications in diverse fields. The Lloyd algorithm is one of the most popular iterative schemes for computing the CVTs but its theoretical analysis is far from complete. In this paper, some new analytical results on the local and global convergence of the Lloyd algorithm are presented. These results are derived through careful utilization of the optimization properties shared by CVTs. Numerical experiments are also provided to substantiate the theoretical analysis.