Centroidal Voronoi Tessellations Applications And Algorithms Pdf

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A centroidal Voronoi tessellation is a Voronoi tessellation whose generating points are the centroids centers of mass of the corresponding Voronoi regions. We give some applica-tions of such tessellations to problems in image compression, quadrature, finite difference methods, distribution of resources, cellular biology, statistics, and the territorial behavior of animals. We discuss methods for computing these tessellations, provide some analyses concerning both the tessellations and the methods for their determination, and, finally, present the results of some numerical experiments. Documents: Advanced Search Include Citations.

Lloyd’s Algorithm on GPU

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An Edge-Weighted Centroidal Voronoi Tessellation Model for Image Segmentation Abstract: Centroidal Voronoi tessellations CVTs are special Voronoi tessellations whose generators are also the centers of mass centroids of the Voronoi regions with respect to a given density function and CVT-based methodologies have been proven to be very useful in many diverse applications in science and engineering.

In the context of image processing and its simplest form, CVT-based algorithms reduce to the well-known k -means clustering and are easy to implement. In this paper, we develop an edge-weighted centroidal Voronoi tessellation EWCVT model for image segmentation and propose some efficient algorithms for its construction. Our EWCVT model can overcome some deficiencies possessed by the basic CVT model; in particular, the new model appropriately combines the image intensity information together with the length of cluster boundaries, and can handle very sophisticated situations.

We demonstrate through extensive examples the efficiency, effectiveness, robustness, and flexibility of the proposed method. Article :. Date of Publication: 23 June PubMed ID: DOI: Need Help?

Centroidal Voronoi tessellation

In geometry , a centroidal Voronoi tessellation CVT is a special type of Voronoi tessellation in which the generating point of each Voronoi cell is also its centroid center of mass. It can be viewed as an optimal partition corresponding to an optimal distribution of generators. Gersho's conjecture, proven for one and two dimensions, says that "asymptotically speaking, all cells of the optimal CVT, while forming a tessellation , are congruent to a basic cell which depends on the dimension. In two dimensions, the basic cell for the optimal CVT is a regular hexagon as it is proven to be the most dense packing of circles in 2D Euclidean space. Its three dimensional equivalent is the rhombic dodecahedral honeycomb , derived from the most dense packing of spheres in 3D Euclidean space. Centroidal Voronoi tessellations are useful in data compression , optimal quadrature , optimal quantization , clustering , and optimal mesh generation. A weighted centroidal Voronoi diagrams is a CVT in which each centroid is weighted according to a certain function.

Voronoi diagram

Although the results of standard SP-QPSO shows its ability to achieve the best results in each tested problem in local search as well as global search, these two mentioned techniques are applied to compare the performance of managing initialization part versus convergence of agents through the searching procedure respectively. To confirm the performance of these three algorithms, twelve benchmark functions are engaged to carry out the experiments in 2, 10, 50, and dimensions. Results are explained and compared to indicate the importance of our study.

In mathematics , a Voronoi diagram is a partition of a plane into regions close to each of a given set of objects. In the simplest case, these objects are just finitely many points in the plane called seeds, sites, or generators. For each seed there is a corresponding region , called Voronoi cells , consisting of all points of the plane closer to that seed than to any other.

Lloyd’s Algorithm on GPU

It is used as the basis for a number of applications.

Centroidal Voronoi tessellations: Applications and algorithms (1999)

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5 Comments

  1. Cancio S. 13.05.2021 at 17:20

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  2. Ursula S. 13.05.2021 at 18:44

    PDF | A centroidal Voronoi tessellation is a Voronoi tessellation whose generating points are the centroids (centers of mass) of the.

  3. Dreux P. 14.05.2021 at 12:22

    In terms of distance function and spatial continuity in Voronoi diagram, a generic generating method of Voronoi diagram, named statistical Voronoi diagram, is proposed in this paper based upon statistics with mean vector and covariance matrix.

  4. Sean W. 21.05.2021 at 02:47

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  5. Winteloso 21.05.2021 at 09:54

    Centroidal Voronoi Tessellations: Applications and Algorithms peacetexarkana.org​org/stable/?seq=1&cid=pdf-reference#references_tab_contents.