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.

Voronoi diagram

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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

It is used as the basis for a number of applications. While the computation of the ordinary Voronoi diagram on GPU is a well explored topic, its extension to CVDs presents some challenges that the present study intends to overcome. Unable to display preview. Download preview PDF. Skip to main content.

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. Unable to display preview. Download preview PDF. Skip to main content. This service is more advanced with JavaScript available.

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

Centroidal Voronoi Tessellations: Applications and Algorithms

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 CVT, the generating point of each Voronoi cell coincides with its center of mass; CVT sampling locates the design samples at the centroids of each Voronoi cell in the input space. CVT sampling is a geometric, space-filling sampling method which is similar to k-means clustering in its simplest form. The pysmo.

Lloyd’s Algorithm on GPU

Centroidal Voronoi tessellations: Applications and algorithms (1999)

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. Besides, in order to make good on the discreteness of spatial Voronoi cell, the cross Voronoi cell accomplished the discrete ranges in its continuous domain. In the light of Mahalanobis distance, not only ordinary Voronoi and weighted Voronoi are implemented, but also the theory of Voronoi diagram is improved further. Last but not least, through Gaussian distribution on spatial data, the validation and soundness of this method are proofed by empirical results. Since the Voronoi diagram, a spatial tessellation based on closeness to points in a specific subset of a plane, was put forward by Russian mathematician Voronoi and named after him in [ 1 ], a multiple of academicians have conducted deeply researches on it, e. The investigations about Voronoi, e.

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  1. Yolande G. 27.12.2020 at 10:02

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