Clustering technique is one of the most important and basic tool for data mining. We propose a new clustering technique using K-Means algorithm and Voronoi diagram to unfold the hidden pattern in a given dataset. In the first phase we use K-Means algorithm to create set of small clusters and in the next phase using Voronoi diagram we create actual clusters. K-Means and Voronoi diagram based clu...

Two linear time (and hence asymptotically optimal) algorithms for computing the Euclidean distance transform of a two-dimensional binary image are presented. The algorithms are based on the construction and regular sampling of the Voronoi diagram whose sites consist of the unit (feature) pixels in the image. The rst algorithm, which is of primarily theoretical interest, constructs the complete ...

A Voronoi diagram of a set of n sites partitions a finite set of m points into regions of different areas, called the capacities of the sites. In this paper we are interested in Voronoi diagrams in which the capacities are given as constraints. We compute such capacity-constrained Voronoi diagrams in finite spaces by starting with an arbitrary partition that fulfills the capacity constraint wit...

Angular Voronoi diagram was introduced by Asano et al. as fundamental research for a mesh generation. In an angular Voronoi diagram, the edges are curves of degree three. From view of computational robustness we need to treat the curves carefully, because they might have a singularity. We enumerate all the possible types of curves that appear as an edge of an angular Voronoi diagram, which tell...

The geometry of circles in the plane is inextricably tied with the group of Möbius transformations, which take circles to circles. This geometry can be seen in a more symmetric after transforming the plane to the sphere, by stereographic projection. Interpretations will be discussed for Voronoi diagrams, Delaunay triangulations,etc. from this point of view. Fortune’s algorithm for constructing ...

Consider the continuum of points along the edges of a network, i.e., an undirected graph with positive edge weights. We measure distance between these points in terms of the shortest path distance along the network, known as the network distance. Within this metric space, we study farthest points. We introduce network farthest-point diagrams, which capture how the farthest points—and the distan...

Graph theoretic approaches plays important role in the path planning problems. The usefulness of Graph Theoretic approaches mainly the voronoi diagram is provided for the path planning in static and dynamic environment in this paper. Voronoi Diagram plays important role in computing the optimal path between the source & destination in static as well as dynamic environment. So, through the liter...

In Euclidean geometry, it is well-known that the k-order Voronoi diagram in R can be computed from the vertical projection of the k-level of an arrangement of hyperplanes tangent to a convex potential function in R: the paraboloid. Similarly, we report for the Klein ball model of hyperbolic geometry such a concave potential function: the northern hemisphere. Furthermore, we also show how to bui...

Voronoi diagrams are extremely versatile as a data structure for many geometric applications. Computing this diagram “exactly” for a polyhedral set in 3D has been a quest of computational geometers for over two decades; this quest is still unrealized. We will locate the difficulty in this quest, thanks to a recent result of Everett et al (2009). More generally, it points to the need for alterna...