Rounding Voronoi diagram

Rounding Voronoi Diagram

Computational geometry classically assumes real-number arithmetic which does not exist in actual computers. A solution consists in using integer coordinates for data and exact arithmetic for computations. This approach implies that if the results of an algorithm are the input of another, these results must be rounded to match this hypothesis of integer coordinates. In this paper, we treat the c...

Time - Based Voronoi Diagram ∗

We consider a variation of Voronoi diagram, or time-based Voronoi diagram, for a set S of points in the presence of transportation lines or highways in the plane. A shortest time-distance path from a query point to any given point in S is a path that takes the least travelling time. The travelling speeds and hence travelling times of the subpaths along the highways and in the plane are differen...

Saliency Detection with VORONOI Diagram

Many applications are serviced by the Voronoi tessellation required to split image into Voronoi regions. An automatic method to learn and detect salient region for color image with support of the Voronoi diagram is presented. Salient regions are modeled as flexible circumstance corresponding to centers of mass. The centers are predicted by local contrast-based representation with local maxima. ...

Hierarchical planar voronoi diagram approximations

Voronoi diagram of a circle set from Voronoi diagram of a point set: II. Geometry

Presented in this paper are algorithms to compute the positions of vertices and equations of edges of the Voronoi diagram of a circle set on a plane, where the radii of the circles are not necessarily equal and the circles are not necessarily disjoint. The algorithms correctly and efficiently work in conjunction with the first paper of the series dealing with the construction of the correct top...