This article presents a new algorithm to recognize natural distinctive places such as corridors, halls, narrowings, corridors with open doors on the left side etc., from indoor environments using Hidden Markov Models. The environment is modelled as a graph. This graph is obtained from a Voronoi Diagram from measurements of laser scanner. The characteristics of Voronoi Diagram (nodes, number of ...

This paper investigates geometric and algorithmic properties of the Voronoi diagram with a transportation network on the Euclidean plane. With a transportation network, the distance is measured as the length of the shortest (time) path. In doing so, we introduce a needle, a generalized Voronoi site. We present an O(nm + m + nm log n) algorithm to compute the Voronoi diagram with a transportatio...

Presented in this paper is a sweepline algorithm to compute the Voronoi diagram of a set of circles in a two-dimensional Euclidean space. The radii of the circles are non-negative and not necessarily equal. It is allowed that circles intersect each other, and a circle contains others. The proposed algorithm constructs the correct Voronoi diagram as a sweepline moves on the plane from top to bot...

Given a family of k disjoint connected polygonal sites in general position and of total complexity n, we consider the farthest-site Voronoi diagram of these sites, where the distance to a site is the distance to a closest point on it. We show that the complexity of this diagram is O(n), and give an O(n log n) time algorithm to compute it. We also prove a number of structural properties of this ...

It is well known that the complexity, i.e., the number of vertices, edges and faces, of the 3-dimensional Voronoi diagram of n points can be as bad as (n 2): Interest has recently arisen as to what happens, both in deterministic and probabilistic situations, when the three dimensional points are restricted to lie on the surface of a 2-dimensional object. In this paper we consider the situation ...

We present a simplified system of axioms for Abstract Voronoi Diagrams that should pave the way for new applications in theory and practice.

We give a new simple on-line incremental algorithm for the additively weighted Voronoi diagram, whose primitive operations are completely based on orientation tests. It is known that the closest site diagram can be disconnected, and that the furthest site diagram can have disconnected faces. The algorithm avoids such nuisances by using the oriented projective plane as an underlying geometry. In...

given a set  of  points in the plane and a constant ,-center problem is to find two closed disks which each covers the whole , the diameter of the bigger one is minimized, and the distance of the two centers is at least . constrained -center problem is the -center problem in which the centers are forced to lie on a given line . in this paper, we first introduce -center problem and its constrain...

A new concept called a boat-sail distance is introduced on the surface of water with flow, and it is used to define a generalized Voronoi diagram, in such a way that the water surface is partitioned into regions belonging to the nearest harbors with respect to this distance. The problem of computing this Voronoi diagram is reduced to a boundary value problem of a partial differential equation, ...

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. ...