We present a new and simple randomized algorithm for constructing the Delaunay triangulation using nearest neighbor graphs for point location. It runs in linear expected time for points in the plane with polynomially bounded spread, i.e., if the ratio between the largest and smallest pointwise distance is polynomially bounded. This also holds for point sets with bounded spread in higher dimensi...

In this paper, we investigate the feasibility of using graph-based descriptions to learn the view structure of 3D objects. The graphs used in our study are constructed from the Delaunay triangulations of corner features. The investigation is divided into two parts. We commence by considering how relational structures can be encoded in a way which can be used to generate parametric eigenspaces. ...

We use projected Delaunay tetrahedra and a maximum independent set approach to compute large subsets of convex quadrangulations on a given set of points in the plane. The new method improves over the popular pairing method based on triangulating the point set.

Given a set P of n points in the plane, we show how to compute in O(n logn) time a subgraph of their Delaunay triangulation that has maximum degree 7 and is a strong planar t-spanner of P with t = (1 + √ 2) ∗ δ, where δ is the spanning ratio of the Delaunay triangulation. Furthermore, given a Delaunay triangulation, we show a distributed algorithm that computes the same bounded degree planar sp...

ÐThis paper describes an efficient algorithm for inexact graph matching. The method is purely structural, that is to say, it uses only the edge or connectivity structure of the graph and does not draw on node or edge attributes. We make two contributions. Commencing from a probability distribution for matching errors, we show how the problem of graph matching can be posed as maximum-likelihood ...

We present a method for reconstructing surfaces from point sets. The main novelty lies in a structure-preserving approach where the input point set is first consolidated by structuring and resampling the planar components, before reconstructing the surface from both the consolidated components and the unstructured points. The final surface is obtained through solving a graph-cut problem formula...

This document describes morphological operators designed for partition images. Two approaches are addressed. In the first one, each cell of the partition is considered independently of the others and various anti-extensive operators can be defined on it. However, these operators can be applied directly on the whole partition. There is no need to extract each cell to transform it. The second app...

In this paper, we study the weak point matching problem for a given set of n points and a class of equilateral triangles. The problem is to find the maximum cardinality matching of the points using equilateral triangles such that each triangle contains exactly two points and each point lies at most in one triangle. Under the non-degeneracy assumption, we present an O(n) time algorithm using the...

We describe an algorithm that takes as input n points in the plane and a parameter , and produces as output an embedded planar graph having the given points as a subset of its vertices in which the graph distances are a (1 + )-approximation to the geometric distances between the given points. For point sets in which the Delaunay triangulation has bounded sharpest angle, our algorithm’s output h...

Index Structures: We continue our discussion of useful geometric data structure for computer games. So far we have discussed data structures for representing meshes (and more generally, cell complexes), geometric graphs (such as the visibility graph, θ-graph), and spatial subdivisions (such as the Delaunay triangulation). Usually, when we think of data structures for 1-dimensional data (such as...