Voronoi diagram and medial axis algorithm for planar domains with curved boundaries I. Theoretical foundations
Reads0
Chats0
TLDR
The underlying theory for an algorithm that computes the Voronoi diagram and medial axis of a planar domain bounded by free-form (polynomial or rational) curve segments is presented and unambiguous characterizations for edges in both these categories are given.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 1999-02-01 and is currently open access. It has received 74 citations till now. The article focuses on the topics: Voronoi diagram & Power diagram.read more
Citations
More filters
Book ChapterDOI
Stability and Computation of Medial Axes - a State-of-the-Art Report
TL;DR: This survey paper focuses on results that shed light on this instability of the medial axis of a geometric shape and uses the new insights to generate simplified and stable modifications ofThe medial axis.
Spatial tessellations. Concepts and Applications of Voronoi diagrams
TL;DR: In this paper, the Voronoi diagram generalizations of the Voroni diagram algorithm for computing poisson Voroni diagrams are defined and basic properties of the generalization of Voroni's algorithm are discussed.
Book ChapterDOI
Curved Voronoi diagrams
TL;DR: The concept of Medial Axis is introduced which generalizes the concept of Voronoi diagram to infinite sets and it is possible to efficiently construct a certified approximation of the medial axis of a bounded set from the Vor onoi diagram of a sample of points on the boundary of the set.
Journal ArticleDOI
On the role of medial geometry in human vision.
TL;DR: This work presents a unified theory of perceptual grouping and object recognition where through various sequences of transformations of the MA representation, visual fragments are grouped in various configurations to form object hypotheses, and are related to stored models.
Journal ArticleDOI
Text region extraction in a document image based on the Delaunay tessellation
TL;DR: The study reveals that specific triangles in text areas can be clustered together and identified as text body and Experiments show the method is also very efficient.
References
More filters
Computational geometry. an introduction
TL;DR: This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry.
Journal ArticleDOI
Voronoi diagrams—a survey of a fundamental geometric data structure
TL;DR: The Voronoi diagram as discussed by the authors divides the plane according to the nearest-neighbor points in the plane, and then divides the vertices of the plane into vertices, where vertices correspond to vertices in a plane.
Book
Spatial Tessellations: Concepts and Applications of Voronoi Diagrams
TL;DR: In this article, the Voronoi diagram generalizations of the Voroni diagram algorithm for computing poisson Voroni diagrams are defined and basic properties of the generalization of Voroni's algorithm are discussed.
Book
Computational Geometry: An Introduction
TL;DR: In this article, the authors present a coherent treatment of computational geometry in the plane, at the graduate textbook level, and point out the way to the solution of the more challenging problems in dimensions higher than two.