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Delaunay triangulation

About: Delaunay triangulation is a research topic. Over the lifetime, 5816 publications have been published within this topic receiving 126615 citations. The topic is also known as: Delone triangulation.


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Proceedings ArticleDOI
11 Jan 2004
TL;DR: The almost-Delaunay simplices are defined, some of their properties are derived, and algorithms for computing them are given, especially for neighbor analysis in three dimensions.
Abstract: Delaunay tessellations and Voronoi diagrams capture proximity relationships among sets of points in any dimension. When point coordinates are not known exactly, as in the case of 3D points representing protein atom coordinates, the Delaunay tessellation may not be robust; small perturbations in the coordinates may cause the Delaunay simplices to change. In this paper, we define the almost-Delaunay simplices, derive some of their properties, and give algorithms for computing them, especially for neighbor analysis in three dimensions. We sketch applications in proteins that will be described more fully in a companion paper in biology. http://www.cs.unc.edu/∼debug/papers/AlmDel.

73 citations

Journal ArticleDOI
01 Aug 1993
TL;DR: The paper deals with the parallelization of Delaunay triangulation algorithms, giving more emphasis to pratical issues and implementation than to theoretical complexity.
Abstract: The paper deals with the parallelization of Delaunay triangulation algorithms, giving more emphasis to pratical issues and implementation than to theoretical complexity. Two parallel implementations are presented. The first one is built on De Wall, an Ed triangulator based on an original interpretation of the divide & conquer paradigm. The second is based on an incremental construction algorithm. The parallelization strategies are presented and evaluated. The target parallel machine is a distributed computing environment, composed of coarse grain processing nodes. Results of first implementations are reported and compared with the performance of the serial versions running on a Unix workstation.

73 citations

Proceedings ArticleDOI
28 Jun 2009
TL;DR: In this paper, the authors proposed a method for decomposing clumps of nuclei using high-level geometric constraints that are derived from low-level features of maximum curvature computed along the contour of each clump.
Abstract: Cell-based fluorescence imaging assays have the potential to generate massive amount of data, which requires detailed quantitative analysis. Often, as a result of fixation, labeled nuclei overlap and create a clump of cells. However, it is important to quantify phenotypic read out on a cell-by-cell basis. In this paper, we propose a novel method for decomposing clumps of nuclei using high-level geometric constraints that are derived from low-level features of maximum curvature computed along the contour of each clump. Points of maximum curvature are used as vertices for Delaunay triangulation (DT), which provides a set of edge hypotheses for decomposing a clump of nuclei. Each hypothesis is subsequently tested against a constraint satisfaction network for a near optimum decomposition. The proposed method is compared with other traditional techniques such as the watershed method with/without markers. The experimental results show that our approach can overcome the deficiencies of the traditional methods and is very effective in separating severely touching nuclei.

73 citations

Proceedings ArticleDOI
01 Nov 1997
TL;DR: This paper presents a spatial data mining method named SMiYN (Spatial data Mining by Triangulated Irregular Network), which is based on Delaunay Triangulation, and demonstrates important advantages over the previous works.
Abstract: It becomes an important task to discover significant pattern or characteristics which may implicitly exist in huge spatial dntabases, such as geographical or medical databases. In this paper, we present a spatial data mining method named SMiYN (Spatial data Mining by Triangulated Irregular Network), which is based on Delaunay Triangulation. Sh47ZN demonstrates important advantages over the previous works. First, it discovers even sophisticated pattern like nested doughnuts, and hierarchical structure of cluster distribution. Second, in order to execute SMTIN, we do not need to know a priori the nature of distribution, for example the number of clusters, which is indispensable to other methods. Third, experiments show that SMTIN requires less CPU processing time than other methods such as BIRCH and CLARANS. Finally it is not ordering sensitive and handles efticiently outliers.

72 citations

Journal ArticleDOI
TL;DR: It is shown that a triangulation of a set of n points in the plane that minimizes the maximum angle can be computed in time $O (n^2 \log n)$ and space $O(n)$.
Abstract: It is shown that a triangulation of a set of n points in the plane that minimizes the maximum angle can be computed in time $O(n^2 \log n)$ and space $O(n)$. The algorithm is fairly easy to implement and is based on the edge-insertion scheme that iteratively improves an arbitrary initial triangulation. It can be extended to the case where edges are prescribed, and, within the same time- and space-bounds, it can lexicographically minimize the sorted angle vector if the point set is in general position. Experimental results on the efficiency of the algorithm and the quality of the triangulations obtained are included.

72 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202393
2022203
2021130
2020185
2019204
2018223