Topic
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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20 Apr 1998
TL;DR: A unified view of algorithmic solutions proposed in the computer science literature that are based on the Delaunay complex of the points is presented.
Abstract: The reconstruction of a shape or surface from a finite set of points is a practically significant and theoretically challenging problem. This paper presents a unified view of algorithmic solutions proposed in the computer science literature that are based on the Delaunay complex of the points.
109 citations
TL;DR: This paper design a novel feature based on minutia neighborhood structure and a more stable triangulation algorithm (low-order Delaunay triangles), which are both insensitive to fingerprint distortion, which considerably narrows down the search space in fingerprint databases and is stable for various fingerprints.
Abstract: Fingerprint indexing is a key technique in automatic fingerprint identification systems (AFIS). However, handling fingerprint distortion is still a problem. This paper concentrates on a more accurate fingerprint indexing algorithm that efficiently retrieves the top N possible matching candidates from a huge database. To this end, we design a novel feature based on minutia neighborhood structure (we call this minutia detail and it contains richer minutia information) and a more stable triangulation algorithm (low-order Delaunay triangles, consisting of order 0 and 1 Delaunay triangles), which are both insensitive to fingerprint distortion. The indexing features include minutia detail and attributes of low-order Delaunay triangle (its handedness, angles, maximum edge, and related angles between orientation field and edges). Experiments on databases FVC2002 and FVC2004 show that the proposed algorithm considerably narrows down the search space in fingerprint databases and is stable for various fingerprints. We also compared it with other indexing approaches, and the results show our algorithm has better performance, especially on fingerprints with distortion.
109 citations
01 Jan 2005
TL;DR: An algorithm to implement natural neighbour interpolation in two and three dimensions, which has the same time complexity as the insertion of a single point in a Voronoi diagram or a Delaunay triangulation.
Abstract: Although the properties of natural neighbour interpolation and its usefulness with scattered and irregularly spaced data are well-known, its implementation is still a problem in practice, especially in three and higher dimensions. We present in this paper an algorithm to implement the method in two and three dimensions, but it can be generalized to higher dimensions. Our algorithm, which uses the concept of flipping in a triangulation, has the same time complexity as the insertion of a single point in a Voronoi diagram or a Delaunay triangulation.
108 citations
TL;DR: A new data structure to compute the Delaunay triangulation of a set of points in the plane is proposed, which combines good worst case complexity, fast behavior on real data, small memory occupation and the possibility of fully dynamic insertions and deletions.
Abstract: We propose a new data structure to compute the Delaunay triangulation of a set of points in the plane. It combines good worst case complexity, fast behavior on real data, small memory occupation and the possibility of fully dynamic insertions and deletions. The location structure is organized into several levels. The lowest level just consists of the triangulation, then each level contains the triangulation of a small sample of the level below. Point location is done by walking in a triangulation to determine the nearest neighbor of the query at that level, then the walk restarts from the neighbor at the level below. Using a small subset (3%) to sample a level allows a small memory occupation; the walk and the use of the nearest neighbor to change levels quickly locate the query.
105 citations
TL;DR: This paper presents simple point insertion and deletion operations in Voronoi diagrams and Delaunay triangulations which may be useful for a wide variety of applications, either where interactivity is important, or where local modification of the topology is preferable to global rebuilding.
105 citations