Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Object recognition using wavelets, L-G graphs and synthesis of regions
Pattern Recognition
An algorithm for point cluster generalization based on the Voronoi diagram
Computers & Geosciences
A sweep-line algorithm for spatial clustering
Advances in Engineering Software
Clustering with r-regular graphs
Pattern Recognition
Reconstructing orthogonal polyhedra from putative vertex sets
Computational Geometry: Theory and Applications
Geospatial clustering in data-rich environments: features and issues
KES'05 Proceedings of the 9th international conference on Knowledge-Based Intelligent Information and Engineering Systems - Volume Part IV
Algorithm that mimics human perceptual grouping of dot patterns
BVAI'05 Proceedings of the First international conference on Brain, Vision, and Artificial Intelligence
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A sound notion of the neighborhood of a point is essential for analyzing dot patterns. The past work in this direction has concentrated on identifying pairs of points that are neighbors. Examples of such methods include those based on a fixed radius, k-nearest neighbors, minimal spanning tree, relative neighborhood graph, and the Gabriel graph. This correspondence considers the use of the region enclosed by a point's Voronoi polygon as its neighborhood. It is argued that the Voronoi polygons possess intuitively appealing characteristics, as would be expected from the neighborhood of a point. Geometrical characteristics of the Voronoi neighborhood are used as features in dot pattern processing. Procedures for segmentation, matching, and perceptual border extraction using the Voronoi neighborhood are outlined. Extensions of the Voronoi definition to other domains are discussed.