A fast voronoi-diagram algorithm with quaternary tree bucketing
Information Processing Letters
Distance transformations in digital images
Computer Vision, Graphics, and Image Processing
The design and analysis of spatial data structures
The design and analysis of spatial data structures
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Algorithmic Foundations of Geographic Information Systems, this book originated from the CISM Advanced School on the Algorithmic Foundations of Geographic Information Systems
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
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Voronoi diagram is a basic data structure in geometry. It has been increasingly attracting the investigation into diverse applications since it was introduced into GIS field. Most current methods for computing Voronoi diagrams are implemented in vector mode. However, the vector-based methods are good only for points and difficult for complex objects. At the same time, most current raster methods are implemented only in a uniformed-grid raster mode. There is a lack of hierarchical method implemented in a hierarchical space such as quadtrees. In this paper such a hierarchical method is described for computing generalized Voronoi diagrams by means of hierarchical distance transform and hierarchical morphological operators based on the quadtree structure. Three different solutions are described and illustrated with experiments for different applications. Furthermore, the errors caused by this method are analyzed and are reduced by constructing the dynamical hierarchical distance structure elements.