Elsevier

Pattern Recognition

Volume 28, Issue 12, December 1995, Pages 1839-1844
Pattern Recognition

Voronoi tessellation of points with integer coordinates: Time-efficient implementation and online edge-list generation

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Abstract

The Voronoi tessellation in the plane can be computed in a particularly time-efficient manner for generators with integer coordinates, such as typically acquired from a raster image. The Voronoi tessellation is constructed line by line during a single scan of the input image, simultaneously generating an edge-list data structure (DCEL) suitable for postprocessing by graph traversal algorithms. In contrast to the generic case, it can be shown that the topology of the grid permits the algorithm to run faster on complex scenes. Consequently, in Computer Vision applications, the computation of the Voronoi tessellation represents an attractive alternative to raster-based techniques in terms of both computational complexity and quality of data structures.

Section snippets

bio1About the Author—ROBERT L. OGNIEWICZ received the M.S. and the Ph.D. in electrical engineering from the Swiss Federal Institute of Technology (ETH), Zurich, Switzerland, in 1988 and 1992, respectively. From 1992 to 1994 he was a postdoctoral fellow at the Communication Technology Laboratory of the ETH. Currently, he is a postdoctoral fellow at the Division of Applied Sciences, Harvard University, Cambridge, U.S.A. His research interests include pattern recognition, computer vision and

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bio1About the Author—ROBERT L. OGNIEWICZ received the M.S. and the Ph.D. in electrical engineering from the Swiss Federal Institute of Technology (ETH), Zurich, Switzerland, in 1988 and 1992, respectively. From 1992 to 1994 he was a postdoctoral fellow at the Communication Technology Laboratory of the ETH. Currently, he is a postdoctoral fellow at the Division of Applied Sciences, Harvard University, Cambridge, U.S.A. His research interests include pattern recognition, computer vision and artificial intelligence, with special interest in shape representation and recognition. He is a member of the IEEE and the IEEE Computer Society.

bio2About the Author—OLAF KÜBLER received an education in theoretical physics at the Universities of Karlsruhe and Heidelberg, Germany, and the Swiss Federal Institute of Technology (ETH) in Zurich, Switzerland. He obtained the doctorate in theoretical nuclear physics in 1970. In 1972, he joined the Institute of Cell Biology at ETH-Zurich to direct research in processing electron microscopical images of molecular structures. Since 1979, he is Professor of Image Science at the Electrical Engineering Department of ETH-Zurich. Research activities at his laboratory involve segmentation of 2D and 3D image data, percetual grouping, description and representation of 2D and 3D shapes, and systems for quantitative image evaluation. Main application areas are analysis of 3D medical MRI data, Robot Vision and interpretation of aerial photographs.

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