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A Connection Between Zn and Generalized Triangular Grids
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Centre for Image Analysis. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis.
2008 (English)In: International Symposium on Visual Computing (ISVC 2008), Las Vegas, Nevada, Berlin / Heidelberg: Springer , 2008, 1157-1166 p.Conference paper, Published paper (Refereed)
Abstract [en]

In this paper we show how non-standard three-dimensional grids, such as the face-centered cubic (fcc), the body-centered cubic (bcc), and the diamond grids can be embedded in ℤ4. The fcc grid is a hyperplane in ℤ4, the diamond grid is the union of two parallel hyperplanes. The union of four hyperplanes (in a circular way) gives the bcc grid. Based on these connections, several types of neighborhood structures are introduced on these grids. These structures span from the most natural ones (crystal bonds, Voronoi neighbors) to infinite families.

Place, publisher, year, edition, pages
Berlin / Heidelberg: Springer , 2008. 1157-1166 p.
Series
Lecture Notes in Computer Science, ISSN 0302-9743 ; 5359
National Category
Computer Vision and Robotics (Autonomous Systems) Discrete Mathematics
Research subject
Computerized Image Analysis
Identifiers
URN: urn:nbn:se:uu:diva-87937DOI: 10.1007/978-3-540-89646-3_115ISBN: 978-3-540-89645-6 (print)OAI: oai:DiVA.org:uu-87937DiVA: diva2:133942
Available from: 2009-01-15 Created: 2009-01-15 Last updated: 2010-03-01Bibliographically approved

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Publisher's full texthttp://dx.doi.org/10.1007/978-3-540-89646-3_115

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Strand, Robin

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