IWCIA 2004: Combinatorial Image Analysis pp 88-97

# Supercover of Non-square and Non-cubic Grids

• Troung Kieu Linh
• Atsushi Imiya
• Robin Strand
• Gunilla Borgefors
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3322)

## Abstract

We define algebraic discrete geometry of hexagonal- and rhombic-dodecahedral- grids on a plane in a space, respectively. Since, a hexagon and a rhombic-dodecahedron are elements for tilling on a plane and in a space, respectively, a hexagon and a rhombic-dodecahedron are suitable as elements of discrete objects on a plane and in a space, respectively. For the description of linear objects in a discrete space, algebraic discrete geometry provides a unified treatment employing double Diophantus equations. In this paper, we introduce supercove for the hexagonal- and rhombic-dodecahedral- grid-systems on a plane and in a space, respectively.

## Keywords

Grid System Hexagonal Grid Discrete Object Pattern Recognition Letter Euclidean Line
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

1. 1.
Her, I.: Geometric transformations on the hexagonal grid. IEEE Trans. Image Processing 4, 1213–1222 (1995)
2. 2.
Liu, Y.-K.: The generation of straight lines on hexagonal grids. Computer Graphic Forum 12, 27–31 (1993)
3. 3.
Stauton, R.C.: An analysis on hexagonal thinning algorithms and skeletal shape representation. Pattern Recognition 29, 1131–1146 (1996)
4. 4.
Middleton, L., Sivaswamy, J.: Edge detection in a hexagonal-image processing framework. Image and Vision Computing 19, 1071–1081 (2001)
5. 5.
McAndrew, A., Osborn, C.: The Euler characteristic on the face-centerd cubic lattice. Pattern Recognition Letters 18, 229–237 (1997)
6. 6.
Saha, P.K., Rosenfeld, A.: Strongly normal set of convex polygons or polyhedra. Pattern Recognition Letters 19, 1119–1124 (1998)
7. 7.
Schramm, J.M.: Coplanar tricubes. LNCS, vol. 1347, pp. 87–98. Springer, Heidelberg (1997)Google Scholar
8. 8.
Vittone, J., Chassery, J.M.: Digital naive planes understanding. In: Proceedings of SPIE, vol. 3811, pp. 22–32 (1999)Google Scholar
9. 9.
Reveilles, J.-P.: Combinatorial pieces in digital lines and planes. In: Proceedings of SPIE, vol. 2573, pp. 23–34 (1995)Google Scholar
10. 10.
Andres, E., Nehlig, P., Francon, J.: Supercover of straight lines, planes, and triangle. LNCS, vol. 1347, pp. 243–254. Springer, Heidelberg (1997)Google Scholar
11. 11.
Kimuro, K., Nagata, T.: Image processing on an omni-directional view using a hexagonal pyramid. In: Proc. of JAPAN-USA Symposium on Flexible Automation, vol. 2, pp. 1215–1218 (1992)Google Scholar
12. 12.
Benosman, R., Kang, S.-B. (eds.): Panoramic Vision, Sensor, Theory, and Applications. Springer, New York (2001)Google Scholar
13. 13.
Shar, K., White, D., Kimerling, A.J.: Geodesic discrete global grid systems. Cartography and Geographic Information Systems 30, 121–134 (2003)
14. 14.
Randall, D.A., Ringler, T.D., Heikes, R.P., Jones, P., Baumgardner, J.: Climate modeling with spherical geodesic grids. IEEE, Computing in Science and Engineering 4, 32–41 (2002)Google Scholar
15. 15.
Morgan, F.: Riemannian Geometry: A beginner’s Guide. Jones and Bartlett Publishers, USA (1993)
16. 16.
Zdunkowski, W., Boot, A.: Dynamics of the Atmosphere. Cambridge University Press, Cambridge (2003)Google Scholar
17. 17.
Stijnman, M.A., Bisseling, R.H., Barkema, G.T.: Partitioning 3D space for parallel many-particle simulations. Computer Physics Communications 149, 121–134 (2003)
18. 18.
Ibanez, L., Hamitouche, C., Roux, C.: Ray tracing and 3D object representation in the BCC and FCC grids. LNCS, vol. 1347, pp. 235–241. Springer, Heidelberg (1997)Google Scholar

## Authors and Affiliations

• Troung Kieu Linh
• 1
• Atsushi Imiya
• 2
• Robin Strand
• 3
• Gunilla Borgefors
• 3
1. 1.School of Science and TechnologyChiba University
2. 2.IMITChiba UniversityChibaJapan
3. 3.Centre for Image AnalysisUppsalaSweden