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http://dx.doi.org/10.9708/jksci.2012.17.1.161

Three Dimensional Euclidean Minimum Spanning Tree for Connecting Nodes of Space with the Shortest Length  

Kim, Chae-Kak (Dept. of Social Welfare, Kimpo College)
Kim, In-Bum (Dept. of Internet Information, Kimpo College)
Publication Information
Journal of the Korea Society of Computer and Information / v.17, no.1, 2012 , pp. 161-169 More about this Journal
Abstract
In general, Euclidean minimum spanning tree is a tree connecting input nodes with minimum connecting cost. But the tree may not be optimal when applied to real world problems of three dimension. In this paper, three dimension Euclidean minimum spanning tree is proposed, connecting all input nodes of 3-dimensional space with minimum cost. In experiments for 30,000 input nodes with 100% space ratio, the tree produced by the proposed method can reduce 90.0% connection cost tree, compared with the tree by two dimension Prim's minimum spanning tree. In two dimension plane, the proposed tree increases 251.2% connecting cost, which is pointless in 3-dimensional real world. Therefore, the proposed method can work well for many connecting problems in real world space of three dimensions.
Keywords
Euclidean Minimum Spanning Tree; Space Ratio; 3-Dimensional Space; Prim's MST Algorithm; Connecting Cost;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
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1 H. Lee, "Convert 2D Video Frames into 3D Video Frames," Journal of the Korea Society of Computer and Information, Vol.14, No.6, pp.117-123, 2009.
2 A. Zhang, W. Sun, S. Hu, C. Qian , "Automatic Global Registration of Multiple 3D Data Sets from Outdoor Urban Environments Based on Feature Units," SCCG'04 Proceedings of the 20th Spring Conference on Computer Graphics, pp.193-199, 2004.
3 J. Go, Y. Choi, S. Jang, K. Lee, "The Analysis of 3D Position Accuracy of Multi-Looking Camera," Journal of Korea Spatial Information Society, Vol.19, No.3, pp.33-42, 2011.
4 S. Kim, J. Kang, Y. Choe, S. Park, I. Shim, S. Ahn, M. Chung, "The Development of Sensor System and 3D World Modeling for Autonomous Vehicle," Journal of Institute of Control, Robotics and Systems, Vol.17, No.6, pp.531-538, 2011.   DOI   ScienceOn
5 N. Zhu, A.C.S. Chung, "Minimum Average-Cost Path for Real Time 3D Coronary Artery Segmentation of CT Images," MICCAI'11 Proc. of the 14th international conference on Medical Image Computing and Computer Assisted Intervention, Vol.III, pp.436-444, 2011.
6 T.H. Cormen, C.E Leiserson, R.L. Rivest and C. Stein, "Introduction to Algorithms," 2nd Ed., THe MIT Press, pp.561-579, 2001.
7 I. Kim, S. Kim, "Mechanism for Building Approximation Edge Minimum Spanning Tree Using Portals on Input Edges," The KIPS Transactions: PartA, Vol.16A, No.6, pp.509-518, 2009.   DOI   ScienceOn
8 B. Chun, Y. Kim, "A Method for Character Segm entation using MST," Journal of the Korea Society of Computer and Information, Vol.11, No.3, pp.73-78, 2006.
9 P. Amat, W. Puech, S. Druon, J. P. Pedeboy, "Lossless 3D Steganography Based on MST and Connectivity Modification," Image Communication, Vol.25, No.6, pp.400-412, 2010.
10 H. Woo, G. Kim, "Detection of Entry/Exit Zones for Visual Surveillance System using Graph Theoretic Clustering," Journal of the Institute of Electronics Engineers of Korea SC, Vol.46, No.6, pp.1-8, 2009.