Abstract
The Hilbert curve is a way of mapping the multidimensional space into the one-dimensional space. Such mappings are of interest in a number of application domains including image processing and, more recently, in the indexing of multidimensional data. However, little has been discussed on its high dimensional algorithms due to the complexity. In this paper, a novel algorithm is presented for analyzing an N-dimensional Hilbert curve, which discusses how to obtain the constructing information of an N-dimensional Hilbert curve.
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References
Peano, G.: Sur une courbe qui remplit touteune aire plane. Math. Ann. 36, 157–160 (1890)
Biswas, S.: One-dimensional B–B polynomial and Hilbert scan for graylevel image coding. Pattern Recognition 37, 789–800 (2004)
Stevens, R.J., Lehar, A.F., Preston, F.H.: Manipulation and presentation of multi-dimensional image data using the peano scan. IEEE Trans. Pattern Anal. Machine Intell. PAMI-5, 520–526 (1983)
Chen, H., Chang, Y.: Neighbor-finding based on space-filling curves. Information Systems 30, 205–226 (2005)
Mokbel, M.F., Aref, W.G.: Irregularity in multi-dimensional space-filling curves with applications in multimedia databases. In: Proceedings of the 10th ACM SIGMIS Information and knowledge management (October 2001)
Hilbert, D.: Űber die stetige Abbildung einer Linie auf ein Flächenstück. Math. Ann. 38, 459–460 (1891)
Moon, B., Jagadish, H.V., Faloutsos, C., Saltz, J.H.: Analysis of the Clustering Properties of the Hilbert Space-Filling Curve. IEEE Transactions on knowledge and data engineering 13, 124–141 (2001)
Kamata, S., Eason, R.O., Bandou, Y.: A New Algorithm for N-Dimensional Hilbert Scanning. IEEE Trans on Image Processing 8(7) (1999)
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© 2005 Springer-Verlag Berlin Heidelberg
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Li, C., Feng, Y. (2005). Algorithm for Analyzing N-Dimensional Hilbert Curve. In: Fan, W., Wu, Z., Yang, J. (eds) Advances in Web-Age Information Management. WAIM 2005. Lecture Notes in Computer Science, vol 3739. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11563952_60
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DOI: https://doi.org/10.1007/11563952_60
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29227-2
Online ISBN: 978-3-540-32087-6
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