An N-dimensional pseudo-Hilbert scan algorithm for an arbitrarily-sized hypercuboid

Jian Zhang, Seiichiro Kamata

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The N-dimensional (N-D) Hilbert curve is a one-to-one mapping between N-D space and one-dimensional (1-D) space. It is studied actively in the area of digital image processing as a scan technique (Hilbert scan) because of its property of preserving the spacial relationship of the N-D patterns. Currently there exist several Hilbert scan algorithms. However, these algorithms have two strict restrictions in implementation. First, recursive functions are used to generate a Hilbert curve, which makes the algorithms complex and computationally expensive. Second, all the sides of the scanned region must have same size and each size must be a power of two, which limits the application of the Hilbert scan greatly. In this paper, a nonrecursive N-D Pseudo-Hilbert scan algorithm based on two look-up tables is proposed. The merit of the algorithm is that the computation is fast and the implementation is much easier than the original one. The simulation indicates that the Pseudo-Hilbert scan can preserve point neighborhoods as much as possible and take advantage of the high correlation between neighboring lattice points. It also shows competitive performance of the Pseudo-Hilbert scan in comparison with other common scan techniques.

Original languageEnglish
Title of host publicationIECON Proceedings (Industrial Electronics Conference)
Pages2459-2464
Number of pages6
DOIs
Publication statusPublished - 2007
Event33rd Annual Conference of the IEEE Industrial Electronics Society, IECON - Taipei
Duration: 2007 Nov 52007 Nov 8

Other

Other33rd Annual Conference of the IEEE Industrial Electronics Society, IECON
CityTaipei
Period07/11/507/11/8

Fingerprint

Recursive functions
Image processing

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

Zhang, J., & Kamata, S. (2007). An N-dimensional pseudo-Hilbert scan algorithm for an arbitrarily-sized hypercuboid. In IECON Proceedings (Industrial Electronics Conference) (pp. 2459-2464). [4460283] https://doi.org/10.1109/IECON.2007.4460283

An N-dimensional pseudo-Hilbert scan algorithm for an arbitrarily-sized hypercuboid. / Zhang, Jian; Kamata, Seiichiro.

IECON Proceedings (Industrial Electronics Conference). 2007. p. 2459-2464 4460283.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Zhang, J & Kamata, S 2007, An N-dimensional pseudo-Hilbert scan algorithm for an arbitrarily-sized hypercuboid. in IECON Proceedings (Industrial Electronics Conference)., 4460283, pp. 2459-2464, 33rd Annual Conference of the IEEE Industrial Electronics Society, IECON, Taipei, 07/11/5. https://doi.org/10.1109/IECON.2007.4460283
Zhang J, Kamata S. An N-dimensional pseudo-Hilbert scan algorithm for an arbitrarily-sized hypercuboid. In IECON Proceedings (Industrial Electronics Conference). 2007. p. 2459-2464. 4460283 https://doi.org/10.1109/IECON.2007.4460283
Zhang, Jian ; Kamata, Seiichiro. / An N-dimensional pseudo-Hilbert scan algorithm for an arbitrarily-sized hypercuboid. IECON Proceedings (Industrial Electronics Conference). 2007. pp. 2459-2464
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