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

Jian Zhang, Sei Ichiro 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 publicationProceedings of the 33rd Annual Conference of the IEEE Industrial Electronics Society, IECON
Pages2459-2464
Number of pages6
DOIs
Publication statusPublished - 2007 Dec 1
Event33rd Annual Conference of the IEEE Industrial Electronics Society, IECON - Taipei, Taiwan, Province of China
Duration: 2007 Nov 52007 Nov 8

Publication series

NameIECON Proceedings (Industrial Electronics Conference)

Conference

Conference33rd Annual Conference of the IEEE Industrial Electronics Society, IECON
CountryTaiwan, Province of China
CityTaipei
Period07/11/507/11/8

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering

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    Zhang, J., & Kamata, S. I. (2007). An N-dimensional pseudo-Hilbert scan algorithm for an arbitrarily-sized hypercuboid. In Proceedings of the 33rd Annual Conference of the IEEE Industrial Electronics Society, IECON (pp. 2459-2464). [4460283] (IECON Proceedings (Industrial Electronics Conference)). https://doi.org/10.1109/IECON.2007.4460283