A new algorithm for N-dimensional Hilbert scanning

Seiichiro Kamata, Richard O. Eason, Yukihiro Bandou

Research output: Contribution to journalArticle

53 Citations (Scopus)

Abstract

There have been many applications of Hilbert curve, such as image processing, image compression, computer hologram, etc. The Hilbert curve is a one-to-one mapping between N-dimensional space and one-dimensional (1-D) space which preserves point neighborhoods as much as possible. There are several algorithms for N-dimensional Hilbert scanning, such as the Butz algorithm and the Quinqueton algorithm. The Butz algorithm is a mapping function using several bit operations such as shifting, exclusive OR, etc. On the other hand, the Quinqueton algorithm computes all addresses of this curve using recursive functions, but takes time to compute a one-to-one mapping correspondence. Both algorithms are complex to compute and both are difficult to implement in hardware. In this paper, we propose a new, simple, nonrecursive algorithm for N-dimensional Hilbert scanning using look-up tables. The merit of our algorithm is that the computation is fast and the implementation is much easier than previous ones.

Original languageEnglish
Pages (from-to)964-973
Number of pages10
JournalIEEE Transactions on Image Processing
Volume8
Issue number7
DOIs
Publication statusPublished - 1999
Externally publishedYes

Fingerprint

Hilbert
Scanning
Curve
Recursive functions
Recursive Functions
D-space
Look-up Table
Hologram
Image Compression
Holograms
Image compression
Image Processing
Image processing
Correspondence
Hardware

Keywords

  • Hilbert scan
  • Multidimensional analysis
  • Peano curve

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Computer Graphics and Computer-Aided Design
  • Software
  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Computer Vision and Pattern Recognition

Cite this

A new algorithm for N-dimensional Hilbert scanning. / Kamata, Seiichiro; Eason, Richard O.; Bandou, Yukihiro.

In: IEEE Transactions on Image Processing, Vol. 8, No. 7, 1999, p. 964-973.

Research output: Contribution to journalArticle

Kamata, Seiichiro ; Eason, Richard O. ; Bandou, Yukihiro. / A new algorithm for N-dimensional Hilbert scanning. In: IEEE Transactions on Image Processing. 1999 ; Vol. 8, No. 7. pp. 964-973.
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