A new algorithm for N-dimensional Hilbert scanning

Sei Ichiro Kamata*, Richard O. Eason, Yukihiro Bandou

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

62 Citations (Scopus)


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
Issue number7
Publication statusPublished - 1999
Externally publishedYes


  • Hilbert scan
  • Multidimensional analysis
  • Peano curve

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design


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