N-dimensional hilbert scanning and its application to data compression

Arnulfo Perez, Seiichiro Kamata, Eiji Kawaguchi

Research output: Contribution to journalConference articlepeer-review

3 Citations (Scopus)


Hubert scanning defines a mapping, h :-U, that maps the unit interval onto the n-dimensional unit hypercube continuously. In the discrete case the mapping can be described in terms of Reflected Binary Gray Codes (RBGC). In order to extend the quantized mapping to arbitrary precision it is necessary to define induction rules. Induction rules are defined in terms of a single canonical sequence and a set of rotations. In general, in an n-dimensional hypercube there are n2" possible orientations of a canonical form. Beyond two dimensions, it is possible to have non-trivially different paths between two possible orientations and it is better to define the induction rule in terms of the end points of the RBGC subsequences. Hilbert coding is used for n-dimensional binary data compression. The effectiveness of this method to data compression is confirmed. Experimental evaluation shows Hilbert-Wyle coding to be consistently better than other standard compression methods.

Original languageEnglish
Pages (from-to)430-441
Number of pages12
JournalProceedings of SPIE - The International Society for Optical Engineering
Publication statusPublished - 1991 Jun 1
Externally publishedYes
EventImage Processing Algorithms and Techniques II 1991 - San Jose, United States
Duration: 1991 Feb 11991 Feb 7

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


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