N-dimensional Hilbert scanning and its application to data compression

Arnulfo Perez, Seiichiro Kamata, Eiji Kawaguchi

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

2 Citations (Scopus)

Abstract

Hilbert scanning defines a mapping, h n: R → U n, 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 n 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
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
EditorsMehmet R. Civanlar, Sanjit K. Mitra, Robert J.II Moorhead
PublisherPubl by Int Soc for Optical Engineering
Pages430-441
Number of pages12
Volume1452
Publication statusPublished - 1991
Externally publishedYes
EventSPIE/IS&T Symposium on Electronic Imaging Science and Technology - San Jose, CA, USA
Duration: 1991 Feb 241991 Mar 1

Other

OtherSPIE/IS&T Symposium on Electronic Imaging Science and Technology
CitySan Jose, CA, USA
Period91/2/2491/3/1

Fingerprint

data compression
Data compression
induction
Binary codes
Scanning
scanning
coding
binary data
canonical forms
intervals
evaluation

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Condensed Matter Physics

Cite this

Perez, A., Kamata, S., & Kawaguchi, E. (1991). N-dimensional Hilbert scanning and its application to data compression. In M. R. Civanlar, S. K. Mitra, & R. J. II. Moorhead (Eds.), Proceedings of SPIE - The International Society for Optical Engineering (Vol. 1452, pp. 430-441). Publ by Int Soc for Optical Engineering.

N-dimensional Hilbert scanning and its application to data compression. / Perez, Arnulfo; Kamata, Seiichiro; Kawaguchi, Eiji.

Proceedings of SPIE - The International Society for Optical Engineering. ed. / Mehmet R. Civanlar; Sanjit K. Mitra; Robert J.II Moorhead. Vol. 1452 Publ by Int Soc for Optical Engineering, 1991. p. 430-441.

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

Perez, A, Kamata, S & Kawaguchi, E 1991, N-dimensional Hilbert scanning and its application to data compression. in MR Civanlar, SK Mitra & RJII Moorhead (eds), Proceedings of SPIE - The International Society for Optical Engineering. vol. 1452, Publ by Int Soc for Optical Engineering, pp. 430-441, SPIE/IS&T Symposium on Electronic Imaging Science and Technology, San Jose, CA, USA, 91/2/24.
Perez A, Kamata S, Kawaguchi E. N-dimensional Hilbert scanning and its application to data compression. In Civanlar MR, Mitra SK, Moorhead RJII, editors, Proceedings of SPIE - The International Society for Optical Engineering. Vol. 1452. Publ by Int Soc for Optical Engineering. 1991. p. 430-441
Perez, Arnulfo ; Kamata, Seiichiro ; Kawaguchi, Eiji. / N-dimensional Hilbert scanning and its application to data compression. Proceedings of SPIE - The International Society for Optical Engineering. editor / Mehmet R. Civanlar ; Sanjit K. Mitra ; Robert J.II Moorhead. Vol. 1452 Publ by Int Soc for Optical Engineering, 1991. pp. 430-441
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