### 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 language | English |
---|---|

Title of host publication | Proceedings of SPIE - The International Society for Optical Engineering |

Editors | Mehmet R. Civanlar, Sanjit K. Mitra, Robert J.II Moorhead |

Publisher | Publ by Int Soc for Optical Engineering |

Pages | 430-441 |

Number of pages | 12 |

Volume | 1452 |

Publication status | Published - 1991 |

Externally published | Yes |

Event | SPIE/IS&T Symposium on Electronic Imaging Science and Technology - San Jose, CA, USA Duration: 1991 Feb 24 → 1991 Mar 1 |

### Other

Other | SPIE/IS&T Symposium on Electronic Imaging Science and Technology |
---|---|

City | San Jose, CA, USA |

Period | 91/2/24 → 91/3/1 |

### Fingerprint

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Condensed Matter Physics

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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.

}

TY - GEN

T1 - N-dimensional Hilbert scanning and its application to data compression

AU - Perez, Arnulfo

AU - Kamata, Seiichiro

AU - Kawaguchi, Eiji

PY - 1991

Y1 - 1991

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0025758008&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025758008&partnerID=8YFLogxK

M3 - Conference contribution

VL - 1452

SP - 430

EP - 441

BT - Proceedings of SPIE - The International Society for Optical Engineering

A2 - Civanlar, Mehmet R.

A2 - Mitra, Sanjit K.

A2 - Moorhead, Robert J.II

PB - Publ by Int Soc for Optical Engineering

ER -