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

Pages (from-to) | 964-973 |

Number of pages | 10 |

Journal | IEEE Transactions on Image Processing |

Volume | 8 |

Issue number | 7 |

DOIs | |

Publication status | Published - 1999 |

Externally published | Yes |

### Fingerprint

### 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

*IEEE Transactions on Image Processing*,

*8*(7), 964-973. https://doi.org/10.1109/83.772242

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

Research output: Contribution to journal › Article

*IEEE Transactions on Image Processing*, vol. 8, no. 7, pp. 964-973. https://doi.org/10.1109/83.772242

}

TY - JOUR

T1 - A new algorithm for N-dimensional Hilbert scanning

AU - Kamata, Seiichiro

AU - Eason, Richard O.

AU - Bandou, Yukihiro

PY - 1999

Y1 - 1999

N2 - 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.

AB - 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.

KW - Hilbert scan

KW - Multidimensional analysis

KW - Peano curve

UR - http://www.scopus.com/inward/record.url?scp=0032625739&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032625739&partnerID=8YFLogxK

U2 - 10.1109/83.772242

DO - 10.1109/83.772242

M3 - Article

C2 - 18267509

AN - SCOPUS:0032625739

VL - 8

SP - 964

EP - 973

JO - IEEE Transactions on Image Processing

JF - IEEE Transactions on Image Processing

SN - 1057-7149

IS - 7

ER -