### Abstract

The N-dimensional (N-D) Hilbert curve is a one-to-one mapping between N-D space and one-dimensional (1-D) space. It is studied actively in the area of digital image processing as a scan technique (Hilbert scan) because of its property of preserving the spacial relationship of the N-D patterns. Currently there exist several Hilbert scan algorithms. However, these algorithms have two strict restrictions in implementation. First, recursive functions are used to generate a Hilbert curve, which makes the algorithms complex and computationally expensive. Second, all the sides of the scanned region must have same size and each size must be a power of two, which limits the application of the Hilbert scan greatly. In this paper, a nonrecursive N-D Pseudo-Hilbert scan algorithm based on two look-up tables is proposed. The merit of the algorithm is that the computation is fast and the implementation is much easier than the original one. The simulation indicates that the Pseudo-Hilbert scan can preserve point neighborhoods as much as possible and take advantage of the high correlation between neighboring lattice points. It also shows competitive performance of the Pseudo-Hilbert scan in comparison with other common scan techniques.

Original language | English |
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Title of host publication | IECON Proceedings (Industrial Electronics Conference) |

Pages | 2459-2464 |

Number of pages | 6 |

DOIs | |

Publication status | Published - 2007 |

Event | 33rd Annual Conference of the IEEE Industrial Electronics Society, IECON - Taipei Duration: 2007 Nov 5 → 2007 Nov 8 |

### Other

Other | 33rd Annual Conference of the IEEE Industrial Electronics Society, IECON |
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City | Taipei |

Period | 07/11/5 → 07/11/8 |

### Fingerprint

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

*IECON Proceedings (Industrial Electronics Conference)*(pp. 2459-2464). [4460283] https://doi.org/10.1109/IECON.2007.4460283

**An N-dimensional pseudo-Hilbert scan algorithm for an arbitrarily-sized hypercuboid.** / Zhang, Jian; Kamata, Seiichiro.

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

*IECON Proceedings (Industrial Electronics Conference).*, 4460283, pp. 2459-2464, 33rd Annual Conference of the IEEE Industrial Electronics Society, IECON, Taipei, 07/11/5. https://doi.org/10.1109/IECON.2007.4460283

}

TY - GEN

T1 - An N-dimensional pseudo-Hilbert scan algorithm for an arbitrarily-sized hypercuboid

AU - Zhang, Jian

AU - Kamata, Seiichiro

PY - 2007

Y1 - 2007

N2 - The N-dimensional (N-D) Hilbert curve is a one-to-one mapping between N-D space and one-dimensional (1-D) space. It is studied actively in the area of digital image processing as a scan technique (Hilbert scan) because of its property of preserving the spacial relationship of the N-D patterns. Currently there exist several Hilbert scan algorithms. However, these algorithms have two strict restrictions in implementation. First, recursive functions are used to generate a Hilbert curve, which makes the algorithms complex and computationally expensive. Second, all the sides of the scanned region must have same size and each size must be a power of two, which limits the application of the Hilbert scan greatly. In this paper, a nonrecursive N-D Pseudo-Hilbert scan algorithm based on two look-up tables is proposed. The merit of the algorithm is that the computation is fast and the implementation is much easier than the original one. The simulation indicates that the Pseudo-Hilbert scan can preserve point neighborhoods as much as possible and take advantage of the high correlation between neighboring lattice points. It also shows competitive performance of the Pseudo-Hilbert scan in comparison with other common scan techniques.

AB - The N-dimensional (N-D) Hilbert curve is a one-to-one mapping between N-D space and one-dimensional (1-D) space. It is studied actively in the area of digital image processing as a scan technique (Hilbert scan) because of its property of preserving the spacial relationship of the N-D patterns. Currently there exist several Hilbert scan algorithms. However, these algorithms have two strict restrictions in implementation. First, recursive functions are used to generate a Hilbert curve, which makes the algorithms complex and computationally expensive. Second, all the sides of the scanned region must have same size and each size must be a power of two, which limits the application of the Hilbert scan greatly. In this paper, a nonrecursive N-D Pseudo-Hilbert scan algorithm based on two look-up tables is proposed. The merit of the algorithm is that the computation is fast and the implementation is much easier than the original one. The simulation indicates that the Pseudo-Hilbert scan can preserve point neighborhoods as much as possible and take advantage of the high correlation between neighboring lattice points. It also shows competitive performance of the Pseudo-Hilbert scan in comparison with other common scan techniques.

UR - http://www.scopus.com/inward/record.url?scp=49949085464&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=49949085464&partnerID=8YFLogxK

U2 - 10.1109/IECON.2007.4460283

DO - 10.1109/IECON.2007.4460283

M3 - Conference contribution

AN - SCOPUS:49949085464

SN - 1424407834

SN - 9781424407835

SP - 2459

EP - 2464

BT - IECON Proceedings (Industrial Electronics Conference)

ER -