### Abstract

The 2-dimensional Hilbert scan (HS) is a one-to-one mapping between 2-dimensional (2-D) space and one-dimensional (1-D) space along the 2-D Hilbert curve. Because Hilbert curve can preserve the spatial relationships of the patterns effectively, 2-D HS has been studied in digital image processing actively, such as compressing image data, pattern recognition, clustering an image, etc. However, the existing HS algorithms have some strict restrictions when they are implemented. For example, the most algorithms use recursive function to generate the Hilbert curve, which makes the algorithms complex and takes time to compute the one-to-one correspondence. And some even request the sides of the scanned rectangle region must be a power of two, that limits the application scope of HS greatly. Thus, in order to improve HS to be proper to real-time processing and general application, we proposed a Pseudo-Hilbert scan (PHS) based on the look-up table method for arbitrarily-sized arrays in this paper. Experimental results for both HS and PHS indicate that the proposed generalized Hilbert scan algorithm also reserves the good property of HS that the curve preserves point neighborhoods as much as possible, and gives competitive performance in comparison with Raster scan.

Original language | English |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 290-299 |

Number of pages | 10 |

Volume | 4153 LNCS |

Publication status | Published - 2006 |

Event | International Workshop on Intelligent Computing in Pattern Analysis/Synthesis, IWICPAS 2006 - Xi'an Duration: 2006 Aug 26 → 2006 Aug 27 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 4153 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | International Workshop on Intelligent Computing in Pattern Analysis/Synthesis, IWICPAS 2006 |
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City | Xi'an |

Period | 06/8/26 → 06/8/27 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 4153 LNCS, pp. 290-299). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4153 LNCS).

**A pseudo-hilbert scan algorithm for arbitrarily-sized rectangle region.** / Zhang, Jian; Kamata, Seiichiro; Ueshige, Yoshifumi.

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

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 4153 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4153 LNCS, pp. 290-299, International Workshop on Intelligent Computing in Pattern Analysis/Synthesis, IWICPAS 2006, Xi'an, 06/8/26.

}

TY - GEN

T1 - A pseudo-hilbert scan algorithm for arbitrarily-sized rectangle region

AU - Zhang, Jian

AU - Kamata, Seiichiro

AU - Ueshige, Yoshifumi

PY - 2006

Y1 - 2006

N2 - The 2-dimensional Hilbert scan (HS) is a one-to-one mapping between 2-dimensional (2-D) space and one-dimensional (1-D) space along the 2-D Hilbert curve. Because Hilbert curve can preserve the spatial relationships of the patterns effectively, 2-D HS has been studied in digital image processing actively, such as compressing image data, pattern recognition, clustering an image, etc. However, the existing HS algorithms have some strict restrictions when they are implemented. For example, the most algorithms use recursive function to generate the Hilbert curve, which makes the algorithms complex and takes time to compute the one-to-one correspondence. And some even request the sides of the scanned rectangle region must be a power of two, that limits the application scope of HS greatly. Thus, in order to improve HS to be proper to real-time processing and general application, we proposed a Pseudo-Hilbert scan (PHS) based on the look-up table method for arbitrarily-sized arrays in this paper. Experimental results for both HS and PHS indicate that the proposed generalized Hilbert scan algorithm also reserves the good property of HS that the curve preserves point neighborhoods as much as possible, and gives competitive performance in comparison with Raster scan.

AB - The 2-dimensional Hilbert scan (HS) is a one-to-one mapping between 2-dimensional (2-D) space and one-dimensional (1-D) space along the 2-D Hilbert curve. Because Hilbert curve can preserve the spatial relationships of the patterns effectively, 2-D HS has been studied in digital image processing actively, such as compressing image data, pattern recognition, clustering an image, etc. However, the existing HS algorithms have some strict restrictions when they are implemented. For example, the most algorithms use recursive function to generate the Hilbert curve, which makes the algorithms complex and takes time to compute the one-to-one correspondence. And some even request the sides of the scanned rectangle region must be a power of two, that limits the application scope of HS greatly. Thus, in order to improve HS to be proper to real-time processing and general application, we proposed a Pseudo-Hilbert scan (PHS) based on the look-up table method for arbitrarily-sized arrays in this paper. Experimental results for both HS and PHS indicate that the proposed generalized Hilbert scan algorithm also reserves the good property of HS that the curve preserves point neighborhoods as much as possible, and gives competitive performance in comparison with Raster scan.

UR - http://www.scopus.com/inward/record.url?scp=33750058556&partnerID=8YFLogxK

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M3 - Conference contribution

AN - SCOPUS:33750058556

SN - 354037597X

SN - 9783540375975

VL - 4153 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 290

EP - 299

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -