An N-dimensional pseudo-hilbert scan for arbitrarily-sized hypercuboids

Jian Zhang, Seiichiro Kamata

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The N-dimensional (N-D) Hilbert curve is a one-to-one mapping betweenN-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 ofits property of preserving the spatial 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 complexand computationally expensive. Second, all the sides of the scanned region must have the same size and the length must be a power of two, which limitsthe application of the Hilbert scan greatly. Thus in order to remove these constraints and improve the Hilbert scan for general application, a nonrecursive N-D Pseudo-Hilbert scan algorithm based on two look-up tables is proposed in this paper. The merit of the proposed algorithm is that implementation is much easier than the original one while preserving the original characteristics. The experimental results indicate that the Pseudo-Hilbert scancan preserve point neighborhoods as much as possible and take advantage of the high correlation between neighboring lattice points, and it also shows the competitive performance of the Pseudo-Hilbert scan in comparison with other common scan techniques. We believe that this novel scan technique undoubtedly leads to many new applications in those areas can benefit from reducing the dimensionality of the problem.

Original languageEnglish
Pages (from-to)846-858
Number of pages13
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
VolumeE91-A
Issue number3
DOIs
Publication statusPublished - 2008

Fingerprint

Hilbert
Recursive functions
D-space
Image processing
Digital Image Processing
Curve
Recursive Functions
Look-up Table
Lattice Points
Dimensionality
Restriction
Experimental Results

Keywords

  • Euclidean distance
  • Hilbert scan
  • Hypercube
  • Look-up table
  • Space-filling curve

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Computer Graphics and Computer-Aided Design
  • Applied Mathematics
  • Signal Processing

Cite this

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abstract = "The N-dimensional (N-D) Hilbert curve is a one-to-one mapping betweenN-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 ofits property of preserving the spatial 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 complexand computationally expensive. Second, all the sides of the scanned region must have the same size and the length must be a power of two, which limitsthe application of the Hilbert scan greatly. Thus in order to remove these constraints and improve the Hilbert scan for general application, a nonrecursive N-D Pseudo-Hilbert scan algorithm based on two look-up tables is proposed in this paper. The merit of the proposed algorithm is that implementation is much easier than the original one while preserving the original characteristics. The experimental results indicate that the Pseudo-Hilbert scancan preserve point neighborhoods as much as possible and take advantage of the high correlation between neighboring lattice points, and it also shows the competitive performance of the Pseudo-Hilbert scan in comparison with other common scan techniques. We believe that this novel scan technique undoubtedly leads to many new applications in those areas can benefit from reducing the dimensionality of the problem.",
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