IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Online ISSN : 1745-1337
Print ISSN : 0916-8508
Regular Section
An N-Dimensional Pseudo-Hilbert Scan for Arbitrarily-Sized Hypercuboids
Jian ZHANGSei-ichiro KAMATA
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2008 Volume E91.A Issue 3 Pages 846-858

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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 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 complex and 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 limits the 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 scan can preserve point neighborhoods as much as possible and take advantage of the high correlation between neigh-boring 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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© 2008 The Institute of Electronics, Information and Communication Engineers
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