TY - GEN

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

AU - Zhang, Jian

AU - Kamata, Sei Ichiro

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.

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U2 - 10.1109/IECON.2007.4460283

DO - 10.1109/IECON.2007.4460283

M3 - Conference contribution

AN - SCOPUS:49949085464

SN - 1424407834

SN - 9781424407835

T3 - IECON Proceedings (Industrial Electronics Conference)

SP - 2459

EP - 2464

BT - Proceedings of the 33rd Annual Conference of the IEEE Industrial Electronics Society, IECON

T2 - 33rd Annual Conference of the IEEE Industrial Electronics Society, IECON

Y2 - 5 November 2007 through 8 November 2007

ER -