A Pseudo-Hilbert Scan for Arbitrarily-Sized Arrays
A Pseudo-Hilbert Scan for Arbitrarily-Sized Arrays
复制标题
任意大小数组的伪希尔伯特扫描
DOI：
10.1093/ietfec/e90-a.3.682
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
Yoshifumi Ueshige
中科院分区：
文献类型：
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作者：
Jian Zhang;S. Kamata;Yoshifumi Ueshige
二维希尔伯特曲线是二维空间和一维空间之间的一对一映射。它作为一种扫描技术（希尔伯特扫描）在数字图像处理领域得到了积极的研究，因为它具有保持二维图案空间关系的特性。目前存在几种希尔伯特扫描算法。然而，这些算法在实现上有两个严格的限制。首先，使用递归函数来生成希尔伯特曲线，这使得算法复杂且计算昂贵。其次，扫描矩形的两边必须具有相同的大小，并且每个大小必须是2的幂，这极大地限制了Hilbert扫描的应用。本文提出了一种基于两个查找表的伪希尔伯特扫描算法。该方法改进了希尔伯特扫描，使其更适合于实时处理和一般应用。仿真结果表明，伪希尔伯特扫描可以尽可能多地保留点邻域，并利用相邻格点之间的高度相关性。它也显示了竞争力的性能的伪希尔伯特扫描与其他扫描技术相比。
The 2-dimensional (2-D) Hilbert curve is a one-to-one mapping between 2-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 2-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, both sides of the scanned rectangle 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 Pseudo-Hilbert scan algorithm based on two look-up tables is proposed. The proposed method improves the Hilbert scan to be suitable for real-time processing and general application. 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 scan techniques.