Compression of two-dimensional data
IEEE Transactions on Information Theory
Linear clustering of objects with multiple attributes
SIGMOD '90 Proceedings of the 1990 ACM SIGMOD international conference on Management of data
Irregularity in multi-dimensional space-filling curves with applications in multimedia databases
Proceedings of the tenth international conference on Information and knowledge management
Performance of multi-dimensional space-filling curves
Proceedings of the 10th ACM international symposium on Advances in geographic information systems
Analysis of the Clustering Properties of the Hilbert Space-Filling Curve
IEEE Transactions on Knowledge and Data Engineering
Hilbert Scan and Image Compression
ICPR '00 Proceedings of the International Conference on Pattern Recognition - Volume 3
IEICE - Transactions on Information and Systems
A Pseudo-Hilbert Scan for Arbitrarily-Sized Arrays
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
On the metric properties of discrete space-filling curves
IEEE Transactions on Image Processing
A new algorithm for N-dimensional Hilbert scanning
IEEE Transactions on Image Processing
An analysis of some common scanning techniques for lossless image coding
IEEE Transactions on Image Processing
Space-filling approach for fast window query on compressed images
IEEE Transactions on Image Processing
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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 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.