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
Analysis of the Clustering Properties of the Hilbert Space-Filling Curve
IEEE Transactions on Knowledge and Data Engineering
An address generator of a pseudo-Hilbert scan in a rectangle region
ICIP '97 Proceedings of the 1997 International Conference on Image Processing (ICIP '97) 3-Volume Set-Volume 1 - Volume 1
Hilbert Scan and Image Compression
ICPR '00 Proceedings of the International Conference on Pattern Recognition - Volume 3
IEICE - Transactions on Information and Systems
Convergence with Hilbert's space filling curve
Journal of Computer and System Sciences
A Locally Adaptive Peano Scanning Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
Classification of binary random patterns
IEEE Transactions on Information Theory
On the metric properties of discrete space-filling curves
IEEE Transactions on Image Processing
An algorithm for encoding and decoding the 3-D Hilbert order
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 Hilbert curve is a one-to-one mapping between multidimensional space and one-dimensional (1-D) space. Due to the advantage of preserving high correlation of multidimensional points, it receives much attention in many areas. Especially in image processing, Hilbert curve is studied actively as a scan technique (Hilbert scan). Currently there have been several Hilbert scan algorithms, but they usually have strict implementation conditions. For example, they use recursive functions to generate scans, which makes the algorithms complex and difficult to implement in real-time systems. Moreover the length of each side in a scanned region should be same and equal to the power of two, which limits the application of Hilbert scan greatly. In this paper, to remove the constraints and improve the Hilbert scan for a general application, an effective generalized three-dimensional (3-D) Hilbert scan algorithm is proposed. The proposed algorithm uses two simple look-up tables instead of recursive functions to generate a scan, which greatly reduces the computational complexity and saves storage memory. Furthermore, the experimental results show that the proposed generalized Hilbert scan can also take advantage of the high correlation between neighboring lattice points in an arbitrarily-sized cuboid region, and give competitive performance in comparison with some common scan techniques.