An N-Dimensional Pseudo-Hilbert Scan for Arbitrarily-Sized Hypercuboids
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Algorithm for analyzing n-dimensional hilbert curve
WAIM'05 Proceedings of the 6th international conference on Advances in Web-Age Information Management
A pseudo-hilbert scan algorithm for arbitrarily-sized rectangle region
IWICPAS'06 Proceedings of the 2006 Advances in Machine Vision, Image Processing, and Pattern Analysis international conference on Intelligent Computing in Pattern Analysis/Synthesis
A generalized 3-D Hilbert scan using look-up tables
Journal of Visual Communication and Image Representation
Using Hilbert scan on statistical color space partitioning
Computers and Electrical Engineering
Image coarsening by using space-filling curve for decomposition-based image enhancement
Journal of Visual Communication and Image Representation
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There have been many applications of the Hilbert curve, such as image processing, image compression, computer hologram, etc. The Hilbert curve is a one-to-one mapping between N-dimensional space and one-dimensional (l-D) space which preserves point neighborhoods as much as possible. There are several algorithms for N-dimensional Hilbert scanning, such as the Butz algorithm and the Quinqueton algorithm. The Butz algorithm is a mapping function using several bit operations such as shifting, exclusive OR, etc. On the other hand, the Quinqueton algorithm computes all addresses of this curve using recursive functions, but takes time to compute a one to-one mapping correspondence. Both algorithms are complex to compute and both are difficult to implement in hardware. In this paper, we propose a new, simple, nonrecursive algorithm for N-dimensional Hilbert scanning using look-up tables. The merit of our algorithm is that the computation is fast and the implementation is much easier than previous ones