A Pseudo-Hilbert scan for arbitrarily-sized cuboid region

The 3-dimensional (3-D) Hilbert scan is a one-to-one mapping between 3-D data and 1-D data along the 3-D Hilbert curve. It has been applied widely in moving-image processing, such as image compression, pattern recognition, clustering an image, etc. Now, although there have been some 3-D Hilbert scanning algorithms, they usually have strict limitation on the scanned region. This make Hilbert scan very difficult to be applied in practice. So an effective scanning algorithm for arbitrarily-sized cuboid region is significative to improve the correlative digital image processing technology. In this paper, we proposed a novel Pseudo-Hilbert scanning algorithm based on the look-up tables method for arbitrarilysized cuboid region. Although the proposed algorithm is designed for 3-D space scanning, it can be also applied in an arbitrary-sized rectangle. The algorithm don't only remove the strict constrains but also reserve the good property of the Hubert curve that scanning curve preserves point neighborhoods as much as possible. The good performance of the algorithm is demonstrated by the simulation results.