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 image processing, such as image compression, object recognition, and image clustering, etc. Now, although there exist some 3-D Hilbert scanning algorithms, they usually have strict limitation on the scanned region. This makes Hilbert scan difficult to be applied in practice. So an effective scanning algorithm for arbitrarily-sized cuboid region is significant 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 arbitrarily-sized 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 does not only remove the strict constrains but also reserve the good property of the Hilbert curve preserving point neighborhoods as much as possible. The good performance of the algorithm is demonstrated by the simulation results.