A pseudo-hilbert scan algorithm for arbitrarily-sized rectangle region

The 2-dimensional Hilbert scan (HS) is a one-to-one mapping between 2-dimensional (2-D) space and one-dimensional (1-D) space along the 2-D Hilbert curve. Because Hilbert curve can preserve the spatial relationships of the patterns effectively, 2-D HS has been studied in digital image processing actively, such as compressing image data, pattern recognition, clustering an image, etc. However, the existing HS algorithms have some strict restrictions when they are implemented. For example, the most algorithms use recursive function to generate the Hilbert curve, which makes the algorithms complex and takes time to compute the one-to-one correspondence. And some even request the sides of the scanned rectangle region must be a power of two, that limits the application scope of HS greatly. Thus, in order to improve HS to be proper to real-time processing and general application, we proposed a Pseudo-Hilbert scan (PHS) based on the look-up table method for arbitrarily-sized arrays in this paper. Experimental results for both HS and PHS indicate that the proposed generalized Hilbert scan algorithm also reserves the good property of HS that the curve preserves point neighborhoods as much as possible, and gives competitive performance in comparison with Raster scan.