Approximately even partition algorithm for coding the Hilbert curve of arbitrary-sized image

The Hilbert curve is one of space filling curves and it requires that the region is of size 2^k × 2^k, where k ∈N. This study relaxes this constraint and generates a pseudo-Hilbert curve of arbitrary dimension. The intuitive method such as Chung et al.´s algorithm is to use Hilbert curves in the decomposed areas directly and then have them connected. However, they must generate a sequence of the scanned quadrants additionally before encoding and decoding the Hilbert order of one pixel. In this study, by using the approximately even partition approach, the authors propose a new Hilbert curve, the Hilbert* curve, which permits any square regions. Experimental results show that the clustering property of the Hilbert* curve is similar to that of the standard Hilbert curve. Next, the authors also propose encoding/decoding algorithms for the Hilbert* curves. Since the authors do not need to additionally generate and scan the sequence of quadrants, the proposed algorithm outperforms Chung et al.´s algorithms for the square region. Then, the authors apply the Hilbert* curves in Chung et al.´s algorithms for the Hilbert curve of arbitrary dimension and experimental results show that the proposed encoding/decoding algorithms out perform the Chung et al.´s approach.