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

Abstract

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.