Comparison of Pixel Correlation Induced by Space-Filling Curves on 2D Image Data

Space-filling curves are well known for preserving pixel locality when they are used as paths to traverse 2D image data. Some prediction-based compression algorithms make use of these curves to ensure high pixel values correlation during 2D image data traversal. This work explores the distribution of pixel correlation induced by all possible space-filling curves on 2D image data and demonstrates that commonly used curves, such as the Hilbert or the Peano curves, do not provide the best possible pixel correlation for natural photographic images. Using experimental data collected on a large set of such images, we demonstrate that row-prime ordering is the best choice for preserving maximum pixel values correlation while reducing the dimensionality of 2D natural photographic image data.