Sub-band coding of hexagonal images

TL;DR

This paper introduces novel wavelet-based compression schemes for hexagonal images, leveraging their geometric advantages to improve reconstruction quality at low bit rates.

Contribution

It presents two new tree-based coding schemes, SBHex and BBHex, specifically designed for hexagonal lattice geometry, enhancing compression performance.

Findings

Better reconstruction quality at low bits per pixel.

Hexagonal sampling preserves more information than Cartesian sampling.

Proposed schemes outperform traditional Cartesian grid coding methods.

Abstract

According to the circle-packing theorem, the packing efficiency of a hexagonal lattice is higher than an equivalent square tessellation. Consequently, in several contexts, hexagonally sampled images compared to their Cartesian counterparts are better at preserving information content. In this paper, novel mapping techniques alongside the wavelet compression scheme are presented for hexagonal images. Specifically, we introduce two tree-based coding schemes, referred to as SBHex (spirally-mapped branch-coding for hexagonal images) and BBHex (breadth-first block-coding for hexagonal images). Both of these coding schemes respect the geometry of the hexagonal lattice and yield better compression results. Our empirical results show that the proposed algorithms for hexagonal images produce better reconstruction quality at low bits per pixel representations compared to the tree-based coding counterparts for the Cartesian grid.