  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.
