A hexagonal lattice has been researched to improve computer vision and image processing. However, image alignment on the lattice has not been fully discussed yet. In this paper, we perform image alignment on hexagonal and square lattices. Then we compare and evaluate them. We used hexagonal lattices of two sizes. One has the same pixel interval between adjacent pixels as the square lattice, which results in higher resolution than the square one. Another has the same pixel area as the square lattice, which has the same resolution as the square one. The results show that the image alignment of both the hexagonal lattices outperforms that of the square lattice with respect to accuracy and the success rate. Importantly, the results also show that converting an existing large image on the square lattice into the smaller image on the hexagonal ones of both the sizes could improve image alignment.

Digital two-dimensional images are usually sampled on square lattices, while the receptors of the human eye are following a hexagonal structure. It is the main motivation for adopting hexagonal lattices. The fundamental operation in many image processing algorithms is to extract the gradient information. As such, various gradient operators have been proposed for square lattices and have been thoroughly optimized. Accurate gradient operators for hexagonal lattices have, however, not been researched well enough, while the distance between neighbor pixels is constant. We therefore derive consistent gradient operators on hexagonal lattices and compare them with the existing optimized filters on square lattices. The results show that the derived filters on hexagonal lattices achieve a better signal-to-noise ratio than those on square lattices. Results on artificial images also show that the derived filters on hexagonal lattices outperform the square ones with respect to accuracy of gradient intensity and orientation detection.