Markov random fields for square and hexagonal textures

Computer vision on lattices based on hexagonal pixels is considered to be advantageous due to the consistent connectivity within the lattice. This leads to more sensible definitions for neighbourhoods and positive benefits when processing curved structures. This work concentrates on the autobinomial Markov random field model for texture generation and examines the benefits of using a hexagonal lattice. The results showed that the range of textures produced is similar in both square and hexagonal images. In the case of hexagonal images however, there are definite advantages in replication of textures with symmetries along 60° axes. Furthermore, a first order hexagonal model combines the features of the first and second order square model. This provides similar performance with fewer parameters.