The co-occurrence matrix in square and hexagonal lattices

There are many situations where processing of images on alternate lattices can yield positive advantages. One such case is processing of images upon hexagonal lattices where the uniform connectivity can lead to many efficiencies. However, before processing can be evaluated on hexagonal lattices it must be ascertained that fundamental operations can be carried out effectively. One such commonly used tool is the co-occurrence matrix, which examines second order statistical information within the image. This work derived the co-occurrence matrix for hexagonal lattices and contrasted its performance with square lattices. The results found that the hexagonal co-occurrence matrix performs similarly to the square case. Also, in cases where the image features lie strongly oriented at angles of 60°, the hexagonal case will have distinct advantages. It is proposed that the best approach to analyse textural information in an image is to use a combination of square and hexagonal co-occurrence matrices.