Square to hexagonal lattices conversion

Abstract In order to build up hexagonal digital pictures from square ones, each point of the hexagonal lattice is given the value of its nearest neighbour in a superimposed square lattice. This simple rule has the advantage to transform a binary set into a binary set and a grey-tone function into a grey-tone function. In case of convolution, it gives almost identical results. For the increasing transformations, the results are satisfying as soon as the square digital set contains neither grain nor pore reduced to one isolated point, i.e. if the euclidian set corresponding to it is open-closed by a disk of radius a , the step of the square grid. If this set is also open-closed by a disk of radius 2 a , then the rule of conversion also preserves the homotopy. At last, the three Minkowski's functionals are estimated with a good precision. These properties are also valid for the class of grey-tone functions.