On the rose of directions measurements on the discrete grid of an automatic image analyser

Estimation of the rose of directions is a simple way to analyse the anisotropy of structures made of lines, objects or interconnected phases. However, when used on an automatic image analyser with a square frame, the rose of directions obtained from circles is not uniform. This problem is analysed here. It originates in the interpretation of the discrete rose of directions, which is not a histogram, but an averaging with non-constant angular mask and weight function. New coefficients are proposed to get a pseudo-rose of directions which is uniform for isotropic structures such as assemblies of circles.