Image analysis determination of stereology based fabric tensors

Fabric tensors that characterize the distribution of directional data from microscopic observations are considered to be a useful measure of anisotropy for granular materials. This paper describes the measurement of several stereology based fabric tensors, such as the surface area tensor S-ij, mean free path tensor lambda(ij) and porosity tensor N-ij, the formulations in three dimensions of which can be obtained by making observations in three mutually perpendicular planes. The measurement techniques and the implementation of these measurement techniques using image analysis are described. The implementation of these techniques is illustrated using typical images, The sensitivity, generality, practical implications and limitations of the techniques are also discussed.