Stereological Determination of Orientations,Second-Order Quantities and Correlations for Random Spatial Fibre Systems

This paper presents methods for the stereological analysis of spatial fibre systems on the base of planar or thin sections. Under the assumption that the cross-section figures of the tubular fibres can be measured, the orientation distribution of the fibre system and its line density L_v can be determined from one section only and without distributional assumptions. A simple way to study the degree of randomness of fibre systems consists in the statistical analysis of the point pattern of centres of intersection figures. More sophisticated methods are of stereological nature and yield the spatial reduced second moment measure. Similarly also correlations between two fibre systems can be quantified. The methods are demonstrated by two examples concerning samples of human brain.