Estimating three-dimensional line process densities from tube counts

This paper examines the question of inference on three-dimensional line process densities from intersection counts with cylinders, when isotropy of the line process cannot be assumed. It is shown how to modify results derived for planar sections. A motivating application is the study of root development by inserting minirhizotrons into soil. Aspects of experimental design are suggested, such as placing tubes at an angle of 54° to the vertical where they will be insensitive to the degree of anisotropy. The case where axial symmetry may not be assumed is introduced, and is shown to be considerably more complex. An analysis of some experimental data is included.