Dependence of the surface fractal dimension of soil pores on image resolution and magnification

Two recent investigations have reported contradictory trends concerning the effect of image resolution on the surface fractal dimension of soil pores, evaluated via image analysis. In one case, dealing with a preferential flow pathway and an ideal fractal, image resolution had no influence on the estimated fractal dimension, whereas in the other case, involving images of soil thin sections, the surface fractal dimension decreased significantly with image resolution. In the present paper, we try to determine the extent to which these conflicting observations may have been due to the different ways in which image resolution was varied. By narrowing down (up to 400 times) the field of view on progressively smaller portions of a textbook surface fractal, the von Koch island, one causes its apparent surface fractal dimension to decrease significantly. On the other hand, changing the resolution of images of soil thin sections (up to 6 times), while keeping the magnification constant, does not lead to appreciable changes in the surface fractal dimension. These results demonstrate that there is no real conflict in earlier reports, as long as both the resolution and the magnification of images are taken into account in image-based evaluations of surface fractal dimensions of soil pores.