Influence of image resolution and thresholding on the apparent mass fractal characteristics of preferential flow patterns in field soils

Preferential flow is ubiquitous in field soils, where it has important practical implications for water and contaminant transport. Dyes are frequently used to visualize preferential flow pathways. The fact that stain patterns in pictures of soil profiles often exhibit convoluted geometries, reminiscent of fractals, has encouraged a number of authors to use the principles of fractal geometry to describe stain patterns. This description typically involves two numbers, a mass and a surface fractal dimension. The evaluation of either one via image analysis requires numerous subjective choices to be made, including choices regarding image resolution, the definition adopted for the "fractal" dimension, and the thresholding algorithm used to generate binary images. The present article analyzes in detail the influence of these various choices on the mass fractal dimension of stained preferential flow patterns. A theoretical framework in which to envisage these choices is developed, using the classical quadratic von Koch island as an example. This framework is then applied to a set of pictures of an actual stain pattern in an orchard soil. The results suggest that the (apparent) mass fractal dimension of the stain pattern varies between 1.56 and 1.88, depending on choices made at different stages in the evaluation of the fractal dimension. In each case considered, the dimension, determined by a straight line fit in a log-log plot, has extremely high statistical significance, with R > 0.999. Of the various parameters subject to choice, image resolution seems to have the most pronounced influence on the value of the fractal dimension, which increases markedly at higher resolution (smaller-pixel size). By analogy with the case of the quadratic von Koch island, this dependence on image resolution, as well as the fact that the surface area of the stain pattern does not decrease with pixel size, suggests that the stain pattern is not a mass fractal; that is, there is no reason to believe that its various dimensions differ from 2. The approach adopted in the present article could be useful whenever fractal dimensions are evaluated via image analysis.