Comparison of gliding box and box-counting methods in soil image analysis

Three soil images with different spatial arrangements and porosities ranging from 5% to 47% were analyzed to calculate their generalized dimensions (Dq). The first partitioning method applied in these calculations was box-counting, in which a grid is used to study the local distribution of porosity at different scales. In all the images, porosity was found to exhibit multi-scaling behavior in the larger box sizes only, i.e., with side lengths ranging from 64 to 256 pixels. Estimates of Dq were obtained by restricting multifractal analysis (MFA) to these box sizes, but this resulted in very few points for linear regression analysis and only a small number of boxes per size due to image size limitations. The gliding box method was subsequently applied to the same range of box sizes using the multiplier method. This yielded less uncertain Dq values, particularly for negative values of q. The gliding box method was therefore found to be more suitable for MFA where the range of usable scales is narrow. Both the numerical differences between Dq values and their standard errors are discussed.