Theory and application of multifractal analysis methods in images for the study of soil structure

Abstract

This work focuses to study soil structure as a complex system characterizing it through their multiscaling behaviour. The soil performs important functions as a medium for plant growth, water storage, modifier of the atmosphere and it is a habitat for organisms. Soil structure can be modelled as the spatial arrangement of
soil particles, aggregates and pores. Fractal geometry has been increasingly applied to quantify soil structure, using fractal generalized dimensions for explaining the
complexity of its structure. Thanks to the X-ray Computed Tomography (CT-Scan) soil samples can be analysed in high resolution. CT-Scan is a relatively recent non-destructive testing method which offers an attractive opportunity for the three-dimensional insight of the inner structure of objects and materials. The ultimate product of the tomography process is the slice, which represents a virtual thin-section of the sample, whose thickness is strictly related to the achievable X-ray computed tomography
spatial resolution. A grayscale value is assigned to each voxel of the reconstructed slice, proportionally to the local X-ray attenuation map. Once a set of consecutive
slices is reconstructed, it is possible to create a three-dimensional digital data set of the sample just combining the slices into a stack. For studying the image stacks we have developed a JAVA plug-in for the image analysis software, ImageJ. After a review of the multifractal theory we have selected the gliding and box counting methods for multifractal and monofractal analysis and implemented in the program. We have satisfactorily tested it with the theoretical and real data, and full documented writing a User manual. Then we have studied several planes in the main directions of a soil aggregate comparing them. Although the study has shown interesting results, the main
conclusion is that two-dimensional analysis is not enough for explaining the overall complexity of the structure. Finally, three soil samples ploughed with different
tillage tools has been characterized with the multifractal methods applying a full three-dimensional analysis. Comparison of computing times and the goodness of
the results are showed.