New segmentation method based on fractal properties using singularity maps

Abstract

To improve our understanding of the factors that control a number of critical soil processes, it is important to properly identify pore space zones. Computed tomography (CT) images provide increasingly reliable information about the geometry of pores and solids in soils at very small scales and are a non-invasive technique. However, the low contrast between voids and pores and the non-bimodal greyscale value (GV) histograms observed in the CT images present a problem with respect to pore identification.In this work, we propose a new segmentation method based on the local GV concentration variability when using singularity maps. We also introduce a new method for creating synthetic CT soil images based on truncated multifractals that simulate low-contrast and non-bimodal GV histograms.From three different bidimensional CT soil images and one synthetic soil image, singularity maps were created to measure the GV concentration at each point by defining areas with self-similar properties that were shown as power-law relationships in Concentration-Area plots (C-A method). The C-A method together with a singularity map (the “Singularity-CA” method) was used to define thresholds that were applied to binarize the CT images. Promising results were obtained when the greyscale images were overlapped with the borders of the binarized images.Once these black and white images were obtained, we compared them with commonly used segmentation methods: the Otsu, Iterative and Maximum Entropy methods. The image comparison was based on the total porosity, cumulative pore size distribution (CPSD), cumulative pore size–area distribution (CPSAD) and misclassification error (ME). We found that the Otsu and the Iterative methods overestimated the size of large pores compared to the ground-truth image, which overestimated the porosity. Conversely, the Singularity-CA method extracted medium and large pores with a good fit compared to the ground-truth image. It was observed that whereas the Otsu and Iterative methods obtained the large pores, the “Singularity-CA” method detected an aggregate of small pores, although many of these small pores were incorrectly identified. This was due to the latter's high sensitivity when detecting anomalous GV values. The Maximum Entropy method always resulted in the lowest porosity in the real CT soil samples and the greatest porosity in the synthetic soil image samples.