Fig 1.
Schematic for correlation function computation in four principal directions (X, Y, X-diagonal and Y-diagonal) in a two-phase porous medium displaying pore (white areas) and solid (black areas) phase.
Thick line segments represent examples providing correlation function’s local values of 1, while thin lines—0.
Fig 2.
Overall scheme of the reconstruction procedure.
Illustrations are provided for each stage using reconstruction of circles as example.
Fig 3.
Main concepts of the morphological analysis.
a) morphological parameters calculated for each pore element, and b) examples of pores extracted from original soil images and their shape classifications (all five shape classes are shown in roundness (4πA/P2)—isometry (D/L) coordinates).
Table 1.
Soil thin-section information.
Fig 4.
Correlation functions for pores (solid and dashed lines) and solid phase (dash dot line).
S2(w) and L2(w) are, respectively, two-point probability and linear functions for pore phase; L2(b) is a linear function for solid phase. All correlation functions are evaluated in four principal directions according to Fig 1. Example is for soil type I exhibiting the largest spatial correlation length of L2(b) across all soil types.
Fig 5.
All original eight soil type images (left column) with their best performing reconstructions based on a cluster function analysis (middle column) or pore morphological analysis (right column) (if reconstruction performance for both analyses is identical, then only one image is shown).
Size of thin section = 2.1×2.1 cm2. Blue shaded areas highlight pore features that were poorly reconstructed: type II) vertical pore; III) complex elongated pores; V) one connected pore dominating entire image; VI) one connected fissure-like pore; VII) numerous horizontal cracks; VIII) horizontal features in the upper-right marked region.
Fig 6.
Total number of pores for original images and their five reconstructions compared for all soil types (I-VIII).
Fig 7.
Comparison between pore-size distribution for original soil type VII and its corresponding best reconstructed image according to pore morphological metrics (a larger pore range is zoomed out for better visibility of the resulting distribution).
Fig 8.
Scatter plot of pore morphology classes using pore shape class 1–5 (Fig 3B) and orientation classes 6–8 (Fig 3B) for original and best reconstructed images for all soil types I-VIII.
Fig 9.
Comparison of C2 cluster functions for original and reconstructed soil images for a) soil type I (best case), and b) soil type V (worst case).
The legend is similar to that of Fig 4 for two-point probability and linear functions.
Fig 10.
Cluster function differences for all reconstructed soil images (calculated as arithmetic average of C2 differences between originals and replicas for each soil type and each orthogonal direction).
Table 2.
Summary of best reconstructions according to different quantitative metrics (numbers 1, 2, 3, 4, or 5 refer to reconstruction method, available in S1 File).