Fractal Mapping of Pore and Solid Attributes

Abstract

A: BI, binarized image; OI, original image; SEM, scanning electron microscope.S S : M M Soil structure depends on its genesis and consists of highly variable pore and solid networks. Several internal and external factors aff ect the a ributes of these networks, with water being the most aggressive agent. In this study, we used selected fractal parameters (called descriptors) to quan fy the basic topological a ributes-compactness and connectedness-as well as lacunarity and roughness of porous materials, with special a en on to sampling error and popula on variance dynamics. Four microhorizons were sampled from a 1.0-by 1.0-by 1.6-m monolith during a long-term drying period under controlled condi ons. A compara ve fractal analysis of selected mul temporal (11 mo) and mul scale (50×, 500×, 1000×, and 5000×) scanning electron microscopy (SEM) images was accomplished for the following layers with contras ng texture or structure: loam topsoil, pure basal c compacted sand, and two amorphous lacustrine clays. The scale invariance (self-similarity) of pore and solid networks was documented. A complex rela onship was found between the descriptor mean values and corresponding variances. Simple power-law rela ons were established between the standard devia on (and variance) and layer depth, as well as scale and sampling me. Pearson's r correlaon criterion was applied to measure the degree of associa on between mul objec ve fractal descriptors. Systema c and standardized fractal analysis of mul scale images is recommended for the sta s cal quan ta ve descrip on of complex and dynamic pore and solid networks.

Probability density function: A tool for simultaneous monitoring of pore/solid roughness and moisture content

“…Korvin (2005) proved, without assuming Lambert's law, that the intensity distribution across the optical image inherits the fractal dimension of the retrieved surface. The fractal nature of the porous materials in the present study had been documented in our previous studies (Oleschko et al, 2000(Oleschko et al, , 2002(Oleschko et al, , 2003Zamora-Castro et al, 2008), by fractal image analysis.…”

“…The undisturbed moisture samples for SEM were taken 10 cm apart along the horizontal sampling line of the monolith (Flores, 2003;Zamora-Castro et al, 2008) during the whole drying period (every day at the beginning, and weekly at the end, of the experiment). These images were stored as a digital Microstructure Atlas and used to compute statistics and detect the visual space/ time singularities in PDF roughness of the contrasting micro-layers .…”

“…These images were stored as a digital Microstructure Atlas and used to compute statistics and detect the visual space/ time singularities in PDF roughness of the contrasting micro-layers . (For detailed description of the monolith see Flores, 2003;Oleschko et al 2002Oleschko et al , 2003Zamora-Castro et al, 2008).…”

“…In our previous researches: (1) we documented the dynamics of the soil structure in response to volumetric water (Q i ) changes during a long-term drying experiment under controlled conditions (Flores, 2003); (2) quantified the microstructure behavior by a set of fractal descriptors (Oleschko et al, 2000(Oleschko et al, , 2002(Oleschko et al, , 2003Zamora-Castro et al, 2008); (3) verified the scale invariance (self-similarity) of the studied pore-and solid networks by fractal analysis of microscopic images (from optic to electronic, 10× to 20,000× scale); (4) used mathematical morphometry (Serra, 1982 andMecke andArns, 2005) to extract the connectivity, tortuosity and compactness of the pore-and solid networks. The connectedness and tortuosity of contrasting networks were measured by Continuous Random Brownian Walks technique (CRBW), while the compactness was quantified by box-and mass counting dimensions (D b and D m ) (Oleschko et al, 2000;Zamora-Castro et al, 2008). In these studies the topological attributes of materials with contrasting mineralogy and structure, as well as with different lacunarity and roughness, were associated statistically by Pearson's r correlation analysis.…”

“…In these studies the topological attributes of materials with contrasting mineralogy and structure, as well as with different lacunarity and roughness, were associated statistically by Pearson's r correlation analysis. Special attention had been paid to material genesis, sampling depth, and temporal/ spatial variations (Oleschko et al, 2000;2002;, as well as to the sampling error, and population variance dynamics (Zamora-Castro et al, 2008).…”