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Variation in Spectral and Mass Dimension on Three-Dimensional Soil Image Processing

Tarquis, A. M.1,2; Sanchez, M. E.1; Antón, J. M.1; Jimenez, Juan3; Saa-Requejo, A.2,4; Andina, D.3; Crawford, J. W.5

Soil Science:
doi: 10.1097/SS.0b013e31824111b6
Technical Article

Abstract: A quantitative characterization of the three-dimensional soil pore architecture is important for understanding soil processes as it relates to the control of biological, chemical, and physical processes across scales. Recent advances in nondestructive imaging, such as X-ray computed tomography (CT), provide an opportunity to analyze pore space features from direct visualization of soil structure. At the same time that these techniques provide new opportunities, they also introduce new processing steps on which the final results depend. Fractal formalism has been shown to be a useful tool in cases where highly complex and heterogeneous media are studied. One of these quantifications is mass dimension (Dm) and spectral dimension (d) applied for water and gas diffusion in soil.

In this work, intact soil samples were collected from four horizons of a Brazilian soil, and three-dimensional images, of 45.1-μm resolution (256 × 256 × 256 voxels), were obtained. Four different threshold criteria were used to transform CT grayscale imagery in binary imagery (pore/solid), based on the frequency of CT units. We calculated the sensitivity of a geometrical parameter (the mass fractal dimension, Dm), a topological parameter (the spectral dimension, d), and the ratio of the two (Dm), which relates to the scaling property of dynamic processes in soil such as diffusion.

Each threshold criterion had a direct influence on the measured porosity and on the value of Dm, showing a clear logarithmic increase in Dm with porosity. Meanwhile, d increased faster, that is, linearly with measured porosity. In all cases, the detailed dependence on porosity was different for each horizon. In contrast, the ratio for each horizon was less sensitive to the thresholding criteria applied to the image.

Thus, the results based on our soil samples suggest that thresholding has a strong influence on parameters that relate to geometrical and topological properties of structure but may have a less important impact on parameters relevant to dynamic processes such as diffusion.

Author Information

1Dpto. de Matemática Aplicada a la Ingeniería Agronómica. E.T.S. Ing. Agrónomos, U.P.M. Ciudad Universitaria, s.n. Madrid 28040, Spain. Dr. A. M. Tarquis is corresponding author. E-mail:

2C.E.I.G.R.A.M., U.P.M. Ciudad Universitaria, s.n. Madrid 28040, Spain.

3E.T.S. Ingenieros de Telecomunicación, U.P.M. Ciudad Universitaria, s.n. Madrid 28040, Spain.

4Dpto. de Edafología y Climatología. E.T.S. Ing. Agrónomos, U.P.M. Ciudad Universitaria, s.n. Madrid 28040, Spain.

5Faculty of Agriculture, Food and Natural Resources, University of Sydney, Sydney, New South Wales 2006, Australia.

Received February 4, 2011.

Accepted for publication November 8, 2011.

Financial Disclosures/Conflicts of Interest: None reported.

© 2012 Lippincott Williams & Wilkins, Inc.