A protocol for fractal studies on porosity of porous media: High quality soil porosity images

Abstract

A protocol for obtaining digital images from natural porous media with a wide range of pore sizes, intended for fractal studies of the porosity, is proposed. Soil porosity is used as paradigm of complex natural porous media in this study. The use of several imaging devices and fluorescent compounds to enhance the contrast between the solid and the pore phase is tested. Finally a protocol is reached using a photo camera and a confocal microscope. It is the first time that confocal microscopy is used for this purpose. Artificial porous images are created through random Sierpinski carpet fractals and the statistical information of real soil images. These ground truth images are used in an objective comparison of automatic segmentation algorithms for the obtained images. A statistical classification on the performance of several automatic segmentation algorithms for this type of images is reached.

Keywords

porous media / micromorphology / image segmentation / confocal microscope / fractal / porosity / photography

References

[1] Bartoli F., Dutartre P., Gomendy V., . Fractals and Soil Structure. Fractals in Soil Science, 1998, Cleveland: CRC Press LLC, 203-232.

[2] Bartoli F., Philippy R., Doirisse M., . Structure and Self-Similarity in Silty and Sandy Soils: The Fractal Approach. Journal of Soil Science, 1991, 42(2): 167-185.

[3] Bergman E. Nutrient Solution Culture of Plants. The Pennsylvania State University College of Agriculture, Extension Service Hort. Mimeo Series II, 1985.

[4] Bullock P., Fedoroff N., Jongerius A., . Handbook of Soil Thin Section Description, 1985, Wolverhampton: Waine Reserch, 152.

[5] Caniego F. J., Martín M. A., San José F. Singularity Features of Pore-Size Soil Distribution: Singularity Strength Analysis and Entropy Spectrum. Fractals, 2001, 9(3): 305-316.

[6] Caniego F., Martín M., San José Martínez F. Rényi Dimensions of Soil Pore Size Distribution. Geoderma, 2003, 112(3/4): 205-216.

[7] Chun H. C., Giménez D., Yoon S. W. Morphology, Lacunarity and Entropy of Intra-Aggregate Pores: Aggregate Size and Soil Management Effects. Geoderma, 2008, 146(1/2): 83-93.

[8] Duda R., Hart P., Stork D. Pattern Classification, 2001, New York: John Wiley & Sons

[9] Edwards W. M., Norton L. D., Redmond C. E. Characterizing Macropores that Affect Infiltration into Nontilled Soil. Soil Science Society of America Journal, 1988, 52 2 483

[10] FitzPatrick E. A. Micromorphology of Soils, 1984, New York: Chapman & Hall

[11] Frykman P., Rogon T. A. Anisotropy in Pore Networks Analyzed with 2-D Autocorrelation (Variomaps). Computers & Geosciences, 1993, 19(7): 887-930.

[12] García-Gutiérrez C. Adquisición y Tratamiento de Imágenesdigitales de Suelo Para el anáLisis Multifractal de la Porosidad: [Dissertation], 2004, Madrid: Escuela Técnica Superior de Ingenieros Agrónomos. Universidad Politécnica de Madrid

[13] García-Gutiérrez C. Caracterización y Modelización de la Estructura y la Textura de Lossuelos Usando Técnicas de Análisis de Imagen y Geometría Fractal. Aplicación al Estudio de la Diffusion en Medios Porosos: [Dissertation], 2010, Madrid: Universidad Politécnica de Madrid

[14] Geyger E., Beckmann W. Apparate und Methodem der mokromorphometrischen Struktur Analyse des Bodens. Die Mikromorphometrische Boden Analyse, 1967, Stuttgart: Ferdinand Enke Verlag, 36-57.

[15] Glasbey C. A. An Analysis of Histogram-Based Thresholding Algorithms. CVGIP: Graphical Models and Image Processing, 1993, 55(6): 532-537.

[16] Glasbey C. A., Horgan G. W. Image Analysis for the Biological Sciences, 1995, New York: John Wiley & Sons

[17] Gomendy V., Bartoli F., Burtin G., . Silty Topsoil Structure and Its Dynamics: The Fractal Approach. Geoderma, 1999, 88(3/4): 165-189.

[18] Hatano R., Kawamura N., Ikeda J., . Evaluation of the Effect of Morphological Features of Flow Paths on Solute Transport by Using Fractal Dimensions of Methylene Blue Staining Pattern. Geoderma, 1992, 53(1/2): 31-44.

[19] Iassonov P., Gebrenegus T., Tuller M. Segmentation of X-Ray Computed Tomography Images of Porous Materials: A Crucial Step for Characterization and Quantitative Analysis of Pore Structures. Water Resources Research, 2009, 45(9): 706-715.

[20] Katz A. J., Thompson A. H. Fractal Sandstone Pores: Implications for Conductivity and Pore Formation. Physical Review Letters, 1985, 54(12): 1325-1328.

[21] Kim J. W., Perfect E., Choi H. Anomalous Diffusion in Two-Dimensional Euclidean and Prefractal Geometrical Models of Heterogeneous Porous Media. Water Resources Research, 2007, 43 1 W1405.

[22] Leica M. Technical Details on Leica’s Confocal Microscope, 2010.

[23] Mandelbrot B. The Fractal Geometry of Nature, 1982, New York: W. H. Freeman and Company

[24] Martín M., Rey J., Taguas F. An Entropy-Based Parametrization of Soil Texture via Fractal Modelling of Particle-Size Distribution. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2001, 457(2008): 937-947.

[25] Martín M., Taguas F. Fractal Modelling, Characterization and Simulation of Particle-Size Distributions in Soil. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1998, 454(1973): 1457-1468.

[26] Minski M. Memoir on Inventing the Confocal Scanning Microscope, 2010.

[27] Moran C. J., McBratney A. B., Koppi A. J. A Rapid Method for Analysis of Soil Macropore Structure. I. Specimen Preparation and Digital Binary Image Production. Soil Science Society of America Journal, 1989, 53(3): 921-928.

[28] Muller J. Characterization of Pore Space in Chalk by Multifractal Analysis. Journal of Hydrology, 1996, 187(1/2): 215-222.

[29] Murphy C. Thin Section Preparation of Soils and Sediments, 1986, Berkhamsted: AB Academic Publishers

[30] Murphy C. P., Bullock P., Turner R. H. The Measurement and Characterisation of Voids in Soil Thin Sections by Image Analysis. Part I. Principles and Techniques. Journal of Soil Science, 1977, 28(3): 498-508.

[31] Ogawa S., Baveye P., Boast C. W., . Surface Fractal Characteristics of Preferential Flow Patterns in Field Soils: Evaluation and Effect of Image Processing. Geoderma, 1999, 88(3/4): 109-136.

[32] Pachepsky Y., Crawford J., Rawls W. Fractals in Soil Science. Developments in Soil Science 27, 2000, 1, Amsterdam: Elsevier

[33] Pachepsky Y., Yakovchenko V., Rabenhorst M. C., . Fractal Parameters of Pore Surfaces as Derived from Micromorphological Data: Effect of Long-Term Management Practices. Geoderma, 1996, 74(3/4): 305-319.

[34] Pagliai M., Lamarca M., Lucamante G. Micromorphometric and Micromorphological Investigations of a Clay Loam Soil in Viticulture under Zero and Conventional Tillage. Journal of Soil Science, 1983, 34(2): 391-403.

[35] Persson A. L. Image Analysis of Shape and Size of Fine Aggregates. Engineering Geology, 1998, 50(1/2): 177-186.

[36] Rozenbaum O., Le Trong E., Rouet J. L., . 2-D Image Analysis: A Complementary Tool for Characterizing Quarry and Weathered Building Limestone. Journal of Cultural Heritage, 2007, 8(2): 151-159.

[37] San José Martínez F., Caniego F. J., García-Gutiérrez C., . Representative Elementary Area for Multifractal Analysis of Soil Porosity Using Entropy Dimension. Nonlinear Processes in Geophysics, 2007, 14(4): 503-511.

[38] Sezgin M., Sankur B. Survey over Image Thresholding Techniques and Quantitative Performance Evaluation. Journal of Electronic Imaging, 2004, 13(1): 146-165.

[39] Sukop M. C., Perfect E., Bird N. R. A. Water Retention of Prefractal Porous Media Generated with the Homogeneous and Heterogeneous Algorithms. Water Resources Research, 2001, 37(10): 2631-2636.

[40] Unnikrishnan R., Pantofaru C., Hebert M. A Measure for Objective Evaluation of Image Segmentation Algorithms, 2005

[41] VandenBygaart A. J., Protz R. The Representative Elementary Area (REA) in Studies of Quantitative Soil Micromorphology. Geoderma, 1999, 89(3/4): 333-346.

[42] Vogel H. J., Kretzschmar A. Topological Characterization of Pore Space in Soil—Sample Preparation and Digital Image-Processing. Geoderma, 1996, 73(1/2): 23-38.

[43] Wang W., Kravchenko A. N., Smucker A. J. M., . Comparison of Image Segmentation Methods in Simulated 2D and 3D Microtomographic Images of Soil Aggregates. Geoderma, 2011, 162(3/4): 231-241.