Preprocessing is the process of adapting the input of our Computational Intelligence (CI) problem to the CI technique applied. Images are inputs of many problems, and Fractal processing of the images to extract relevant geometry characteristics is a very important tool. This chapter is dedicated to Fractal Preprocessing. In Pedology, fractal models were fitted to match the structure of soils and techniques of multifractal analysis of soil images were developed as is described in a state-of-the-art panorama. A box-counting method and a gliding box method are presented, both obtaining from images sets of dimension parameters, and are evaluated in a discussed case study from images of samples, and the second seems preferable. Finally, a comprehensive list of references is given
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aharony, A., 1990, Multifractals in physics – successes, dangers and challenges, Physica A. 168:479–489.
Ahammer, H., De Vaney, T.T.J. and Tritthart, H.A., 2003, How much resolution is enough? Influence of downscaling the pixel resolution of digital images on the generalised dimensions, Physica D. 181 (3–4):147–156.
Allain, C. and Cloitre, M., 1991, Characterizing the lacunarity of random and deterministic fractal sets, Physical Review A. 44:3552–3558.
Anderson, A.N., McBratney, A.B. and FitzPatrick, E.A., 1996, Soil Mass, Surface, and Spectral Fractal Dimensions Estimated from Thin Section Photographs, Soil Sci. Soc. Am. J. 60:962–969.
Anderson, A.N., McBratney, A.B. and Crawford, J.W., Applications of fractals to soil studies. Adv. Agron., 63:1, 1998.
Barnsley, M.F., Devaney, R.L., Mandelbrot, B.B., Peitgen, H.O., Saupe, D. and Voss, R.F., 1988, The Science of Fractal Images. Edited by H.O. Peitgen and D. Saupe, Springer-Verlag, New York.
Bartoli, F., Philippy, R., Doirisse, S., Niquet, S. and Dubuit, M., 1991, Structure and self-similarity in silty and sandy soils; the fractal approach, J. Soil Sci. 42:167–185.
Bartoli, F., Bird, N.R., Gomendy, V., Vivier, H. and Niquet, S., 1999, The relation between silty soil structures and their mercury porosimetry curve counterparts: fractals and percolation, Eur. J. Soil Sci., 50(9).
Bartoli, F., Dutartre, P., Gomendy, V., Niquet, S. and Vivier, H., 1998. Fractal and soil structures. In: Fractals in Soil Science, Baveye, Parlange and Stewart, Eds., CRC Press, Boca Raton, 203–232.
Baveye, P. and Boast, C.W. Fractal Geometry, Fragmentation Processes and the Physics of Scale-Invariance: An Introduction. In Fractals in Soil Science, Baveye, Parlange and Stewart, Eds., CRC Press, Boca Raton, 1998, 1.
Baveye, P., Boast, C.W., Ogawa, S., Parlange, J.Y. and Steenhuis, T., 1998. Influence of image resolution and thresholding on the apparent mass fractal characteristics of preferential flow patterns in field soils, Water Resour. Res. 34, 2783–2796.
Bird, N., Dìaz, M.C., Saa, A. and Tarquis, A.M., 2006. Fractal and Multifractal Analysis of Pore-Scale Images of Soil. J. Hydrol, 322, 211–219.
Bird, N.R.A., Perrier, E. and Rieu, M., 2000. The water retention function for a model of soil structure with pore and solid fractal distributions. Eur. J. Soil Sci. 51, 55–63.
Bird, N.R.A. and Perrier, E.M.A., 2003. The pore-solid fractal model of soil density scaling. Eur. J. Soil Sci. 54, 467–476.
Booltink, H.W.G., Hatano, R. and Bouma, J., 1993. Measurement and simulation of bypass flow in a structured clay soil; a physico-morphological approach. J. Hydrol. 148, 149–168.
Brakensiek, D.L., W.J. Rawls, S.D. Logsdon and Edwards, W.M., 1992. Fractal description of macroporosity. Soil Sci. Soc. Am. J. 56, 1721–1723.
Buczhowski, S., Hildgen, P. and Cartilier, L. 1998. Measurements of fractal dimension by box-counting: a critical analysis of data scatter. Physica A 252, 23–34.
Cheng, Q. and Agerberg, F.P. (1996). Comparison between two types of multifractal modeling. Mathematical Geology, 28(8), 1001–1015.
Cheng, Q. (1997a). Discrete multifractals. Mathematical Geology, 29(2), 245–266.
Cheng, Q. (1997b). Multifractal modeling and lacunarity analysis. Mathematical Geology, 29(7), 919–932.
Crawford, J.W., Baveye, P., Grindrod, P. and Rappoldt, C. Application of Fractals to Soil Properties, Landscape Patterns, and Solute Transport in Porous Media, in Assessment of Non-Point Source Pollution in the Vadose Zone. Geophysical Monograph 108, Corwin, Loague and Ellsworth, Eds., American Geophysical Union, Wahington, DC, 1999, 151.
Crawford, J.W., Ritz, K. and Young, I.M. Quantification of fungal morphology, gaseous transport and microbial dynamics in soil: an integrated framework utilising fractal geometry. Geoderma, 56, 1578, 1993.
Crawford, J.W., Matsui, N. and Young, I.M. 1995., The relation between the moisture-release curve and the structure of soil. Eur. J. Soil Sci. 46, 369–375.
Dathe, A., Eins, S., Niemeyer, J. and Gerold, G. The surface fractal dimension of the soil-pore interface as measured by image analysis. Geoderma, 103, 203, 2001.
Dathe, A., Tarquis, A.M. and Perrier, E., 2006. Multifractal analysis of the pore- and solid-phases in binary two-dimensional images of natural porous structures. Geoderma, doi:10.1016/j.geoderma.2006.03.024, in press.
Dathe, A. and Thullner, M., 2005. The relationship between fractal properties of solid matrix and pore space in porous media. Geoderma, 129, 279–290.
Feder, J., 1989. Fractals. Plenum Press, New York. 283pp
Flury, M. and Fluhler, H., 1994. Brilliant blue FCF as a dye tracer for solute transport studies – A toxicological overview. J.Environ. Qual. 23, 1108–1112.
Flury, M. and Fluhler, H., 1995. Tracer characteristics of brilliant blue. Soil Sci. Soc. Am. J. 59, 22–27.
Flury, M., Fluhler, H., Jury, W.A. and Leuenberger, J., 1994. Susceptibility of soils to preferential flow of water: A field study, Water Resour. Res. 30, 1945–1954.
Gimènez, D., R.R. Allmaras, E.A. Nater and Huggins, D.R., 1997a. Fractal dimensions for volume and surface of interaggregate pores – scale effects. Geoderma 77, 19–38.
Gimènez D., Perfect E., Rawls W.J. and Pachepsky, Y., 1997b. Fractal models for predicting soil hydraulic properties: a review. Eng. Geol. 48, 161–183.
Gouyet, J.G. Physics and Fractal Structures. Masson, Paris, 1996.
Grau, J., Mèndez, V., Tarquis, A.M., Dìaz, M.C. and A. Saa, 2006. Comparison of gliding box and box-counting methods in soil image analysis. Geoderma, doi:10.1016/j.geoderma.2006.03.009, in press.
Griffith, D.A.. Advanced Spatial Statistics. Kluwer Academic Publishers, Boston, 1988.
Hallett, P.D., Bird, N.R.A., Dexter, A.R. and Seville, P.K., 1998. Investigation into the fractal scaling of the structure and strength of soil aggregates. Eur. J. Soil Sci. 49, 203–211.
Hatano, R. and Booltink, H.W.G., 1992. Using Fractal Dimensions of Stained Flow Patterns in a Clay Soil to Predict Bypass Flow. J. Hydrol. 135, 121–131.
Hatano, R., Kawamura, N., Ikeda, J. and Sakuma, T. Evaluation of the effect of morphological features of flow paths on solute transport by using fractal dimensions of methylene blue staining patterns. Geoderma 53, 31, 1992.
Hentschel, H.G.R. and Procaccia, I. (1983). The infinite number of generalized dimensions of fractals and strange attractors. Physica D, 8, 435, 1983.
Kaye, B.G. A Random Walk through Fractal Dimensions. VCH Verlagsgesellschaft, Weinheim, Germany, 1989, 297.
Mandelbrot, B.B. The Fractal Geometry of Nature. W.H. Freeman, San Francisco, CA, 1982.
McCauley, J.L. 1992. Models of permeability and conductivity of porous media. Physica A 187, 18–54.
Moran, C.J., McBratney, A.B. and Koppi, A.J.,1989. A rapid method for analysis of soil macropore structure. I. Specimen preparation and digital binary production. Soil Sci. Soc. Am. J. 53, 921–928.
Muller, J., 1996. Characterization of pore space in chalk by multifractal analysis. J. Hydrology, 187, 215–222.
Muller, J., Huseby, O.K. and Saucier, A. Influence of Multifractal Scaling of Pore Geometry on Permeabilities of Sedimentary Rocks. Chaos, Solitons & Fractals, 5, 1485, 1995.
Muller, J. and McCauley, J.L., 1992. Implication of Fractal Geometry for Fluid Flow Properties of Sedimentary Rocks. Transp. Porous Media 8, 133–147.
Muller, J., Huseby, O.K. and Saucier, A., 1995. Influence of Multifractal Scaling of Pore Geometry on Permeabilities of Sedimentary Rocks. Chaos, Solitons & Fractals 5, 1485–1492.
Ogawa, S., Baveye, P., Boast, C.W., Parlange, J.Y. and Steenhuis, T. Surface fractal characteristics of preferential flow patterns in field soils: evaluation and effect of image processing. Geoderma, 88, 109, 1999.
Oleschko, K., Fuentes, C., Brambila, F. and Alvarez, R. Linear fractal analysis of three Mexican soils in different management systems. Soil Technol., 10, 185, 1997.
Oleschko, K. Delesse principle and statistical fractal sets: 1. Dimensional equivalents. Soil&Tillage Research, 49, 255, 1998a.
Oleschko, K., Brambila, F., Aceff, F. and Mora, L.P. From fractal analysis along a line to fractals on the plane. Soil&Tillage Research, 45, 389, 1998b.
Orbach, R. Dynamics of fractal networks. Science (Washington, DC) 231, 814, 1986.
Pachepsky, Y.A.,Yakovchenko, V., Rabenhorst, M.C., Pooley, C. and Sikora, L.J. . Fractal parameters of pore surfaces as derived from micromorphological data: effect of long term management practices. Geoderma, 74, 305, 1996.
Pachepsky, Y.A., Gimènez, D., Crawford, J.W. and Rawls, W.J. Conventional and fractal geometry in soil science. In Fractals in Soil Science, Pachepsky, Crawford and Rawls, Eds., Elsevier Science, Amsterdam, 2000, 7.
Persson, M., Yasuda, H., Albergel, J., Berndtsson, R., Zante, P., Nasri, S. and Öhrström, P., 2001. Modeling plot scale dye penetration by a diffusion limited aggregation (DLA) model. J. Hydrol. 250, 98–105.
Peyton, R.L., Gantzer, C.J., Anderson, S.H., Haeffner, B.A. and Pfeifer, P. . Fractal dimension to describe soil macropore structure using X ray computed tomography. Water Resource Research, 30, 691, 1994.
Posadas, A.N.D., Gimènez, D., Quiroz, R. and Protz, R., 2003. Multifractal Characterization of Soil Pore Spatial Distributions. Soil Sci. Soc. Am. J. 67, 1361–1369
Protz , R. and VandenBygaart, A.J. 1998. Towards systematic iage analysis in the study of soil micromorphology. Science Soils, 3. (available online at http://link.springer.de/link/service/journals/).
Ripley, B.D. Statistical Inference for Spatial Processes, Cambridge Univ. Press, Cambridge, 1988.
Saucier, A. Effective permeability of multifractal porous media. Physica A, 183, 381, 1992.
Saucier, A. and Muller, J. Remarks on some properties of multifractals. Physica A, 199, 350, 1993.
Saucier, A. and Muller, J. Textural analysis of disordered materials with multifractals. Physica A, 267, 221, 1999.
Saucier, A., Richer, J. and Muller, J., 2002. Statistical mechanics and its applications. Physica A, 311 (1–2): 231–259.
Takayasu, H. Fractals in the Physical Sciences. Manchester University Press, Manchester, 1990.
Tarquis, A.M., Gimènez, D., Saa, A., Dìaz, M.C. and Gascò, J.M., 2003. Scaling and Multiscaling of Soil Pore Systems Determined by Image Analysis. In: Scaling Methods in Soil Physics, Pachepsky, Radcliffe and Selim Eds., CRC Press, 434 pp.
Tarquis, A.M., McInnes, K.J., Keys, J., Saa, A., Garcìa, M.R. and Dìaz, M.C., 2006. Multiscaling Analysis In A Structured Clay Soil Using 2D Images. J. Hydrol, 322, 236–246.
Tel, T. and Vicsek, T., 1987. Geometrical multifractality of growing structures, J. Physics A. General, 20, L835–L840.
VandenBygaart, A.J. and Protz, R., 1999. The representative elementary area (REA) in studies of quantitative soil micromorphology. Geoderma 89, 333–346.
Vicsek, T. 1990. Mass multifractals. Physica A, 168, 490–497.
Vogel, H.J. and Kretzschmar, A., 1996. Topological characterization of pore space in soil-sample preparation and digital image-processing. Geoderma 73, 23–38.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer
About this chapter
Cite this chapter
Tarquis, A.M., Mèndez, V., Grau, J.B., Antòn, J.M., Andina, D. (2007). Fractals as Pre-Processing Tool for Computational Intelligence Application. In: Andina, D., Pham, D.T. (eds) Computational Intelligence. Springer, Boston, MA. https://doi.org/10.1007/0-387-37452-3_8
Download citation
DOI: https://doi.org/10.1007/0-387-37452-3_8
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-37450-5
Online ISBN: 978-0-387-37452-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)