BCFD - a Visual Basic program for calculation of the fractal dimension of digitized geological image data using a box-counting technique

• Autorzy: Verbovšek T.
• Języki publikacji: EN

Abstrakty

EN

The BCFD program was develped for the analysis of digitized objects using a box-counting algorithm, which has the largest number of applications among the fractal methods in the geosciences. Counting is performed by scanning of image pixels in boxes of different sizes, and the number of boxes is determined automatically from the image resolution. The program calculates the fractal dimension D of theobjects in the image, along with the coefficient of determination R2. Input files are thus transferred to ubiquitous BMP images, in a 1-bit monochrome for mat. The pro gram out puts the re sults on screen, into a text file and op tion ally also di rectly into MS Ex cel, where the data can be fur ther used in charts or other cal cu la tions. It was tested with three fractal and three Eu clid ean ob jects with known the o ret i cal val - ues, plus three geo log i cal im age data (a nat u ral river net work and two frac ture net works), and gave re sults with very high or per fect the o - ret i cal ac cu racy. Ap pli ca tion of data val ues ob tained is pre sented with sev eral ex am ples. BCFD is writ ten in Vi sual Ba sic 6.0. The source code is freely avail able, and is open for any mod i fi ca tions or in te gra tion with other soft ware pack ages that are pow ered by Vi sual Ba sic for Ap pli ca tions (VBA) or its equiv a lent.

Słowa kluczowe

EN

program; Visual Basic; image analysis; fractal dimension

• Wydawca: Państwowy Instytut Geologiczny - Państwowy Instytut Badawczy
• Czasopismo: Geological Quarterly
• Rocznik: 2009
• Tom: Vol. 53, No 2
• Strony: 241--248
• Opis fizyczny: bibliogr. 24 poz., rys., tab., wykr

Twórcy

autor

Verbovšek T.

• University of Ljubljana, Faculty of Natural Sciences and Engineering, Department of Geology, Aškerčeva 12, SI-1000 Ljubljana, Slovenia,

Bibliografia

• ANGELES G. R., PERILLO M. E., PICCOLO M. C. and PIERINI J. O. (2004) -Fractal analysis of tidal channels in the Bahía Blanca Estuary (Argentina). Geomorphology, 57: 263-274.
• BARKER J. A. (1988) -Generalized radial flow model for hydraulic tests in fractured Rock. Water Resour. Res., 24 (10): 1796-1804.
• BARTON C. C. (1995) -Fractal analysis and spatial clustering of fractures. In: Fractals in the Earth Sciences (eds. C. C. Barton and P. R. La Pointe): 141-178. Plenum Press, New York.
• BONNET E., BOUR O., ODLING N. E., DAVY P., MAIN I., COWIE P. and BERKOWITZ B. (2001) -Scaling of fracture systems in geological media. Rev. Geophys., 39 (3): 347-383.
• BORRADAILE G. (2003) -Statistics of Earth Science Data. Springer, Berlin.
• BREWER J. and DI GIROLAMO L. (2006) -Limitations of fractal dimension estimation algorithms with implications for cloud studies. Atmos. Res., 82: 433-454.
• DILLON C. G., CAREY P. F. and WORDEN R. H. (2001) -Fractscript: a macro for calculating the fractal dimension of object perimeters in images of multiple objects. Comput. Geosc., 27: 787-794.
• DOUGHTY C. and KARASAKIK. (2002) -Flow and transport in hierarchically fractured rock. J. Hydrol., 263: 1-22.
• FEDER J. (1988) -Fractals. Plenum Press, New York.
• FOROUTAN-POUR K., DUTILLEUL P. and SMITH D. L. (1999) -Advances in the implementation of the box-counting method of fractal dimension estimation. Appl. Math. Comput., 105: 195-210.
• GONZATO G. (1998) -Apractical implementation of the box counting algorithm. Comput. Geosc., 24 (1): 95-100.
• HART-DAVIS G. (1999) -Mastering VBA 6. Sybex, San Francisco, CA.
• KUSUMAYUDHA S. B., ZEN M. T., NOTOSISWOYO S. and SAYOGA GAUTAMAR. (2000) -Fractal analysis of the Oyo River, cave systems, and topography of the Gunungsewu karst area, central Java, Indonesia. Hydrogeol. J., 8: 271-278.
• MANDELBROT B. (1983) -The Fractal Geometry of Nature. W. H. Freeman & Co., New York.
• PATRICK T., ROMAN S., PETRUSHA R. and LOMAX P. (2006) -Visual Basic 2005 in anutshell. O'Reilly Media, Sebastopol, CA.
• PEITGEN H-O., JÜRGENS H. and SAUPE D. (2004) -Chaos and fractals. New Frontiers of Science. Springer-Verlag, New York.
• POLEK J., KARASAKI K., LONG J. C. S. and BARKER J. A. (1990) -Flow to Wells in Fractured Rock with Fractal Structure. Department of Material Science and Mineral Engineering. Univ. California, Berkeley. Rep. LBL-27900, Lawrence Berkeley Laboratory, Berkeley, California: 74-76.
• SCHULLER D. J., RAO A. R. and JEONG G. D. (2001) -Fractal characteristics of dense stream networks. J. Hydrol., 243: 1-16.
• TANG D. and MARANGONI A. G. (2006) -3D fractal dimension of fat crystal networks. Chem. Phys. Lett., 433: 248-252.
• TURCOTTE D. L. (1992) -Fractals and Chaos in Geology and Geophysics. Cambridge Univ. Press, Cambridge.
• VALLEJO L. E. (1997) -Fractals in engineering geology. Preface. Eng. Geol.,48: 159-160.
• VENEZIANO D. and NIEMANN J. D. (2000) -Self-similarity and multifractality of fluvial erosion topography. Mathematical conditions and physical origin. 1. Water Resour. Res., 36 (7): 1923-1936.
• VERBOVŠEK T. (2008)-Diagenetic effects on the well yield of dolomite aquifers in Slovenia. Environ. Geol., 53 (6): 1173-1182.
• WALSH J. J. and WATTERSON J. (1993) -Fractal analysis of fracture patterns using the standard box-counting technique. Valid and invalid methodologies. J. Struct. Geol., 15 (12): 1509-1512.