Multifractal modelling and 3D lacunarity analysis. (English) Zbl 1233.28004
Summary: This study presents a comparative evaluation of lacunarity of 3D grey level models with different types of inhomogeneity. A new method based on the “relative differential box counting” was developed to estimate the lacunarity features of grey level volumes. To validate our method, we generated a set of 3D grey level multifractal models with random, anisotropic and hierarchical properties. Our method gives a lacunarity measurement correlated with the theoretical one and allows a better model classification compared with a classical approach.
MSC:
| 28A80 | Fractals |
References:
| [1] | Dong, P., Int. J. Remote Sens., 21, 17, 3369 (2000) |
| [2] | Feagin, R. A., Physica A, 328, 315 (2003) · Zbl 1028.60080 |
| [3] | Mandelbrot, B. B., The Fractal Geometry of Nature (1983), Freeman: Freeman San Francisco, CA · Zbl 0504.28001 |
| [4] | Evertsz, C. J.G.; Mandelbrot, B. B., Multifractal measures, (Peitgen, H.-O.; Jurgens, H.; Saupe, D., Chaos and Fractals (1992), Springer-Verlag: Springer-Verlag New York), 922-953 |
| [5] | Fabio, D. A.; Aarao, R., Phys. Lett. A, 214, 5-6, 239 (1996) · Zbl 0972.82544 |
| [6] | Cheng, Q.; Agterberg, F. P., Math. Geology, 28, 1, 1 (1996) |
| [7] | Allain, C., M.Cloître, Phys. Rev. A, 44, 6, 3552 (1991) |
| [8] | Chmiela, J.; Słota, D.; Szala, J., Mater. Characterization, 56, 4216 (2006) |
| [9] | Zaia, A.; Eleonori, R.; Maponi, P.; Rossi, R.; Murri, R., IEEE Trans. Inf. Technol. Biomed., 10, 3, 484 (2006) |
| [10] | Jin, X. C.; Ong, S. H.; Jayasooriah, Pattern Recognition Lett., 16, 457 (1995) · Zbl 0939.68818 |
| [11] | Akkari, H.; Bhouri, I.; Dubois, P.; Bedoui, M. H., Math. Model. Nat. Phenom., 3, 6, 48 (2008) · Zbl 1337.92122 |
| [12] | Plotnick, R. E.; Gardner, R. H.; Hargrove, W. W.; Prestegaard, K.; Perlmutter, M., Phys. Rev. E, 53, 5, 1 (1996) |
| [13] | Henebry, G. M.; Kux, H. J.H., Int. J. Remote Sens., 16, 3, 565 (1995) |
| [14] | Marwan, N.; Saparin, P.; Kurths, J., Eur. Phys. J. Special Topics, 143, 109 (2007) |
| [15] | Olsen, L., Pacific J. Math., 183, 1, 143 (1998) · Zbl 0955.28004 |
| [16] | Otsu, N., IEEE Trans. Systems Man Cyber., 9, 62 (1979) |
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