Abstract
Significantly increased resolution of image formation systems (down to a few centimetres) causes a possibility of more effective using of objects textural features and signs in case of thematic processing of radar and optical images. The existing methods of image fractal features measurement allows to evaluate numerically the following topological characteristics of image texture: fractal dimension (FD); directional FD in the analysis directions (DFD); multifractal dimension (MFD) (a widespread case — the spectrum of Renyi dimensions (SRD)); morphological multifractal exponent (MME); fractal signature (FS) and directional FS (DFS); morphological MFS (MMFS) and lacunarity. However today there are no complex methods allowing to measure at the same time parameters of the scaling, multifractal and anisotropic properties of a texture possessing reciprocal relationships. In this work the specificities of new Directional Multifractal Blanket method (morphological) (DMBMM) for fractal features measurement of an image textures synthesized on the basis of two best ABRG and MBMM methods in the groups, are considered. Simultaneous accounting of multifractal, singular and anisotropic properties of the image texture with limited scaling character allowed to increase measuring accuracy both FD, and FS at each analysis scale. This feature is the most representative on comparing with all features considered in this work as the functional correlation of the derived features. The increased informativeness of the developed feature in case of image processing is caused by additional determination, along with multifractal and singular properties, anisotropic properties and their joint account and implied the possibility of its using for the properties description of different images textures and also in images clustering and segmentation tasks.
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Abbreviations
- ABRG:
-
Augmented iterative covering blanket method with rotating grid
- AFS:
-
Anisotropic fractal surface
- DFD:
-
Directional fractal dimension
- DFS:
-
Directional fractal signature
- DMBMM:
-
Directional multifractal blanket method (morphological)
- DMFS:
-
Directional multifractal signature
- DMMFS:
-
Directional morphological multifractal signature
- FD:
-
Fractal dimension
- FS:
-
Fractal signature
- L:
-
Lacunarity
- LFD:
-
Local fractal dimension
- LMME:
-
Local morphological multifractal exponent
- MBMM:
-
Morphological multifractal iterative covering blanket method
- MFD:
-
Multifractal dimension
- MFS:
-
Multifractal signature
- MME:
-
Morphological multifractal exponent
- MMFS:
-
Morphological multifractal signature
- SRD:
-
Spectrum of Renyi dimensions
References
A.A. Potapov, Fractals in radiophysics and radiolocation: sample topology, Universitetskaya kniga, Moscow (2005), (in Russian)
A.A. Potapov, Postulate “the topology maximum at the energy minimum” for textural and fractal-and-scaling processing of multidimensional super weak signals against a back-ground of noises, in L.A. Uvarova, A.B. Nadykto, A.V. Latyshev, ed. by Nonlinearity: Problems, Solutions and Applications, 2nd edn. (Nova Science Publ., New York, 2017)
R.M. Haralick, K. Shanmugan, I. Dinstein, Textural features for image classification. IEEE Trans. SMC 3(6), 610–621 (1973)
B.B. Mandelbrot, The Fractal Geometry of Nature (Freeman, New York, 1982)
A.P. Pentland, Fractal-based description of natural scenes. IEEE Trans. Pattern Annal. Mach. Intell. 6(6), 661–674 (1984)
H.-O. Peitgen, B. Saupe, The Science of Fractal Images (Springer, New York, 1988)
K.J. Falconer, The Geometry of Fractal sets, Cambridge Tracts in Mathematics, Vol. 85, (University Press, Cambridge, 1985)
L.M. Novak, Thinking in Patterns: Fractals and Related Phenomena in Nature (World Scientific, Singapore, 2004)
R.F. Voss, Random fractals: characterization and measurement. Physica Scripta 13, 27–32 (1986)
A.A. Potapov, Yu.V. Guliaev, S.A. Nikitov, A.A. Pakhomov, V.A. German, Latest Techniques of Image Processing (Fizmatlit, Moscow, 2008). (in Russian)
G.A. Andreev, A.A. Potapov, A.V. Gorbunov, Sravnitel'nyy analiz statisticheskikh priznakov opticheskikh i radioizobrazheniy pochvenno-rastitel'nykh ob'yektov, Issledovanie Zemli iz kosmosa 1, 112–121 (1990) (in Russian)
A.A. Potapov, T.V. Galkina, T.I. Orlova, Ya.L. Khlyavich, Dispersion detection method of determined object at texture optical and radar images of earth surface. Radiotekhnika i Electronica 35(11), 2295–2301 (1990) (in Russian)
A.A. Potapov, T.V. Galkina, A.I. Kolesnikov, O klassifikatsii izobrazheniy po ikh teksturnym priznakam, Issledovanie Zemli iz kosmosa, 2, 91–96 (1990). (in Russian)
A.A. Potapov, V.A. German, Methods of measuring the fractal dimension and fractal signatures of a multidimensional stochastic signal. J. Commun. Technol. Electron. 49(12), 1370–1391 (2004). (in Russian)
V.A. Kuznetsov, A.N. Pototsky, Method of measuring directional morphological multifractal signatures of the texture images. Achievements Modern Radio Electron. 3, 39–52 (2017). (in Russian)
S. Peleg, J. Naor, R. Hartley, Multiple resolution texture analysis and classification, IEEE Trans. Pattern. Annal. Mach. Intell. 6(4), 518–523 (1984)
Y. Xia, D. Feng, R. Zhao, Y. Zhang, Multifractal signature estimation for textured image segmentation. Pattern. Recognit Lett. 31, 163–169 (2010)
A.A. Potapov, Topology of sample. J. Nonlinear World 2(1), 4–13 (2004). (in Russian)
G. Jacquet, W. Ohley, C. Fortin, Bone texture characterization by oriented fractal analysis, in Proceedings of the 18th IEEE on Bioengineering, vol. 18, pp. 22–23 (1988)
W.J. Yi, M.S. Heo, S. Lee, Direct measurement of trabecular bone anisotropy using directional fractal dimension and principal axes of inertia. Oral Surg. Oral Med. Oral Pathol Oral Radiol Endod 104, 110–116 (2007)
J. A. Lynch, D. J. Hawkess, J. C. Bukland-Wright, Analysis of texture in macro radiographs of osteoarthritic knees, using the fractal signature. Phys. Med. Biol. 36(6), 709–722 (1991)
P. Podsiadlo, G.W. Stachowiak, The development of the modified hurst orientation transform for the characterization of surface topography of wear particles. Tribology Lett, 3, 215–229 (1998)
M. Wolski, P. Podsiadlo, G.W. Stachowiak, Directional fractal signature analysis of trabecular bone: evaluation of different methods to detect early osteoarthritis in knee radiographs. Proc. Inst. Mech. Eng. 223(2), 211–236 (2009)
M. Wolski, P. Podsiadlo, G.W. Stachowiak, Directional fractal signature analysis of self-structured surface textures. Tribology Lett. 47, 323–340 (2012)
A.A. Potapov, V.V. Bulavkin, V.A. German, O.F. Vyacheslavova, Fractal signature methods for profiling of processed surfaces. Tech. Phys. 75(5), 560–575 (2005). (in Russian)
A.N. Pototskiy, V.A. Kuznetsov, S.F. Galiev, Sposob izmereniya morfologicheskoy mul'tifraktal'noy signatury, Patent RU2647675, (2018). (in Russian)
J. Samarabandu, R. Acharya, E. Hausmann, Analysis of bone x-rays using morphological fractals. IEEE Trans. Med. Imaging 12(3), 466–470 (1993)
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Potapov, A.A., Kuznetsov, V.A., Pototskiy, A.N. (2022). New Fractal Features for Textural Morphologic Analysis. In: Skiadas, C.H., Dimotikalis, Y. (eds) 14th Chaotic Modeling and Simulation International Conference. CHAOS 2021. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-030-96964-6_23
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