Abstract
Fractal image coding (FIC) based on the inverse problem of an iterated function system plays an essential role in several areas of computer graphics and in many other interesting applications. Through FIC, an image can be transformed to compressed representative parameters and be expressed in a simple geometric way. Dealing with digital images requires storing a large number of images in databases, where searching such databases is time consuming. Therefore, finding a new technique that facilitates this task is a challenge that has received increasing attention from many researchers. In this study, a new method that combines fractal dimension (FD) which is an indicator of image complexity with the FIC scheme is proposed. Classifying images in databases according to their texture by using FD helps reduce the retrieval time of query images. The validity of the proposed method is evaluated using geosciences images. Result shows that the method is computationally attractive.
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Alsaidi NM, Rushdan MS, Jabbar W (2015a). A generalized fractal dimension as an image feature. In: proceedings of the 5th international conference on computational and mathematical methods in science and engineering, CMMSE, Spain 3-7 July, pp 107–117, (2015)
Alsaidi NM, Jabbar W (2015b) An improve differential box counting method to estimate fractal dimension. Eng Tech J 33(4):714–722
Ambika DR, Ananth AG (2011) Classification of a satellite rural image based on fractal dimension using box counting method. Int J Comput Appl 16(5):45–48
Barnesly MF (1988) Fractal everywhere, 2nd edn. Academic Press, New York
Barnsley MF, Demko S (1985) Iterated function systems and the global construction of fractals. Proc Royal Soc Lond A399:243–275
De Cola L (1989) Fractal analysis of a classified Landsat scene. Photogram Eng Remote Sens 55(5):601–610
De Jong SM, Burrough PA (1995) A fractal approach to the classification of Mediterranean vegetation types in remotely sensed images. Photogram Eng Remote Sens 61(8):1041–1053
Eckmann J, Ruelle D (1985) Ergodic theory of strange attractors. Rev Mod Phys 57:617–656
Falconar KJ (1986) Random fractals. Math Proc Comb Phil Soc 100:559–582
Falconar KJ (1987) The Hausdorff dimension of some fractals and attractor of overlapping contraction. J Stat Phys 47(1-2): 123–132
Falconar KJ (1988) The Hausdorff dimension of self-affne fractals. Math Proc Comb Phil Soc 103:339–350
Grassberger P (1983) Generalized dimensions of strange attractors. Phys Lett A 97:227
Hutchinson JE (1981) Fractals and self-similarity. Indiana Univ J Math 30(5):713–747
Jabbar W (2014) Fuzzy fractal dimension and its applications. Msc. Thesis, University of Technology, Applied Mathematics
Jacquin E (1992) Image coding based on fractal theory of iterated contractive image transformations. IEEE Trans Image Process 1:18–30
Ji Z, Ziyu L, Angsheng W, Peng C (2006) An approach to extracting fractal in remote sensing image. WUJNS 11(3):606–610
Ju WX, Lam NSN (2009) An improved algorithm for computing local fractal dimension using the triangular prism method. Comput Geosci 35:1224–1233
Lam NS-N (1990) Description and measurement of Landsat TM images using fractals. Photogram Eng Remote Sens 56(2):187–195
Lam NS, Qiu H-L, Quattrochi DA, Emerson CW (2002) An evaluation of fractal methods for characterizing image complexity. Cartogr Geogr Inf Sci 29(1):25–35
Mandelbort B (1967) How long is the coast of Britain? Statistical self-similarity and fractional dimension. Science 156(3775):636–638
Mandelbort BB (1982) Fractal geometry of nature. Freeman, San Francisco, pp 20–25
Myint SW (2003) Fractal approaches in texture analysis and classification of remotely sensed data: comparisons with spatial autocorrelation techniques and simple descriptive statistics. Int J Remote Sens 24(9):1925–1947
Peleg S, Naor J, Hartley R, Avnir D (1984) Multiple resolution texture analysis and classification. IEEE Trans Pattern Anal Mach Intell 6:518–523
Pentland AP (1984) Fractal-based descriptions of natural scenes. IEEE Trans Pattern Anal Mach Intell 6(6):661–674
Sarker N, Chaudhuri BB (1994) An efficient differential box-counting approach to compute fractal dimension of image. IEEE Trans Syst Man Cybern 24:115120
Sun W, Xu G, Gong P, Liang S (2006) Fractal analysis of remotely sensed images: a review of methods and applications (review article). Int J Remote Sens 27(22):4963–4990
Wanxiao S (2006) Three new implementations of the triangular prism method for computing the fractal dimension of remote sensing images. Photogram Eng Remote Sens 72:373–382
Zhang A, Cheng B, Acharya R (1995) An approach to query-by-texture in image database system. In: Proceedings of the SPIE conference on digital image storage and archiving systems, Philadelphia, October 1995
Zhang Z, Yang X, Xiao R (2015) Fractal characterization of settlement patterns and their spatial determinants in coastal zones. ISPRS Int J Geo Inf 4:2728–2741
Zhang A, Cheng B, Acharya R, Menon R (1996) Comparison of wavelet transforms and fractal coding in texture-based image retrieval. In: Grinstein GG, Erbacher RF (eds) Visual data exploration and analysis III, 2656 of SPIE Proceedings, pp 116–125
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Communicated by Cristina Turner.
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Al-Saidi, N.M.G., Al-Bundi, S.S. & Al-Jawari, N.J. A hybrid of fractal image coding and fractal dimension for an efficient retrieval method. Comp. Appl. Math. 37, 996–1011 (2018). https://doi.org/10.1007/s40314-016-0378-9
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DOI: https://doi.org/10.1007/s40314-016-0378-9