A New hybrid Method for Noise Robust Estimation of Image Fractal Dimension
AbstractThis paper presents a modified model to calculate the fractal dimension of digital images. The estimation of fractal dimensions is crucial to fractal analysis and is popularly carried out through methods based on box counting. The problem with these approaches is that, most of them do not remove the potential effects of noise on fractal dimensions properly. Accordingly, this study examines the effects of three different type of noises on fractal dimensions by using different images taken from Background image database. The examination shows that the fractal dimensions change Significantly, after noise adding, so we put forward a noise-robust and efficient fractal dimension calculation method Which is a combination of two methods, the gray-level co-matrix algorithm and improved box counting method. The results of experiments on the Background image dataset confirm the robustness and efficiency of the proposed method.
 W-L Lee and K-Sh Hsieh, "A Robust Algorithm for the Fractal Dimension of Images and its Applications to the Classification of Natural Images and Ultrasonic Liver Images," Signal Processing, Vol. 90, pp. 1894–1904, Jun. 2010.
 P. Pentland, "Fractal-Based Description of Natural Scenes," IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 6, pp. 661–674, Nov. 1984.
 T. Pant, D. Singh and T. Srivastava, "Advanced Fractal Approach for Unsupervised Classification of SAR Images," Advances in Space Research, Vol. 45, pp. 1338-1349, Jun. 2010.
 X. Zhang, Y. Xu and Jackson, R.L., "An Analysis of Generated Fractal and Measured Rough Surfaces in Regards to their Multi-Scale Structure and Fractal Dimension," Tribology International, Vol. 105, pp. 94–101, Jan. 2017.
 X. Zhao and X. Wang, "Fractal Dimension Estimation of RGB Color Images Using Maximum Color Distance," World Scientific Publishing Company, Fractals, Vol. 24, pp.1-7, Aug. 2016.
 M. Fernández-Martínez and M.A. sánchez-Granero, "A New Fractal Dimension for Curves based on Fractal Structures," Topology and its Applications, Vol. 203, pp.108–124, Apr. 2016.
 E. Spodarev, P. Straka and S. Winter, "Estimation of Fractal Dimension and Fractal Curvatures from Digital Images," Chaos, Solitons& Fractals, Vol. 75, pp. 134-152, Jun. 2015.
 C. Yinglei, et al. (2010), "A Method of Calculating Image Fractal Dimension Based on Fractal Brownian Model," in Proc. 2010 International Forum on Information Technology and Applications, Kunming, IEEE, China, pp.19-21.
 H.O. Peitgen, H. Jurgensand D. Saupe, "New Frontiers of Science," in Chaos and Fractals, 2nd ed., 2004, Springer.
 N. Sarkar and B.B. Chaudhuri, "An Efficient Approach to Estimate Fractal Dimension of Textural Images," Pattern Recognition, Vol. 25, pp. 1035–1041, Sep. 1992.
 N. Sarkar and B.B. Chaudhuri, "An Efficient Differential Box-counting Approach to compute Fractal Dimension of Image," IEEE Transactions Systems, Man and Cybernetics, Vol. 24, pp. 115–120, Jan. 1994.
 N. Sarkar and B.B. Chaudhuri, "Multifractal and Generalized Dimensions Of Gray Tone Digital Images," Signal Processing, Vol. 42, pp.181–190, Mar. 1995.
 Y. Shi, et al., "An Anti-noise Determination on Fractal Dimension for Digital Images," in Proc. 2011 Advances in Intelligent and Soft Computing, Berlin, Springer-Verlag, Germany, pp. 469-474.
 J. Li, Q. Du and C. Sun, "An Improved Box-counting Method For Image Fractal Dimension Estimation," Pattern Recognition, Vol. 42, pp. 2460–2469, Nov. 2009.
 X.C. Jin, S.H. Ong and Jayasooriah, "A Practical Method for Estimating Fractal Dimension," Pattern Recognition Letter, Vol. 16, pp. 457–464, May. 1995
 A. Eleyan and H. Demirel, "Co-occurrence Matrix and its Statistical Features as a New Approach for Face Recognition," Turkish Journal of Electrical Engineering and Computer Sciences, Vol. 19, pp. 97-107, Dec. 2011.
 R.M. Haralick, K. Shanmugam and I. Dinstein, "Textural Features for Image Classification," IEEE Transactions on Systems, Man and Cybernetics, Vol. 3, pp. 610–621, Nov. 1973.
 P. Mohanaiah, P. Sathyanaray and L. Gurukumar, "Image Texture Feature Extraction Using GLCM Approach," International Journal of Scientific and Research Publications, Vol. 3, pp. 2250-3153, May. 2013.
 S. R. Nayak and J. Mishra, "On Estimation of Fractal Dimension of Noise Images," Indian journal of science and Technology, Vol. 10, pp. 1-6, May. 2017.