2D and 3D Complexity Analysis on MRI Images using Fractal Dimension


  • I. Jamaludin Department of Diagnostic Imaging and Radiotherapy, Kulliyyah of Allied Health Sciences, International Islamic University Malaysia.
  • M. Z. Che Azemin Department of Optometry and Visual Science, Kulliyyah of Allied Health Sciences, International Islamic University Malaysia.
  • A. H. Sapuan Department of Diagnostic Imaging and Radiotherapy, Kulliyyah of Allied Health Sciences, International Islamic University Malaysia.
  • A. A. Zainuddin Professional Nursing Studies Department, Kulliyyah of Nursing, International Islamic University Malaysia.
  • R. Hassan Department of Radiology, Kulliyyah of Medicine, International Islamic University Malaysia.


Brain, Box-Counting, Fractal Dimension, Magnetic Resonance Imaging.


The brain, which is the most complex structure in the human body, has attracted attention of many researchers to study the possible fractal analysis application upon it. Current interest is seen directed more towards the utilization of complexity analysis as measured by fractal dimension in determining the pathologies effect and degenerative factor on the brain structure volume. In this paper, we used two boxcounting methods: average 2D Fractal Dimension and 3D Fractal Dimension. 47 subjects (19 males, 28 females), aged ranging from 21 to 25 years, were recruited. Brain MRI images were acquired by using 3T MRI system. The images were then thresholded according to Otsu’s method. The processed images were then calculated using fractal analysis, and the values obtained were statistically evaluated using Pearson’s correlation test (r2 = -0.106, p = 0.477). In conclusion, no correlation was seen between average 2D FD and 3D FD.


L. Squarcina, A. De Luca, M. Bellani, P. Brambilla, F. E. Turkheimer, and A. Bertoldo, “Fractal analysis of MRI data for the characterization of patients with schizophrenia and bipolar disorder,” Phys. Med. Biol., vol. 60, no. 4, pp. 1697–1716, 2015.

A. H. Sapuan, N. S. Mustofa, M. Z. Che Azemin, Z. A. Abdul Majid, and I. Jamaludin, “Grey matter volume differences of textual memorization: A Voxel based morphometry study,” in IFMBE Proceedings, 2016, vol. 56, pp. 36–43.

L. Zhang, J. Z. Liu, D. Dean, V. Sahgal, and G. H. Yue, “A threedimensional fractal analysis method for quantifying white matter structure in human brain,” Journal of Neuroscience Methods, vol. 150, no. 2, pp. 242–253, 2006.

V. G. Kiselev, K. R. Hahn, and D. P. Auer, “Is the brain cortex a fractal?,” Neuroimage, vol. 20, no. 3, pp. 1765–1774, 2003.

J. Z. Liu, L. D. Zhang, and G. H. Yue, “Fractal dimension in human cerebellum measured by magnetic resonance imaging.,” Biophys. J., vol. 85, no. 6, pp. 4041–6, 2003.

Farahibozorg, S., Hashemi-Golpayegani, S. M., & Ashburner, J., “Ageand Sex-Related Variations in the Brain White Matter Fractal Dimension Throughout Adulthood : An MRI Study,” Clinical Neuroradiology, vol. 25, no. 1, pp. 19–32, 2015.

A. Di Ieva, F. J. Esteban, F. Grizzi, W. Klonowski, and M. MartinLandrove, “Fractals in the Neurosciences, Part II: Clinical Applications and Future Perspectives,” Neurosci., vol. 21, no. 1, pp. 30–43, 2015.

J. M. Zook and K. M. Iftekharuddin, “Statistical analysis of fractalbased brain tumor detection algorithms,” Magnetic Resonance Imaging, vol. 23, no. 5, pp. 671–678, 2005.

H. Akkari, I. Bhouri, P. Dubois, and M. H. Bedoui, “On the Relations Between 2D and 3D Fractal Dimensions: Theoretical Approach and Clinical Application in Bone Imaging,” Math. Model. Nat. Phenom, vol. 3, no. 6, pp. 48–75, 2008.

A. Alberich-Bayarri, L. Marti-Bonmati, M. Angeles Pérez, R. SanzRequena, J. J. Lerma-Garrido, G. García-Martí, and D. Moratal, “Assessment of 2D and 3D fractal dimension measurements of trabecular bone from high-spatial resolution magnetic resonance images at 3 T.,” Med. Phys., vol. 37, no. 9, pp. 4930–7, 2010.

M. T. Suzuki, “A three dimensional box counting method for measuring fractal dimensions of 3D models,” in Proceedings of the 11th IASTED International Conference on Internet and Multimedia Systems and Applications IMSA 2007, 2007, pp. 42–47.

N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. Syst. Man. Cybern., vol. 9, no. 1, pp. 62–66, 1979.

R. Lopes, P. Dubois, I. Bhouri, M. H. Bedoui, S. Maouche, and N. Betrouni, “Local fractal and multifractal features for volumic texture characterization,” Pattern Recognit., vol. 44, no. 8, pp. 1690–1697, 2011.

J. Jiang, W. Zhu, F. Shi, Y. Zhang, L. Lin, and T. Jiang, “A robust and accurate algorithm for estimating the complexity of the cortical surface,” Journal of Neuroscience Methods, vol. 172, no. 1, pp. 122– 130, 2008.

L. K. Gallos, M. Sigman, and H. A. Makse, “The conundrum of functional brain networks: Small-world efficiency or fractal modularity,” Frontiers in Physiology, vol. 3, 2012.

M. Rubinov and O. Sporns, “Complex network measures of brain connectivity: Uses and interpretations,” Neuroimage, vol. 52, no. 3, pp. 1059–1069, 2010.

F. J. Esteban, J. Sepulcre, N. V. de Mendizábal, J. Goñi, J. Navas, J. R. de Miras, B. Bejarano, J. C. Masdeu, and P. Villoslada, “Fractal dimension and white matter changes in multiple sclerosis,” Neuroimage, vol. 36, no. 3, pp. 543–549, 2007.

R. D. King, B. Brown, M. Hwang, T. Jeon, and A. T. George, “Fractal dimension analysis of the cortical ribbon in mild Alzheimer’s disease,” Neuroimage, vol. 53, no. 2, pp. 471–479, 2010.

Ab Hamid, F., Che Azemin, M. Z., Salam, A., Aminuddin, A., Mohd Daud, N., and Zahari, I, “Retinal vasculature fractal dimension measures vessel density, ” Current Eye Research, vol. 41, no. 6, pp. 823-831, 2016.

Zhao, Guihu, Kristina Denisova, Pejman Sehatpour, Jun Long, Weihua Gui, Jianping Qiao, Daniel C. Javitt, and Zhishun Wang. "Fractal dimension analysis of subcortical gray matter structures in Schizophrenia," PLoS ONE, vol. 11, no. 5: e0155415, pp. 1-23, 2016.




How to Cite

Jamaludin, I., Che Azemin, M. Z., Sapuan, A. H., Zainuddin, A. A., & Hassan, R. (2018). 2D and 3D Complexity Analysis on MRI Images using Fractal Dimension. Journal of Telecommunication, Electronic and Computer Engineering (JTEC), 10(1-8), 161–164. Retrieved from https://jtec.utem.edu.my/jtec/article/view/3754