Box-Counting Fractal Dimension Algorithm Variations on Retina Images

  • Mohd Zulfaezal Che AzeminEmail author
  • Fadilah Ab Hamid
  • Jie Jin Wang
  • Ryo Kawasaki
  • Dinesh Kant Kumar
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 362)


This research work investigates the influences of FD algorithm variation on the measurement of retinal vasculature complexity. Forty retinal vasculature images from publicly available dataset were subjected to four variations of box-counting FD algorithm. Different positions of box-grid were found to significantly affect the measurement of FD (p < 0.0001, d = 0.746) due to non-identical vessels captured for measurement. By averaging multiple box-grid placements the FD mean shows no significant difference (p = 0.12, d = 0.124). Using different smoothing effect (big versus small) results in significantly different FD mean, the variation however was small (d = 0.211). The FD of skeletonized vasculature is significantly different than the segmentation (p < 0.0001) with a modest effect size (d = 0.613). More reliable FD measurement on retinal vasculature could be obtained by averaging the FD values using multiple positions of the grid.


Fractal Dimension Retinal Vasculature Algorithm Variation Multiple Position Vessel Segmentation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This research was supported by Ministry of Education, Malaysia under Research Acculturation Grant Scheme RAGS13-029-0092.


  1. 1.
    Backx, P.H.: Complexity, confusion and controversy continue complicating the contribution of RyR2 channel phosphorylation to heart function. J. Physiol. 592, 1911–1912 (2014)CrossRefGoogle Scholar
  2. 2.
    Sleimen-Malkoun, R., Temprado, J.J., Hong, S.L.: Aging induced loss of complexity and dedifferentiation: consequences for coordination dynamics within and between brain, muscular and behavioral levels. Front. Aging Neurosci. 6, 1–1 (2014)Google Scholar
  3. 3.
    Sandu, A.-L., Staff, R.T., McNeil, C.J., Mustafa, N., Ahearn, T., Whalley, L.J., Murray, A.D.: Structural brain complexity and cognitive decline in late life—a longitudinal study in the Aberdeen 1936 birth cohort. Neuroimage 100, 558–563 (2014)CrossRefGoogle Scholar
  4. 4.
    Naraghi, L., Peev, M.P., Esteve, R., Chang, Y., Berger, D.L., Thayer, S.P., Rattner, D.W., Lillemoe, K.D., Kaafarani, H., Yeh, D.D.: Others: the influence of anesthesia on heart rate complexity during elective and urgent surgery in 128 patients. J. Crit. Care 30, 145–149 (2015)CrossRefGoogle Scholar
  5. 5.
    Squarcina, L., De Luca, A., Bellani, M., Brambilla, P., Turkheimer, F.E., Bertoldo, A.: Fractal analysis of MRI data for the characterization of patients with schizophrenia and bipolar disorder. Phys. Med. Biol. 60, 1697 (2015)CrossRefGoogle Scholar
  6. 6.
    Zappasodi, F., Olejarczyk, E., Marzetti, L., Assenza, G., Pizzella, V., Tecchio, F.: Fractal dimension of EEG activity senses neuronal impairment in acute stroke. PLoS ONE 9, e100199 (2014)CrossRefGoogle Scholar
  7. 7.
    Di Ieva, A., Esteban, F.J., Grizzi, F., Klonowski, W., Martín-Landrove, M.: Fractals in the Neurosciences, part II clinical applications and future perspectives. Neurosci. 21, 30–43 (2015)Google Scholar
  8. 8.
    Che Azemin, M.Z., Mohamad Daud, N., Ab Hamid, F., Zahari, I., Sapuan, A.H.: Influence of refractive condition on retinal vasculature complexity in younger subjects. Sci. World J. 2014 (2014)Google Scholar
  9. 9.
    Azemin, M.Z.C., Ab Hamid, F., Aminuddin, A., Wang, J.J., Kawasaki, R., Kumar, D.K.: Age-related rarefaction in retinal vasculature is not linear. Exp. Eye Res. 116, 355–358 (2013)Google Scholar
  10. 10.
    Lee, J., Zee, B.C.Y., Li, Q.: Detection of neovascularization based on fractal and texture analysis with interaction effects in diabetic retinopathy. PLoS ONE 8, e75699 (2013)CrossRefGoogle Scholar
  11. 11.
    Aliahmad, B., Kumar, D.K., Hao, H., Unnikrishnan, P., Che Azemin, M.Z., Kawasaki, R., Mitchell, P.: Zone specific fractal dimension of retinal images as predictor of stroke incidence. Sci. World J. 2014 (2014)Google Scholar
  12. 12.
    Kawasaki, R., Azemin, M.Z.C., Kumar, D.K., Tan, A.G., Liew, G., Wong, T.Y., Mitchell, P., Wang, J.J.: Fractal dimension of the retinal vasculature and risk of stroke: a nested case-control study. Neurology 76, 1766–1767 (2011)CrossRefGoogle Scholar
  13. 13.
    Wainwright, A., Liew, G., Burlutsky, G., Rochtchina, E., Zhang, Y.P., Hsu, W., Lee, J.M., Wong, T.Y., Mitchell, P., Wang, J.J.: Effect of image quality, color, and format on the measurement of retinal vascular fractal dimension. Invest. Ophthalmol. Vis. Sci. 51, 5525–5529 (2010)CrossRefGoogle Scholar
  14. 14.
    Staal, J., Abràmoff, M.D., Niemeijer, M., Viergever, M.A., van Ginneken, B.: Ridge-based vessel segmentation in color images of the retina. Med. Imaging, IEEE Trans. 23, 501–509 (2004)Google Scholar
  15. 15.
    Karperien, A.: FracLac for ImageJ (2013)Google Scholar
  16. 16.
    Doubal, F.N., Hokke, P.E., Wardlaw, J.M.: Retinal microvascular abnormalities and stroke: a systematic review. J. Neurol. Neurosurg. Psychiatry 80, 158–165 (2009)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Mohd Zulfaezal Che Azemin
    • 1
    Email author
  • Fadilah Ab Hamid
    • 1
  • Jie Jin Wang
    • 2
  • Ryo Kawasaki
    • 3
  • Dinesh Kant Kumar
    • 4
  1. 1.Kulliyyah of Allied Health SciencesInternational Islamic University MalaysiaKuantanMalaysia
  2. 2.Department of Ophthalmology and Westmead Millenium InstituteUniversity of SydneySydneyAustralia
  3. 3.Department of Public HealthYamagata UniversityYamagataJapan
  4. 4.School of Electrical and Computer EngineeringRMIT UniversityMelbourneAustralia

Personalised recommendations