Box-Counting Fractal Dimension Algorithm Variations on Retina Images
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.
KeywordsFractal Dimension Retinal Vasculature Algorithm Variation Multiple Position Vessel Segmentation
This research was supported by Ministry of Education, Malaysia under Research Acculturation Grant Scheme RAGS13-029-0092.
- 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
- 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
- 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.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.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
- 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
- 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.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.Karperien, A.: FracLac for ImageJ (2013)Google Scholar