Box-counting fractal dimension algorithm variations on retina images

Abstract

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.