Multifractal Geometry in Analysis and Processing of Digital Retinal Photographs for Early Diagnosis of Human Diabetic Macular Edema

Abstract

Objective: The purpose of this paper is to determine a quantitative assessment of the human retinal vascular network architecture for patients with diabetic macular edema (DME). Multifractal geometry and lacunarity parameters are used in this study.

Materials and methods: A set of 10 segmented and skeletonized human retinal images, corresponding to both normal (five images) and DME states of the retina (five images), from the DRIVE database was analyzed using the Image J software. Statistical analyses were performed using Microsoft Office Excel 2003 and GraphPad InStat software.

Results: The human retinal vascular network architecture has a multifractal geometry. The average of generalized dimensions (D_q) for q = 0, 1, 2 of the normal images (segmented versions), is similar to the DME cases (segmented versions). The average of generalized dimensions (D_q) for q = 0, 1 of the normal images (skeletonized versions), is slightly greater than the DME cases (skeletonized versions). However, the average of D₂ for the normal images (skeletonized versions) is similar to the DME images. The average of lacunarity parameter, Λ, for the normal images (segmented and skeletonized versions) is slightly lower than the corresponding values for DME images (segmented and skeletonized versions).

Conclusion: The multifractal and lacunarity analysis provides a non-invasive predictive complementary tool for an early diagnosis of patients with DME.

• Diabetic macular edema
• lacunarity
• multifractals
• retinal image analysis
• retinal microcirculation

Acknowledgements

The author would like to thank J. J. Staal and colleagues, as well as Image Sciences Institute for making their databases publicly available, and permission to use retinal digital images from the DRIVE database.43,45 I would also like to thank Assoc. Prof. Mihai Talu, PhD Eng. from The University of Craiova, Romania, for his constructive comments. Finally, I am indebted to Prof. Ronald A. Schachar, MD, PhD, Department of Physics, University of Arlington, Arlington, Texas, USA, for the analysis of retinal images used in this study.