Table of Contents Author Guidelines Submit a Manuscript
Journal of Ophthalmology
Volume 2016 (2016), Article ID 6259047, 13 pages
http://dx.doi.org/10.1155/2016/6259047
Research Article

Reliability of Using Retinal Vascular Fractal Dimension as a Biomarker in the Diabetic Retinopathy Detection

1Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, Netherlands
2University Eye Clinic Maastricht, Maastricht, Netherlands
3Department of Biomedical and Information Engineering, Northeastern University, Shenyang, China

Received 27 November 2015; Accepted 17 August 2016

Academic Editor: Ana Raquel Santiago

Copyright © 2016 Fan Huang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. C. D. Murray, “The physiological principle of minimum work: I. The vascular system and the cost of blood volume,” Proceedings of the National Academy of Sciences of the United States of America, vol. 12, no. 3, pp. 207–214, 1926. View at Publisher · View at Google Scholar
  2. B. B. Mandelbrot, The Fractal Geometry of Nature, vol. 173, Macmillan, New York, NY, USA, 1983.
  3. F. Family, B. R. Masters, and D. E. Platt, “Fractal pattern formation in human retinal vessels,” Physica D: Nonlinear Phenomena, vol. 38, no. 1–3, pp. 98–103, 1989. View at Publisher · View at Google Scholar · View at Scopus
  4. N. Cheung, K. C. Donaghue, G. Liew et al., “Quantitative assessment of early diabetic retinopathy using fractal analysis,” Diabetes Care, vol. 32, no. 1, pp. 106–110, 2009. View at Publisher · View at Google Scholar · View at Scopus
  5. J. W. Y. Yau, R. Kawasaki, F. M. A. Islam et al., “Retinal fractal dimension is increased in persons with diabetes but not impaired glucose metabolism: the Australian Diabetes, Obesity and Lifestyle (AusDiab) study,” Diabetologia, vol. 53, no. 9, pp. 2042–2045, 2010. View at Publisher · View at Google Scholar · View at Scopus
  6. J. Grauslund, A. Green, R. Kawasaki, L. Hodgson, A. K. Sjølie, and T. Y. Wong, “Retinal vascular fractals and microvascular and macrovascular complications in type 1 diabetes,” Ophthalmology, vol. 117, no. 7, pp. 1400–1405, 2010. View at Publisher · View at Google Scholar · View at Scopus
  7. R. Broe, M. L. Rasmussen, U. Frydkjaer-Olsen et al., “Retinal vascular fractals predict long-term microvascular complications in type 1 diabetes mellitus: the Danish Cohort of Pediatric Diabetes 1987 (DCPD1987),” Diabetologia, vol. 57, no. 10, pp. 2215–2221, 2014. View at Publisher · View at Google Scholar · View at Scopus
  8. B. Aliahmad, D. K. Kumar, M. G. Sarossy, and R. Jain, “Relationship between diabetes and grayscale fractal dimensions of retinal vasculature in the Indian population,” BMC Ophthalmology, vol. 14, article 152, 2014. View at Publisher · View at Google Scholar · View at Scopus
  9. D. Ristanović, B. D. Stefanović, and N. Puškaš, “Fractal analysis of dendrite morphology using modified box-counting method,” Neuroscience Research, vol. 84, pp. 64–67, 2014. View at Publisher · View at Google Scholar · View at Scopus
  10. N. T. Milošević, G. N. Elston, B. Krstonošić, and N. Rajković, “Box-count analysis of two dimensional images: methodology, analysis and classification,” in Proceedings of the 19th International Conference on Control Systems and Computer Science (CSCS '13), pp. 306–312, IEEE, Bucharest, Romania, May 2013. View at Publisher · View at Google Scholar · View at Scopus
  11. A. Reichenbach, A. Siegel, D. Senitz, and T. G. Smith Jr., “A comparative fractal analysis of various mammalian astroglial cell types,” Neuroimage, vol. 1, no. 1, pp. 69–77, 1992. View at Publisher · View at Google Scholar · View at Scopus
  12. T.-G. Li, S. Wang, and N. Zhao, “Fractal research of pathological tissue images,” Computerized Medical Imaging and Graphics, vol. 31, no. 8, pp. 665–671, 2007. View at Publisher · View at Google Scholar · View at Scopus
  13. R. Uppaluri, E. A. Hoffman, M. Sonka, P. G. Hartley, G. W. Hunninghake, and G. McLennan, “Computer recognition of regional lung disease patterns,” American Journal of Respiratory and Critical Care Medicine, vol. 160, no. 2, pp. 648–654, 1999. View at Publisher · View at Google Scholar · View at Scopus
  14. A. Wainwright, G. Liew, G. Burlutsky et al., “Effect of image quality, color, and format on the measurement of retinal vascular fractal dimension,” Investigative Ophthalmology & Visual Science, vol. 51, no. 11, pp. 5525–5529, 2010. View at Publisher · View at Google Scholar · View at Scopus
  15. T. MacGillivray and N. Patton, “A reliability study of fractal analysis of the skeletonised vascular network using the ‘box-counting’ technique,” in Proceedings of the 28th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBS '06), pp. 4445–4448, IEEE, New York, NY, USA, 2006.
  16. M. B. M. Mendonça, C. A. A. Garcia, R. A. Nogueira, M. A. F. Gomes, M. M. Valença, and F. Oréfice, “Fractal analysis of retinal vascular tree: segmentation and estimation methods,” Arquivos Brasileiros de Oftalmologia, vol. 70, no. 3, pp. 413–422, 2007. View at Publisher · View at Google Scholar · View at Scopus
  17. F. Huang, J. Zhang, E. Bekkers, B. Dashtbozorg, and B. ter Haar Romeny, “Stability analysis of fractal dimension in retinal vasculature,” in Proceedings of the Ophthalmic Medical Image Analysis Second International Workshop (OMIA '15) Held in Conjunction with MICCAI, X. Chen, M. K. Garvin, J. Liu, E. Trucco, and Y. Xu, Eds., Lecture Notes in Computer Science, pp. 1–8, Springer, Munich, Germany, October 2015.
  18. A. F. Frangi, W. J. Niessen, K. L. Vincken, and M. A. Viergever, “Multiscale vessel enhancement filtering,” in Medical Image Computing and Computer-Assisted Interventation—MICCAI'98, W. M. Wells, A. Colchester, and S. Delp, Eds., vol. 1496 of Lecture Notes in Computer Science, pp. 130–137, Springer, Berlin, Germany, 1998. View at Publisher · View at Google Scholar
  19. J. V. B. Soares, J. J. G. Leandro, R. M. Cesar Jr., H. F. Jelinek, and M. J. Cree, “Retinal vessel segmentation using the 2-D Gabor wavelet and supervised classification,” IEEE Transactions on Medical Imaging, vol. 25, no. 9, pp. 1214–1222, 2006. View at Publisher · View at Google Scholar · View at Scopus
  20. J. Zhang, E. Bekkers, S. Abbasi, B. Dashtbozorg, and B. ter Haar Romeny, “Robust and fast vessel segmentation via gaussian derivatives in orientation scores,” in Image Analysis and Processing—ICIAP 2015: 18th International Conference, Genoa, Italy, September 7–11, 2015, Proceedings, Part I, V. Murino and E. Puppo, Eds., vol. 9279 of Lecture Notes in Computer Science, pp. 537–547, Springer, Berlin, Germany, 2015. View at Publisher · View at Google Scholar
  21. E. Decencière, X. Zhang, G. Cazuguel et al., “Feedback on a publicly distributed image database: the Messidor database,” Image Analysis and Stereology, vol. 33, no. 3, pp. 231–234, 2014. View at Publisher · View at Google Scholar · View at Scopus
  22. J. Staal, M. D. Abràmoff, M. Niemeijer, M. A. Viergever, and B. Van Ginneken, “Ridge-based vessel segmentation in color images of the retina,” IEEE Transactions on Medical Imaging, vol. 23, no. 4, pp. 501–509, 2004. View at Publisher · View at Google Scholar · View at Scopus
  23. M. Foracchia, E. Grisan, and A. Ruggeri, “Luminosity and contrast normalization in retinal images,” Medical Image Analysis, vol. 9, no. 3, pp. 179–190, 2005. View at Publisher · View at Google Scholar · View at Scopus
  24. S. Abbasi-Sureshjani, I. Smit-Ockeloen, J. Zhang, and B. ter Haar Romeny, “Biologically-inspired supervised vasculature segmentation in SLO retinal fundus images,” in Image Analysis and Recognition: 12th International Conference, ICIAR 2015, Niagara Falls, ON, Canada, July 22–24, 2015, Proceedings, vol. 9164 of Lecture Notes in Computer Science, pp. 325–334, Springer, Berlin, Germany, 2015. View at Publisher · View at Google Scholar
  25. T. D. Williams and J. M. Wilkinson, “Position of the fovea centralis with respect to the optic nerve head,” Optometry & Vision Science, vol. 69, no. 5, pp. 369–377, 1992. View at Publisher · View at Google Scholar · View at Scopus
  26. E. Bekkers, R. Duits, and M. Loog, “Training of templates for object recognition in invertible orientation scores: application to optic nerve head detection in retinal images,” in Energy Minimization Methods in Computer Vision and Pattern Recognition, X. C. Tai, E. Bae, T. Chan, and M. Lysaker, Eds., vol. 8932 of Lecture Notes in Computer Science, pp. 464–477, Springer, 2015. View at Google Scholar
  27. J. M. Geusebroek, R. van den Boomgaard, A. Smeulders, and A. Dev, “Color and scale: the spatial structure of color images,” in Computer Vision—ECCV 2000: 6th European Conference on Computer Vision Dublin, Ireland, June 26–July 1, 2000 Proceedings, Part I, vol. 1842 of Lecture Notes in Computer Science, pp. 331–341, Springer, Berlin, Germany, 2000. View at Publisher · View at Google Scholar
  28. B. ter Haar Romeny, J. M. Geusebroek, P. Van Osta, R. van den Boomgaard, and J. Koenderink, “Color differential structure,” in Scale-Space and Morphology in Computer Vision, M. Kerckhove, Ed., vol. 2106 of Lecture Notes in Computer Science, pp. 353–361, Springer, Berlin, Germany, 2001. View at Google Scholar
  29. L. S. Liebovitch and T. Toth, “A fast algorithm to determine fractal dimensions by box counting,” Physics Letters A, vol. 141, no. 8-9, pp. 386–390, 1989. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. K. Falconer, Fractal Geometry: Mathematical Foundations and Applications, John Wiley & Sons, 2004. View at Publisher · View at Google Scholar
  31. A. Rényi, “On the dimension and entropy of probability distributions,” Acta Mathematica Academiae Scientiarum Hungaricae, vol. 10, no. 1-2, pp. 193–215, 1959. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  32. D. Harte, Multifractals: Theory and Applications, CRC Press, 2001.