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

References

• Cunha-Vaz J. Diabetic retinopathy. Singapore: World Scientific Publishing Co. Pte. Ltd.; 2011
   Google Scholar
• Chakrabarti M, Stephen V, John SR, Chakrabarti A. Management strategies in diabetic macular edema. Kerala J Ophthalmol 2009;XXI:7–24
   Google Scholar
• Talu S, Talu M, Giovanzana S, Shah R. The history and use of optical coherence tomography in ophthalmology. HVM Bioflux 2011;3:29–32
   Google Scholar
• Talu S, Balta F, Talu SD, Merticariu A, Talu M. Fourier domain – optical coherence tomography in diagnosing and monitoring of retinal diseases. IFMBE Proceedings MEDITECH; Cluj-Napoca, Romania; Vol. 26. Heidelberg, Germany: Springer-Verlag GmbH; 2009. pp 261–266
   Google Scholar
• Holz FG, Spaide RF, editors. Medical retina. Focus on retinal imaging. Berlin, Heidelberg, Germany: Springer-Verlag; 2010
   Google Scholar
• Patton N, Aslam TM, MacGillivray T, Deary IJ, Dhillon B, Eikelboom RH, et al. Retinal image analysis: concepts, applications and potential. Prog Retin Eye Res 2006;25:99–127
   PubMed Web of Science ®Google Scholar
• Mandelbrot BB. The fractal geometry of nature. San Francisco (CA): W. H. Freeman; 1982
   Google Scholar
• Grizzi F, Chiriva-Internati M. The complexity of anatomical systems. Theor Biol Med Modell 2005;2:26 . doi:10.1186/1742-4682-2-26
   PubMed Web of Science ®Google Scholar
• Nailon WH. Texture analysis methods for medical image characterisation. In: Mao Y, editor. Biomedical imaging. Croatia: InTech; 2010. pp 75–100
   Google Scholar
• Reljin IS, Reljin BD. Fractal geometry and multifractals in analyzing and processing medical data and images. Arch Oncol 2002;10:283–293
   Google Scholar
• Kenkel NC, Walker DJ. Fractals in the biological sciences. Coenoses 1996;11:77–100
   Google Scholar
• Losa GA, Merlini D, Nonnenmacher TF, Weibel E, editors. Fractals in biology and medicine. Vol. IV. Mathematics and bioscience in interaction. Basel, Switzerland: Birkhäuser Verlag; 2005
   Google Scholar
• Nilsson E. Multifractal-based image analysis with applications in medical imaging [master’s thesis]. Sweden: Umea University; 2007
   Google Scholar
• Talu S. Mathematical methods used in monofractal and multifractal analysis for the processing of biological and medical data and images. ABAH Bioflux 2012;4:1–4
   Google Scholar
• Talu S. Texture analysis methods for the characterisation of biological and medical images. ELBA Bioflux 2012;4:8–12
   Google Scholar
• Sztojánov I, Crişan DA, Mina CP, Voinea V. Image processing in biology based on the fractal analysis. In: Chen Y-S, editor. Image processing. Croatia: InTech; 2009. pp 323–344
   Google Scholar
• Family F, Masters BR, Platt DE. Fractal pattern formation in human retinal vessels. Physica D 1989;38:98–103
   Web of Science ®Google Scholar
• Lakshminanarayanan V, Raghuram A, Myerson JW, Varadharajan S. The fractal dimension in retinal pathology. J Modern Optics 2003;50:1701–1703
   Web of Science ®Google Scholar
• Masters BR. Fractal analysis of the vascular tree in the human retina. Annu Rev Biomed Eng 2004;6:427–452
   PubMed Web of Science ®Google Scholar
• Talu S. Fractal analysis of normal retinal vascular network. Oftalmologia 2011;55:11–16
   PubMedGoogle Scholar
• Talu S, Giovanzana S. Fractal and multifractal analysis of human retinal vascular network: a review. HVM Bioflux 2011;3:205–212
   Google Scholar
• Talu S, Giovanzana S. Image analysis of the normal human retinal vasculature using fractal geometry. HVM Bioflux 2012;4:14–18
   Google Scholar
• Liew G, Wang JJ, Cheung N, Zhang YP, Hsu W, Lee ML, et al. The retinal vasculature as a fractal: methodology, reliability, and relationship to blood pressure. Ophthalmology 2008;115:1951–1956
   PubMed Web of Science ®Google Scholar
• Liew G, Wang JJ, Mitchell P, Wong TY. Retinal vascular imaging: a new tool in microvascular disease research. Circ Cardiovasc Imaging 2008;1:156–161
   PubMed Web of Science ®Google Scholar
• Cheung N, Donaghue KC, Liew G, Rogers SL, Wang JJ, Lim SW, et al. Quantitative assessment of early diabetic retinopathy using fractal analysis. Diabetes Care 2009;32:106–110
   PubMed Web of Science ®Google Scholar
• Lopes R, Betrouni N. Fractal and multifractal analysis: a review. Med Image Anal 2009;13:634–649
   PubMed Web of Science ®Google Scholar
• Talu S. Mathematical models of human retina. Oftalmologia 2011;55:74–81
   PubMedGoogle Scholar
• Kyriacos S, Nekka F, Vicco P, Cartilier L. The retinal vasculature: towards an understanding of the formation process. In: Vehel LJ, Lutton E, Tricot G, editors. Fractals in engineering – from theory to industrial applications. Germany: Springer; 1997. pp 383–397
   Google Scholar
• MacGillivray TJ, Patton N, Doubal FN, Graham C, Wardlaw JM. Fractal analysis of the retinal vascular network in fundus images. Conf Proc IEEE Eng Med Biol Soc 2007;1:6455–6458
   Google Scholar
• Perfect E, Tarquis AM, Bird NRA. Accuracy of generalized dimensions estimated from grayscale images using the method of moments. Fractals 2009;17:351–363
   Web of Science ®Google Scholar
• Wainwright A, Liew G, Burlutsky G, Rochtchina E, Zhang YP, Hsu W, et al. Effect of image quality, color, and format on the measurement of retinal vascular fractal dimension. Invest Ophthalmol Vis Sci 2010;51:5525–5529
   PubMed Web of Science ®Google Scholar
• Jelinek HF, Mendonça MBdM, Oréfice F, Garcia CAdA, Nogueira RA, Soares JVB, Junior RCM. Fractal analysis of the normal human retinal vasculature. Internet J Ophthalmol Vis Sci 2010;8 . DOI: 10.5580/1a6a
   Google Scholar
• Azemin MZ, Kumar DK, Wong TY, Kawasaki R, Mitchell P, Wang JJ. Robust methodology for fractal analysis of the retinal vasculature. IEEE Trans Med Imaging 2011;30:243–250
   PubMed Web of Science ®Google Scholar
• Ivanovici M, Richard N. Fractal dimension of color fractal images. IEEE Trans Image Process 2011;20:227–235
   PubMed Web of Science ®Google Scholar
• Avakian A, Kalina RE, Sage EH, Rambhia AH, Elliott KE, Chuang EL, et al. Fractal analysis of region-based vascular change in the normal and non-proliferative diabetic retina. Curr Eye Res 2002;24:274–280
   PubMed Web of Science ®Google Scholar
• Kunicki AC, Oliveira AJ, Mendonça MB, Barbosa CT, Nogueira RA. Can the fractal dimension be applied for the early diagnosis of non-proliferative diabetic retinopathy? Braz J Med Biol Res 2009;42:930–934
   PubMed Web of Science ®Google Scholar
• Walter T, Klein JC. Automatic analysis of color fundus photographs and its application to the diagnosis of diabetic retinopathy. In: Suri SJ, Wilson DL, Laxminarayan L, editors. Handbook of biomedical image analysis. Vol. II: Segmentation models, Part B. Chap. 7. New York: Kluwer Academic/Plenum Publishers; 2005. pp 315–368
   Google Scholar
• Stosic T, Stosic B. Multifractal analysis of human retinal vessels. IEEE Trans Med Imaging 2006;25:1101–1107
   PubMed Web of Science ®Google Scholar
• Gould DJ, Vadakkan TJ, Poché RA, Dickinson ME. Multifractal and lacunarity analysis of microvascular morphology and remodeling. Microcirculation 2011;18:136–151
   PubMed Web of Science ®Google Scholar
• Talu S. Multifractal characterization of human retinal blood vessels. Oftalmologia 2012;56:63–71
   PubMedGoogle Scholar
• Chhabra A, Jensen RV. Direct determination of the f(alpha) singularity spectrum. Phys Rev Lett 1989;62:1327–1330
   PubMed Web of Science ®Google Scholar
• Telesca L, Colangelo G, Lapenna V, Macchiato M. Monofractal and multifractal characterization of geoelectrical signals measured in southern Italy. Chaos Solitons Fractals 2003;18:385–399
   Web of Science ®Google Scholar
• Image Sciences Institute. DRIVE: digital retinal images for vessel extraction. Available from: http://www.isi.uu.nl/Research/Databases/DRIVE/ [last accessed 1 June 2012]
   Google Scholar
• Niemeijer M, Staal JJ, van Ginneken B, Loog M, Abramoff MD. Comparative study of retinal vessel segmentation methods on a new publicly available database. In: Michael Fitzpatrick J, Sonka M, editors. SPIE medical imaging. Vol. 5370. Bellingham (WA): SPIE; 2004. pp 648–656
   Google Scholar
• Staal JJ, Abramoff MD, Niemeijer M, Viergever MA, van Ginneken B. Ridge-based vessel segmentation in color images of the retina. IEEE Trans Med Imaging 2004;23:501–509
   PubMed Web of Science ®Google Scholar
• Image J software, version ImageJ 1.47d. Bethesda (MD): Wayne Rasband, National Institutes of Health. Available from: http://imagej.nih.gov/ij [last accessed 1 June 2012]
   Google Scholar
• FracLac V 2.5 for Image J software. A. Karperien Charles Sturt University, Australia. Available from: http://rsbweb.nih.gov/ij/plugins/fraclac/FLHelp/Introduction.htm [last accessed 1 June 2012]
   Google Scholar
• GraphPad InStat software, version 3.20. San Diego (CA): GraphPad. Available from: http://www.graphpad.com/instat/instat.htm [last accessed 1 June 2012]
   Google Scholar