Ştefan Ţălu1, Sebastian Stach2, Dan Mihai Călugăru3, Carmen Alina Lupaşcu4, Simona Delia Nicoară3. 1. Discipline of Descriptive Geometry and Engineering Graphics, Department of AET, Faculty of Mechanical Engineering, Technical University of Cluj-Napoca, 103-105 B-dul Muncii St., Cluj-Napoca 400641, Cluj, Romania. 2. Department of Biomedical Computer Systems, Institute of Informatics, Faculty of Computer Science and Materials Science, University of Silesia, Będzińska 39, 41-205 Sosnowiec, Poland. 3. Discipline of Ophthalmology, Department of Surgical Specialties and Medical Imaging, Faculty of Medicine, "Iuliu Haţieganu" University of Medicine and Pharmacy Cluj-Napoca, 8 Victor Babeş St., Cluj-Napoca 400012, Cluj, Romania. 4. Department of Mathematics and Informatics, University of Palermo, Via Archirafi 34, Palermo 90123, Italy.
Abstract
AIM: To apply the multifractal analysis method as a quantitative approach to a comprehensive description of the microvascular network architecture of the normal human retina. METHODS: Fifty volunteers were enrolled in this study in the Ophthalmological Clinic of Cluj-Napoca, Romania, between January 2012 and January 2014. A set of 100 segmented and skeletonised human retinal images, corresponding to normal states of the retina were studied. An automatic unsupervised method for retinal vessel segmentation was applied before multifractal analysis. The multifractal analysis of digital retinal images was made with computer algorithms, applying the standard box-counting method. Statistical analyses were performed using the GraphPad InStat software. RESULTS: The architecture of normal human retinal microvascular network was able to be described using the multifractal geometry. The average of generalized dimensions (Dq ) for q=0, 1, 2, the width of the multifractal spectrum (Δα=αmax - αmin ) and the spectrum arms' heights difference (|Δf|) of the normal images were expressed as mean±standard deviation (SD): for segmented versions, D0 =1.7014±0.0057; D1 =1.6507±0.0058; D2 =1.5772±0.0059; Δα=0.92441±0.0085; |Δf|= 0.1453±0.0051; for skeletonised versions, D0 =1.6303±0.0051; D1 =1.6012±0.0059; D2 =1.5531±0.0058; Δα=0.65032±0.0162; |Δf|= 0.0238±0.0161. The average of generalized dimensions (Dq ) for q=0, 1, 2, the width of the multifractal spectrum (Δα) and the spectrum arms' heights difference (|Δf|) of the segmented versions was slightly greater than the skeletonised versions. CONCLUSION: The multifractal analysis of fundus photographs may be used as a quantitative parameter for the evaluation of the complex three-dimensional structure of the retinal microvasculature as a potential marker for early detection of topological changes associated with retinal diseases.
AIM: To apply the multifractal analysis method as a quantitative approach to a comprehensive description of the microvascular network architecture of the normal human retina. METHODS: Fifty volunteers were enrolled in this study in the Ophthalmological Clinic of Cluj-Napoca, Romania, between January 2012 and January 2014. A set of 100 segmented and skeletonised human retinal images, corresponding to normal states of the retina were studied. An automatic unsupervised method for retinal vessel segmentation was applied before multifractal analysis. The multifractal analysis of digital retinal images was made with computer algorithms, applying the standard box-counting method. Statistical analyses were performed using the GraphPad InStat software. RESULTS: The architecture of normal human retinal microvascular network was able to be described using the multifractal geometry. The average of generalized dimensions (Dq ) for q=0, 1, 2, the width of the multifractal spectrum (Δα=αmax - αmin ) and the spectrum arms' heights difference (|Δf|) of the normal images were expressed as mean±standard deviation (SD): for segmented versions, D0 =1.7014±0.0057; D1 =1.6507±0.0058; D2 =1.5772±0.0059; Δα=0.92441±0.0085; |Δf|= 0.1453±0.0051; for skeletonised versions, D0 =1.6303±0.0051; D1 =1.6012±0.0059; D2 =1.5531±0.0058; Δα=0.65032±0.0162; |Δf|= 0.0238±0.0161. The average of generalized dimensions (Dq ) for q=0, 1, 2, the width of the multifractal spectrum (Δα) and the spectrum arms' heights difference (|Δf|) of the segmented versions was slightly greater than the skeletonised versions. CONCLUSION: The multifractal analysis of fundus photographs may be used as a quantitative parameter for the evaluation of the complex three-dimensional structure of the retinal microvasculature as a potential marker for early detection of topological changes associated with retinal diseases.
Authors: Jakob Grauslund; Anders Green; Ryo Kawasaki; Lauren Hodgson; Anne Katrin Sjølie; Tien Y Wong Journal: Ophthalmology Date: 2010-02-21 Impact factor: 12.079
Authors: Laurence Shen Lim; Carol Yim-Lui Cheung; Charumathi Sabanayagam; Su Chi Lim; E Shyong Tai; Lei Huang; Tien Yin Wong Journal: Invest Ophthalmol Vis Sci Date: 2013-04-26 Impact factor: 4.799
Authors: Gerald Liew; Jie Jin Wang; Ning Cheung; Yong Ping Zhang; Wynne Hsu; Mong Li Lee; Paul Mitchell; Gabriella Tikellis; Bronwen Taylor; Tien Yin Wong Journal: Ophthalmology Date: 2008-08-09 Impact factor: 12.079
Authors: Peter M Maloca; Richard F Spaide; Emanuel Ramos de Carvalho; Harald P Studer; Pascal W Hasler; Hendrik P N Scholl; Tjebo F C Heeren; Julia Schottenhamml; Konstantinos Balaskas; Adnan Tufail; Catherine Egan Journal: Graefes Arch Clin Exp Ophthalmol Date: 2020-01-06 Impact factor: 3.117