title: Analysis of normal human retinal vascular network architecture using multifractal geometry.
abstract: OBJECTIVE
  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) forq=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) forq=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.
  
  
  CONCLUSIONS
  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.affiliation: 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.
authors.forename: Ştefan
authors.initials: Ş
authors.lastname: Ţălu
authors.affiliation: Department of Biomedical Computer Systems, Institute of Informatics, Faculty of Computer Science and Materials Science, University of Silesia, Będzińska 39, 41-205 Sosnowiec, Poland.
authors.forename: Sebastian
authors.initials: S
authors.lastname: Stach
authors.affiliation: 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.
authors.forename: Dan Mihai
authors.initials: DM
authors.lastname: Călugăru
authors.affiliation: Department of Mathematics and Informatics, University of Palermo, Via Archirafi 34, Palermo 90123, Italy.
authors.forename: Carmen Alina
authors.initials: CA
authors.lastname: Lupaşcu
authors.affiliation: 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.
authors.forename: Simona Delia
authors.initials: SD
authors.lastname: Nicoară
keywords: generalized dimensions; multifractal; retinal image analysis; retinal microvasculature; retinal vessel segmentation; standard box-counting method