Fractal Dimension with Object Rotation: A Case Study with Glaucoma Eye

Abstract

The present research work explores application of perimeter method to determine fractal dimension for both glaucoma and non glaucoma eye. Fractal dimension is a real value treated as over simplified diagnostics parameter to determine earlier detection of glaucoma. A perimeter method is a well known method adopted to determine the fractal dimension of natural objects such as leaves and some biological organs. But no attempt has been made to consider importance of selecting an initial point and rotation of object to determine the fractal dimension. Hence this work explains procedure to determine fractal dimension considering rotation of object and selecting the initial point. The results obtained signify that rotation of object and selecting the initial point definitely influences fractal dimension for glaucoma eye, as found in this present case study. The fractal dimension found to be lesser for glaucoma eye because of attaining regular shape of optic cup and it is accounted by losses of optic nerve and blood vessels in different stages. The fractal dimension could be treated as an alternative method for manual deduction of glaucoma through cup-disc diameter ratio by ophthalmologist. The author concludes that as soon as eye attacked by glaucoma disease, fractal dimension starts to decrease leading to lesser values. The fractal dimension values found to be in the range of 1.4242 to 1.5986 for glaucoma and for non glaucoma 1.8643 to 2.3027. Hence fractal dimension as soon as it reaches 1.5986 (1.6) signifies earlier detection of glaucoma. The rotation of object also considered in the interval of 600 (00 to 3000) to determine the fractal dimension. One more finding is that transforming from irregular shape of optic cup to regular shape from non-glaucoma to glaucoma could be visualized in different stages of images, under section four.