الفهرس 
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Abstract
Over the past several decades advanced mathematics has quietly insinuated itself into many facets of our day to day life. Mathematics is at the heart of technologies serving human needs. In fact, the process of utilizing mathematics is often much more important than the actual content. In addition to problem solving, Mathematics should be used in phenomena modeling, logical reasoning, generalizing and of course for serving in better living. Arguably no technology has had a more positive and profound eect on our lives than advances in medical imaging and in no technology is the role of mathematics more pronounced. Partial differential equation (PDE) methods have been widely used in the field of medical image analysis. Examples include invariant shape analysis, image segmentation, image restoration, and image registration. The basic idea is to represent an image as a function. In this Thesis, we plan to develop fast PDE-based approach for accurate analysis of human retina layers from optical coherence tomography (OCT) images. In this dissertation, we discuss the mathematical basis of level set approach to apply in different engineering field, specifically solving the segmentation difficulties related to image processing. We developed joint models to get better segmentation results. In order to measure the accuracy of our approach, We conducted the experiments extensively on medical images collected from eye institutes in Louisville and Massachusetts to validate the performance of our developed technique and also, prove the effectiveness and reasonability of the proposed models. We integrate the whole work of the introduced models in the all chapters in designing a computer aided diagnostic (CAD) system to show the assets of these models in getting such system. Because accurate diagnosis is a must for successful timely treatment, the identification can be notably improved by employing disease-specific CAD systems based on optical coherence tomography (OCT). To the best of our knowledge, the proposed CAD system is the first to use and segment the OCT scans into 12 distinct layers for early detecting of diabetic retinopathy (DR).