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Classification in functional spaces using the BV norm with applications to ophthalmologic images and air traffic complexity

Abstract : In this thesis, we deal with two different problems using Total Variation concept. The first problem concerns the classification of vasculitis in multiple sclerosis fundus angiography, aiming to help ophthalmologists to diagnose such autoimmune diseases. It also aims at determining potential angiography details in intermediate uveitis in order to help diagnosing multiple sclerosis. The second problem aims at developing new airspace congestion metric, which is an important index that is used for improving Air Traffic Management (ATM) capacity. In the first part of this thesis, we provide preliminary knowledge required to solve the above-mentioned problems. First, we present an overview of the Total Variation and express how it is used in our methods. Then, we present a tutorial on Support Vector Machines (SVMs) which is a learning algorithm used for classification and regression. In the second part of this thesis, we first provide a review of methods for segmentation and measurement of blood vessel in retinal image that is an important step in our method. Then, we present our proposed method for classification of retinal images. First, we detect the diseased region in the pathological images based on the computation of BV norm at each point along the centerline of the blood vessels. Then, to classify the images, we introduce a feature extraction strategy to generate a set of feature vectors that represents the input image set for the SVMs. After that, a standard SVM classifier is applied in order to classify the images. Finally, in the third part of this thesis, we address two applications of TV in the ATM domain. In the first application, based on the ideas developed in the second part, we introduce a methodology to extract the main air traffic flows in the airspace. Moreover, we develop a new airspace complexity indicator which can be used to organize air traffic at macroscopic level. This indicator is then compared to the regular density metric which is computed just by counting the number of aircraft in the airspace sector. The second application is based on a dynamical system model of air traffic. We propose a method for developing a new traffic complexity metric by computing the local vectorial total variation norm of the relative deviation vector field. Its aim is to reduce complexity. Three different traffic situations are investigated to evaluate the fitness of the proposed method.
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Submitted on : Tuesday, November 25, 2014 - 11:35:02 AM
Last modification on : Tuesday, October 19, 2021 - 11:02:48 AM
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  • HAL Id : tel-01086942, version 1



Bang Giang Nguyen. Classification in functional spaces using the BV norm with applications to ophthalmologic images and air traffic complexity. Optimization and Control [math.OC]. Université de Toulouse 3 Paul Sabatier, 2014. English. ⟨tel-01086942⟩



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