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Theses

Distance entre distributions : application à l'imagerie médicale et à l'aéronautique

Abstract : In the medical field, over the past two decades, a growing number of quantitative image analysis have been developed including regions of interest analysis, voxel-by-voxel analysis and histogram analysis. The latter is widely use in Multiple Sclerosis research to quantify the diffuse pathological prominent in this disease. A disadvantage of this approach is that all the information included in the histogram is not exploited; only arbitrary measures are chosen to describe the histogram; including the average, the median, the percentiles... Thus, first, we proposed to integrate in a classifier all the information included in the histogram and not just some local descriptors, in order to improve the classification performance of the Multiple Sclerosis populations (i.e. groups in therapeutic trials and in fine groups at different prognosis). Thereafter, given that the histogram is an overly simplistic estimate of a probability distribution, we present one of the possible applications of information geometry on probability distributions and we demonstrate the interest of using non-Euclidean geometry in the context of the Alzheimer’s disease population classification. Furthermore, we have made the analogy with the field of aeronautics, specifically in the study of flight delays. Indeed, the analysis currently carried out is at a macroscopic level and provides an indicator of average delay, without considering the intermediate mechanisms that may lead to the final delays. Thus, in the clustering of airport delays, we have replaced the average indicator with a more complete parametric statistical model : Distributions.
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Sana Rebbah. Distance entre distributions : application à l'imagerie médicale et à l'aéronautique. Optimisation et contrôle [math.OC]. Université Toulouse 3 Paul Sabatier, 2019. Français. ⟨NNT : 2019TOU30124⟩. ⟨tel-02557245⟩

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