Étude des fonctions B-splines pour la fusion d'images segmentées par approche bayésienne

Abstract : In this thesis we are treated the problem of nonparametric estimation probability distributions. At first, we assumed that the unknown density f was approximated by a basic mixture quadratic B-spline. Then, we proposed a new estimate of the unknown density function f based on quadratic B-splines, with two methods estimation. The first is based on the maximum likelihood method and the second is based on the Bayesian MAP estimation method. Then we have generalized our estimation study as part of the mixture and we have proposed a new estimator mixture of unknown distributions based on the adapted estimation of two methods. In a second time, we treated the problem of semi supervised statistical segmentation of images based on the hidden Markov model and the B-sline functions. We have shown the contribution of hybridization of the hidden Markov model and B-spline functions in unsupervised Bayesian statistical image segmentation. Thirdly, we presented a fusion approach based on the maximum likelihood method, through the nonparametric estimation of probabilities, for each pixel of the image. We then applied this approach to multi-spectral and multi-temporal images segmented by our nonparametric and unsupervised algorithm.
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Atizez Hadrich Ben Arab. Étude des fonctions B-splines pour la fusion d'images segmentées par approche bayésienne. Statistiques [math.ST]. Université du Littoral Côte d'Opale, 2015. Français. ⟨NNT : 2015DUNK0385⟩. ⟨tel-01306291⟩

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