Développement de méthodes de traitement d'images pour la détermination de paramètres variographiques locaux

Abstract : Geostatistics provides many tools to characterize and deal with data spread in space. Most of these tools are based on the analysis and the modeling of a function called variogram. By characterizing the spatial correlation inherent to any data set, the variogram enables to build different spatial operators as estimation (kriging) and simulation ones. Variographic models are relatively intuitive: some variographic parameters can directly be interpreted as structural characteristics. These approaches are however limited since they are not enable to properly take into account the local data structure. There are several types of non-stationary geostatistical models. However, they are difficult to use in practice because they need a complicated, not really intuitive setting. Besides, they are not enable to take into account some types of non-stationarity. In order to answer the need for an effective and efficient consideration of non-stationarity of a data set, we have chosen, in the context of this PhD thesis, to compute local variographic parameters, called Moving Parameters (M-Parameters), by using image processing methods. Our approach relies mainly on the determination of morphological parameters of size and dimension. It follows from the determination of M-Parameters a better match between variographic models and structural characteristics of the data. These different methods for computing M-Parameters have been applied to bathymetry data, to data revealing complex geological bodies and to environmental data sets, such as air pollution in urban areas for example. These examples illustrate the improvements in the results of the geostatistical process using M-Parameters. Finally, based on the observation that some phenomena do not respect an euclidean metric (such as air pollution in urban areas), we have studied the influence of the choice of the distance metric on kriging results. Using geodesic distances, we have been able to obtain kriging results which are impossible to reproduce with an euclidean distance.
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Jean Felder. Développement de méthodes de traitement d'images pour la détermination de paramètres variographiques locaux. Traitement du signal et de l'image [eess.SP]. École Nationale Supérieure des Mines de Paris, 2011. Français. ⟨NNT : 2011ENMP0076⟩. ⟨pastel-00681301⟩

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