Caractérisation de la géométrie locale et globale de textures directionnelles par reconstruction d'hypersurfaces et transformations d'espace : application à l'analyse stratigraphique des images sismiques

Abstract : Directional textures are the particular class of textured images representing hypersurfaces (dermal lines, material fibers, seismic horizons, etc.). For this type of textures, the reconstruction of hypersurfaces describes their geometry and structure. From the preliminary estimation of the orientation field, reconstructions can be obtained by means of the minimization of a partial differential equation under constraints, linearized and iteratively resolved in the Fourier domain.In this work, the reconstructions of hypersurfaces are considered as means of description both upstream and downstream of the geometry of the directional textures. In an upstream approach, the reconstruction of local and dense streams of hypersurfaces leads to a spatial transformation model to locally unfold the texture or its gradient field and to improve the estimation of the orientation field compared with the classic tensor structure. In a downstream approach, reconstructions of hypersurfaces carried out on any polygonal supports, either isolated or imbricated, lead to more accurate reconstructions than existing methods. The proposed approaches implement chains of conformal space transformations (transformation of Schwarz-Christoffel, Möbius, etc.) in order to respect the constraints and to access fast PDE solution schemes.
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Salma Doghraji. Caractérisation de la géométrie locale et globale de textures directionnelles par reconstruction d'hypersurfaces et transformations d'espace : application à l'analyse stratigraphique des images sismiques. Automatique / Robotique. Université de Bordeaux, 2017. Français. ⟨NNT : 2017BORD0814⟩. ⟨tel-01731593⟩

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