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Theses

Analyse d’image geometrique et morphometrique par diagrammes de forme et voisinages adaptatifs generaux

Abstract : Minkowski functionals define set topological and geometrical measurements, insufficient for the characterization, because different sets may have the same functionals. Thus, other shape functionals, geometrical and morphometrical are used. A shape diagram, defined thanks to two morphometrical functionals, provides a representation allowing the study of set shapes. In quantitative image analysis, these functionals and diagrams are often limited to binary images and achieved in a global and monoscale way. The General Adaptive Neighborhoods (GANs) simultaneously adaptive with the analyzing scales, the spatial structures and the image intensities, enable to overcome these limitations. The GAN-based Minkowski functionals are introduced, which allow a gray-tone image analysis to be realized in a local, adaptive and multiscale way.The GANs, defined around each point of the spatial support of a gray-tone image, are homogeneous with respect to an analyzing criterion function represented in an algebraic model, according to an homogeneity tolerance. The shape functionals computed on the GAN of each point of the spatial support of the image, define the so-called GAN-based shape maps. The map histograms and diagrams provide statistical distributions of the shape of the gray-tone image local structures, contrary to the classical histogram that provides a global distribution of image intensities. The impact of axiomatic criteria variations is analyzed through these maps, histograms and diagrams. Thus, multiscale maps are built, defining GAN-based shape functions.
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Séverine Rivollier. Analyse d’image geometrique et morphometrique par diagrammes de forme et voisinages adaptatifs generaux. Autre. Ecole Nationale Supérieure des Mines de Saint-Etienne, 2010. Français. ⟨NNT : 2010EMSE0575⟩. ⟨tel-00560838v2⟩

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