Topological tools for discrete shape analysis

Abstract : These last years, the domain of image analysis has drastically evolved. Digital topology offer a set of tools adapted to image analysis, especially the skeletonization process (also called homotopic thinning) which can simplify input data while keeping specific information untouched. In this thesis, we focus on how digital topology, especially skeletons, can help material image analysis.The goal of a skeletonization process is to remove unnecessary information from an input, and provide a simplified object, called the skeleton, having the same characteristics than the original data. It is then possible to perform some computations on the skeleton and generalise their results to the original data. In the first part of this thesis, we propose some new tools for preserving, during skeletonization, important geometrical features of the original data, and obtain a skeleton with the same visual appearance than the input.In the second part, we present the cubical complex framework, where objects are no more made only of voxels. We propose in this framework new skeletonization algorithms, some of them preserving automatically the visual aspect of the input during the thinning process (no filtering parameter from the user is required). We then show how a skeleton, in the cubical complexes framework, can be decomposed into basic parts, and we show some applications of these algorithms to material image analysis and medical image analysis
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John Chaussard. Topological tools for discrete shape analysis. Modeling and Simulation. Université Paris-Est, 2010. English. ⟨NNT : 2010PEST1011⟩. ⟨tel-00587411⟩

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