In the proposed thesis, we address two challenges related to skeletons. The first is to formulate novel ways to define and compute curve skeletons - a specific type of skeleton. The second is to employ skeletons to enhance surface reconstruction for geometry affected by severe amounts of missing data. In solving these challenges we discuss three different approaches. In the first approach we focus our attention to watertight geometry. We propose a curve skeletonization algorithm that evolves the shapeu27s surface towards a curve by means of a motion that accentuates its local shape anisotropy. In the second approach we shift our attention to acquired data, where severe amounts of missing data introduce a significant challenge. To tackle this issue, we propose a technique that robustly extracts curve skeletons by interpreting its branches as local axes of rotational symmetry. We also propose an application that, by exploiting the extracted skeletons, helps to repair the data by performing a skeleton-based volumetric inpainting. Our last approach further explores the idea of volumetric inpainting by replacing curve skeletons with medial skeletons. Thanks to the fact that medial skeletons provide a natural volumetric representation of the shape, we propose a surface reconstruction method that considers volumetric smoothness as a novel and effective shape prior.
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