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Skeletal Representations and Applications

When representing a solid object there are alternatives to the use of traditional explicit (surface meshes) or implicit (zero crossing of implicit functions) methods. Skeletal representations encode shape information in a mixed fashion: they are composed of a set of explicit primitives, yet they are able to efficiently encode the shape's volume as well as its topology. I will discuss, in two dimensions, how symmetry can be used to reduce the dimensionality of the data (from a 2D solid to a 1D curve), and how this relates to the classical definition of skeletons by Medial Axis Transform. While the medial axis of a 2D shape is composed of a set of curves, in 3D it results in a set of sheets connected in a complex fashion. Because of this complexity, medial skeletons are difficult to use in practical applications. Curve skeletons address this problem by strictly requiring their geometry to be one dimensional, resulting in an intuitive yet powerful shape representation. In this report I will define both medial and curve skeletons and discuss their mutual relationship. I will also present several algorithms for their computation and a variety of scenarios where skeletons are employed, with a special focus on geometry processing and shape analysis.