Geometric skeletons are effective means of shape representation capable of capturing a solid shape's essential volumetric characteristics and topology. In two dimensions the precisely defined curves of the ``Medial Axis Transform'' are the commonly accepted form of geometric skeletons. However, in three dimensions, the transform can contain surfaces often connected in a complex fashion, making them difficult to use in practical applications. Curve skeletons address this issue by providing a simple curvilinear alternative to the medial axis, but at the price of not being clearly defined. In this talk I will introduce several ways of looking at the medial axis, and illustrate how its properties can be mimicked for the computation of curve skeletons. Additionally, by exploiting their volumetric qualities, I will show you how these skeletons can act as regularizers to solve challenging surface reconstruction problems, where large portions of missing data make the problem highly ill-conditioned.

École Polytechnique Fédérale de Lausanne, School of Computer and Communication Sciences

Computer Graphics and Geometry Laboratory, BC 347, Station 14, CH-1015 Lausanne – 2010-2015 LGG, EPFL

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