Dey, Tamal K.Sun, JianAlla Sheffer and Konrad Polthier2014-01-292014-01-2920063-905673-24-X1727-8384https://doi.org/10.2312/SGP/SGP06/143-152Many applications in geometric modeling, computer graphics, visualization and computer vision benefit from a reduced representation called curve-skeletons of a shape. These are curves possibly with branches which compactly represent the shape geometry and topology. The lack of a proper mathematical definition has been a bottleneck in developing and applying the the curve-skeletons. A set of desirable properties of these skeletons has been identified and the existing algorithms try to satisfy these properties mainly through a procedural definition. We define a function called medial geodesic on the medial axis which leads to a methematical definition and an approximation algorithm for curve-skeletons. Empirical study shows that the algorithm is robust against noise, operates well with a single user parameter, and produces curve-skeletons with the desirable properties. Moreover, the curveskeletons can be associated with additional attributes that follow naturally from the definition. These attributes capture shape eccentricity, a local measure of how far a shape is away from a tubular one.Categories and Subject Descriptors (according to ACM CCS): I.3.3 [Computer Graphics]: Line and Curve Generation