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We present a simple and robust method for computing skeletons for arbitrary planar objects and centerlines for 3D objects. We augment the Fast Marching Method (FMM) widely used in level set applications by computing the paramterized boundary location every pixel came from during the boundary evolution. The resulting parameter field is then thresholded to produce the skeleton branches created by boundary features of a given size. The presented algorithm is straightforward to implement, has low memory costs and short execution times, and is robust with respect to the used threshold and initial shape noisiness. The produced skeletons are very similar to the ones delivered by more complex algorithms. Various 2D and 3D applications are presented.