The medial axis skeleton is a thin line graph that preserves the topology of a region. The skeleton has often been cited as a useful representation for shape description, region interpretation, and object recognition. Unfortunately, the computation of the skeleton is extremely sensitive to variations in the bounding contour. In this paper, we describe a robust method for computing the medial axis skeleton across a variety of scales. The resulting scale-space is parametric with the complexity of the skeleton, where the complexity is defined as the number of branches in the skeleton.