Complexity as a Scale-Space for the Medial Axis Transform

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. Tiny perturbations in the contour often lead to spurious branches of the skeleton. 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 representation. The complexity is defined as the number of branches in the skeleton. A set of curves is computed to represent the bounding contour across a variety of complexity measures. The curves possessing larger complexity measures represent greater detail than curves with smaller measures. A medial axis skeleton is computed directly from each contour. The result is a set of skeletons that repres..