Medial Axis Computation using a Hierarchical Spline Approximation of the Signed Distance Function

We present a new method for computing the medial axis of a given closed smooth curve or surface. It is based on an algorithm for approximating the signed distance function using polynomial splines over hierarchical T-meshes, which has recently been presented in [36]. Since the signed distance function is not differentiable along the medial axis, the hierarchical T-meshes is automatically refined along the medial axis. Based on this observation, we generate an approximation of the medial axis by applying suitable thinning, cleaning and smoothing algorithms to the voxels in the deepest level of the hierarchical T-mesh. Finally, the accuracy of the result is validated by analyzing the Hausdorff distance between the original boundary surface and the boundary of the volume which is represented by the approximate medial axis transform.