Although useful in many applications,
the medial axis transform (MAT) has a few fit-falls,
one of which is its extreme sensitivity to the boundary
perturbation.
In this paper, we first summarizes the previous attempts to
get around this by bounding the one-sided Hausdorff distance
of the MAT with respect to the boundary perturbation.
We illustrate these results and their optimality with various examples.
Finally, we suggest an application of them in pruning.
In particular, we discuss the advantage of the results for the domains
which are not weakly injective, over those for the weakly injective
ones.
