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Abstract:
Although the Hausdorff distance is a popular device
to measure the differences between sets,
it is not natural for some specific classes of sets,
especially for the medial axis transform
which is defined as the set of all pairs
of the centers and the radii of the maximal balls
contained in another set.
In spite of its many advantages and possible applications,
the medial axis transform has one great weakness,
namely its instability under the Hausdorff distance
when the boundary of the original set is perturbed.
Though many attempts have been made for the resolution of this phenomenon,
most of them are heuristic in nature
and lack precise error analysis.
