On the Stability of Medial Axis of a Union of Disks in the Plane

We show that the medial axis of union of disks in the plane is stable provided that the topology is preserved and every disk meets the boundary in a single arc. If the second condition is removed, the medial axis is no longer stable, but if pruned using any of four significance measures (circumradius, erosion thickness, object angle or potential residue) it remains stable.

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