Why the Multi-Sphere Shape Generator Works: Medial-Axis Placement of Spheres

Abstract

The Multi-Sphere Shape Generator (MSS) [1] places spheres according to a feature-enhanced residual field, but the geometric basis of this strategy has remained unknown. We prove that every local maximum of the residual field lies on the medial axis of the target shape, implying that MSS places spheres at the centers of maximal inscribed spheres without explicit skeleton extraction. Numerical tests show that deviations from the exact medial axis are limited to the voxel resolution. This result provides a mathematical explanation for the placement strategy that underlies the accuracy of MSS.