多球形状生成器为何有效：球的中轴放置
Why the Multi-Sphere Shape Generator Works: Medial-Axis Placement of Spheres
AI总结：
该研究通过数学证明揭示了多球形状生成器（MSS）的球放置策略基于目标形状中轴，其放置的球对应最大内接球中心，偏差仅受体素分辨率限制，为MSS的准确性提供了数学依据。
AI中文摘要：
多球形状生成器（MSS）[1]根据特征增强的残差场放置球，但该策略的几何基础仍未知。我们证明残差场的每个局部最大值都位于目标形状的中轴上，这意味着MSS无需显式骨架提取，即可将球放置在最大内接球的中心。数值测试显示，与精确中轴的偏差仅局限于体素分辨率范围内。该结果为支撑MSS准确性的放置策略提供了数学解释。
英文摘要：
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.
