论文标题
封闭界面的内侧轴是Lipschitz稳定的，相对于豪斯多夫的距离稳定
The medial axis of closed bounded sets is Lipschitz stable with respect to the Hausdorff distance under ambient diffeomorphisms
论文作者
论文摘要
我们证明，闭合集的内侧轴是hausdorff稳定的：让$ \ m athcal {s} \ subseteq \ subseteq \ mathbb {r}^d $ be（固定）封闭集（包含一个边界球体）。考虑$ c^{1,1}的空间$ \ mathbb {r}^d $的空间本身，这使边界球不变。从这个空间（赋予某些Banach规范）到$ \ Mathbb {r}^d $的封闭子集的空间的地图（与Hausdorff距离授予），将diffemormorphism $ f $映射到$ f（$ f（\ mathcal）的内侧轴的闭合（\ natecal {s} s}）$，是lips lips，lips，这扩展了Chazal和Soufflet的先前稳定性结果，该轴是$ C^2 $歧管的内侧轴的稳定性，$ C^2 $环境差异性。
We prove that the medial axis of closed sets is Hausdorff stable in the following sense: Let $\mathcal{S} \subseteq \mathbb{R}^d$ be (fixed) closed set (that contains a bounding sphere). Consider the space of $C^{1,1}$ diffeomorphisms of $\mathbb{R}^d$ to itself, which keep the bounding sphere invariant. The map from this space of diffeomorphisms (endowed with some Banach norm) to the space of closed subsets of $\mathbb{R}^d$ (endowed with the Hausdorff distance), mapping a diffeomorphism $F$ to the closure of the medial axis of $F(\mathcal{S})$, is Lipschitz. This extends a previous stability result of Chazal and Soufflet on the stability of the medial axis of $C^2$ manifolds under $C^2$ ambient diffeomorphisms.
