Curve skeletons of 3D objects are central to many geometry analysis tasks in the field of computer graphics. A desirable skeleton has to meet at least four requirements: (1) topologically homotopic to the primitive shape, (2) truly well-centred, (3) feature preserving and (4) has a reasonable degree of smoothness. There are at least a couple of difficulties with skeletonization. On the one hand, finding the “best” skeleton is related to visual perception, to some extent, and thus hard to be completely solved by a pure geometric technique. On the other hand, how to exactly characterize the centredness of a skeleton, without a pre-computed medial axis surface, still remains challenging.

Due to the fact that skeletons are able to encode the overall structure, a skeleton has been used to guide segmentation of a shape, which implies that there exists a dual relationship between segmentation and skeletonization. Based on the underlying duality, we propose to generate skeletons from a reliable segmentation result that is more easily available by deep learning or alternative techniques. In implementation, we first extract a collection of samples and then compute the Voronoi diagram restricted in the volume w.r.t. those samples, followed by transforming the clipped Voronoi diagram into a graph $\mathcal{G}$. We further equip each edge in $\mathcal{G}$ with a centredness score. The user-specific segmentation result is then used to decompose $\mathcal{G}$ into a set of subgraphs ${\mathcal{G}}_{i=1}^k$. The next task is to compute the Steiner tree for each subgraph while requiring that the Steiner trees of two adjacent parts ${\mathcal{G}}_i$ and ${\mathcal{G}}_j$ must be linked together. The global structure of the final skeleton inherits the proximity configuration of the user-specific segmentation, and thus is topologically homotopic to the primitive shape. At the same time, the centredness of the final skeleton is taken into full consideration by maximizing the overall centredness score. We also integrate the other two requirements carefully into our algorithmic framework. We conduct extensive experiments to evaluate the new approach in terms of the above-mentioned aspects. The experimental results show that our approach has an obvious advantage over the state-of-the-arts. As a by-product of our algorithm, users can obtain skeletons with different levels of details by editing the segmentation configurations.

3D对象的曲线骨架是计算机图形学领域许多几何分析任务的核心。理想的骨架必须至少满足四个要求：（1）与原始形状在拓扑上是同构的；（2）真正地对中；（3）保留特征；（4）具有合理的平滑度。骨架化至少有两个困难。一方面，找到“最佳”骨骼在某种程度上与视觉感知有关，因此很难通过纯几何技术完全解决。另一方面，如何在没有预先计算的中间轴表面的情况下准确表征骨骼的中心度仍然具有挑战性。

由于骨架能够对整个结构进行编码，因此已经使用骨架来引导形状的分割，这意味着分割和骨架化之间存在双重关系。基于潜在的对偶性，我们建议从可靠的分割结果生成骨骼，而深度学习或替代技术更容易获得分割结果。在实现中，我们首先提取样本集合，然后计算样本数量限制的Voronoi图，然后将裁剪的Voronoi图转换为图$\mathcal{G}$。我们进一步在$\mathcal{G}$中心得分。然后，将特定于用户的细分结果用于分解$\mathcal{G}$ 进入一组子图 ${\mathcal{G}}_{\mathrm{一世}=\mathrm{1个}}^{ķ}$。下一个任务是为每个子图计算Steiner树，同时要求两个相邻部分的Steiner树${\mathcal{G}}_{\mathrm{一世}}$ 和 ${\mathcal{G}}_{Ĵ}$必须链接在一起。最终骨架的整体结构继承了用户特定细分的接近度配置，因此在拓扑上与原始形状同构。同时，通过最大化整体居中度分数来充分考虑最终骨骼的居中性。我们还将其他两个要求仔细地集成到我们的算法框架中。我们进行了广泛的实验，以从上述方面评估新方法。实验结果表明，相对于最新技术，我们的方法具有明显的优势。作为我们算法的副产品，用户可以通过编辑分段配置来获得具有不同细节级别的骨骼。