SIAM Journal on Imaging Sciences, Volume 13, Issue 1, Page 53-77, January 2020.
We show how to compute the circular area invariant of planar curves, and the spherical volume invariant of surfaces, in terms of line and surface integrals, respectively. We use the divergence theorem to express the area and volume integrals as line and surface integrals, respectively, against particular kernels; our results also extend to higher-dimensional hypersurfaces. The resulting surface integrals are computable analytically on a triangulated mesh. This gives a simple computational algorithm for computing the spherical volume invariant for triangulated surfaces that does not involve discretizing the ambient space. We discuss potential applications to feature detection on broken bone fragments of interest in anthropology.

中文翻译：

---

通过边界积分计算圆形面积和球形体积不变量

SIAM影像科学杂志，第13卷，第1期，第53-77页，2020年1月。
我们展示了如何分别根据线积分和表面积分计算平面曲线的圆形面积不变性和表面的球形体积不变性。我们使用散度定理将面积和体积积分分别表示为针对特定内核的线和表面积分。我们的结果还扩展到了高维超曲面。生成的表面积分可以在三角网格上进行分析计算。这提供了一种简单的计算算法，用于计算三角化表面的球体体积不变量，而不会涉及离散化环境空间。我们讨论了在人类学中感兴趣的骨折片段特征检测方面的潜在应用。