# Computation of Circular Area and Spherical Volume Invariants via Boundary Integrals

arXiv: https://arxiv.org/abs/1905.02176 · HTML: https://mlsanity.com/paper/1905.02176/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 May 2019.

## Built on by (most cited first, 3 of 3)

- [The Batch Artifact Scanning Protocol: A new method using computed tomography (CT) to rapidly create three-dimensional models of objects from large collections en masse](https://mlsanity.com/paper/2205.02691/) (2022)
- [Using machine learning on new feature sets extracted from 3D models of broken animal bones to classify fragments according to break agent](https://mlsanity.com/paper/2205.10430/) (2022)
- [En masse scanning and automated surfacing of small objects using Micro-CT](https://mlsanity.com/paper/2410.07385/) (2024)

## Abstract (arXiv)

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.