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We show how to compute the circular area invariant of planar curves, and thespherical volume invariant of surfaces, in terms of line and surface integrals,respectively. We use the Divergence Theorem to express the area and volumeintegrals as line and surface integrals, respectively, against particularkernels; our results also extend to higher dimensional hypersurfaces. Theresulting surface integrals are computable analytically on a triangulated mesh.This gives a simple computational algorithm for computing the spherical volumeinvariant for triangulated surfaces that does not involve discretizing theambient space. We discuss potential applications to feature detection on brokenbone fragments of interest in anthropology.

Computation of Circular Area and Spherical Volume Invariants via Boundary Integrals