Geometric Optimisation Via Spectral Shifting

We present a geometric optimisation framework that can recover fold-over free maps from non-injective initial states using popular flip-preventing distortion energies. Since energies are infinite for folded configurations, we propose new regularisation scheme shifts the singular values of deformation gradient. This allow us to re-use many existing algorithms, especially locally injective methods initially maps. Our is suitable both value- and invariant-based formulations, systematically contributes multiple stabilisers Hessian. In contrast proxy-based techniques, maintain second-order convergence. Compact expressions energy eigensystems be obtained our extended stretch invariants, enabling use fast projected Newton solvers. Although spectral shifting in general has no theoretical guarantees global minimum an injection, extensive experiments show extremely robust practice, capable generating high-quality severely distorted, degenerate initialisations.