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Since flip-preventing energies are infinite for folded configurations, we propose a new regularisation scheme that shifts the singular values of the deformation gradient. This allow us to re-use many existing algorithms, especially locally injective methods for initially folded maps. Our regularisation is suitable for both singular value- and invariant-based formulations, and systematically contributes multiple stabilisers to the Hessian. In contrast to proxy-based techniques, we maintain second-order convergence. Compact expressions for the energy eigensystems can be obtained for our extended stretch invariants, enabling the use of fast projected Newton solvers. Although spectral shifting in general has no theoretical guarantees that the global minimum is an injection, extensive experiments show that our framework is fast and extremely robust in practice, and capable of generating high-quality maps from severely distorted, degenerate and folded initialisations.<\/jats:p>","DOI":"10.1145\/3585003","type":"journal-article","created":{"date-parts":[[2023,2,27]],"date-time":"2023-02-27T12:04:16Z","timestamp":1677499456000},"page":"1-15","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":10,"title":["Geometric Optimisation Via Spectral Shifting"],"prefix":"10.1145","volume":"42","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2350-4933","authenticated-orcid":false,"given":"Roman","family":"Poya","sequence":"first","affiliation":[{"name":"Siemens Digital Industries Software, Francis House, Cambridge, United Kingdom"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4542-2237","authenticated-orcid":false,"given":"Rogelio","family":"Ortigosa","sequence":"additional","affiliation":[{"name":"Technical University of Cartagena, Cartagena, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1131-8685","authenticated-orcid":false,"given":"Theodore","family":"Kim","sequence":"additional","affiliation":[{"name":"Yale University, New Haven, Connecticutt, United States"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2023,4,7]]},"reference":[{"key":"e_1_3_3_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/2461912.2461931"},{"key":"e_1_3_3_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00279992"},{"key":"e_1_3_3_4_1","first-page":"315","article-title":"Global invertibility of Sobolev functions and the interpenetration of matter","volume":"88","author":"Ball John. 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