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A common approach in the shape transformation stage is to solve a linear least squares problem to find a smoothness\u2010regularized transform that fits the target shape. However, completely solving the linear least squares problem to obtain a transform is wasteful because the correspondences used for constructing the problem are imperfect, especially at early iterations. In this work, we design a novel framework to compute a transform in single step without the exact linear solve. Our key idea is to use only a single step of an iterative linear system solver, conjugate gradient, at each shape transformation stage. For this single\u2010step scheme to be effective, appropriate preconditioning of the linear system is required. We design a novel adaptive Sobolev\u2010Jacobi preconditioning method for our single\u2010step transform to produce a large and regularized shape update suitable for correspondence search in the next iteration. We demonstrate that our preconditioned single\u2010step transform stably accelerates challenging 3D surface registration tasks.<\/jats:p>","DOI":"10.1111\/cgf.70035","type":"journal-article","created":{"date-parts":[[2025,4,14]],"date-time":"2025-04-14T07:09:51Z","timestamp":1744614591000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Preconditioned Single\u2010step Transforms for Non\u2010rigid ICP"],"prefix":"10.1111","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1593-4626","authenticated-orcid":false,"given":"Yucheol","family":"Jung","sequence":"first","affiliation":[{"name":"POSTECH  South Korea"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2162-4627","authenticated-orcid":false,"given":"Hyomin","family":"Kim","sequence":"additional","affiliation":[{"name":"POSTECH  South Korea"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-4423-8544","authenticated-orcid":false,"given":"Hyejeong","family":"Yoon","sequence":"additional","affiliation":[{"name":"POSTECH  South Korea"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8159-4271","authenticated-orcid":false,"given":"Seungyong","family":"Lee","sequence":"additional","affiliation":[{"name":"POSTECH  South Korea"}]}],"member":"311","published-online":{"date-parts":[[2025,4,14]]},"reference":[{"key":"e_1_2_8_2_2","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882311"},{"key":"e_1_2_8_3_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-97-00826-0"},{"key":"e_1_2_8_4_2","first-page":"190","article-title":"Orbifold tutte embeddings","volume":"34","author":"Aigerman Noam","year":"2015","journal-title":"ACM Trans. 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