{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/divergence-free-shape-interpolation-and","title":"Divergence-Free Shape Interpolation and Correspondence","arxiv_id":"1806.10417","date":"2018-06-27","proceeding":null,"authors":["Marvin Eisenberger","Zorah Lähner","Daniel Cremers"],"abstract":"We present a novel method to model and calculate deformation fields between\nshapes embedded in $\\mathbb{R}^D$. Our framework combines naturally\ninterpolating the two input shapes and calculating correspondences at the same\ntime. The key idea is to compute a divergence-free deformation field\nrepresented in a coarse-to-fine basis using the Karhunen-Lo\\`eve expansion. The\nadvantages are that there is no need to discretize the embedding space and the\ndeformation is volume-preserving. Furthermore, the optimization is done on\ndownsampled versions of the shapes but the morphing can be applied to any\nresolution without a heavy increase in complexity. We show results for shape\ncorrespondence, registration, inter- and extrapolation on the TOSCA and FAUST\ndata sets.","url_abs":"http://arxiv.org/abs/1806.10417v2","url_pdf":"http://arxiv.org/pdf/1806.10417v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"divergence-free-shape-interpolation-and","repo_url":"https://github.com/sprengvogel/DivergenceFreeCorrespondence","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"GPL-3.0"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1806.10417","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}