{"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/surface-networks","title":"Surface Networks","arxiv_id":"1705.10819","date":"2017-05-30","proceeding":"CVPR 2018 6","authors":["Ilya Kostrikov","Zhongshi Jiang","Daniele Panozzo","Denis Zorin","Joan Bruna"],"abstract":"We study data-driven representations for three-dimensional triangle meshes,\nwhich are one of the prevalent objects used to represent 3D geometry. Recent\nworks have developed models that exploit the intrinsic geometry of manifolds\nand graphs, namely the Graph Neural Networks (GNNs) and its spectral variants,\nwhich learn from the local metric tensor via the Laplacian operator. Despite\noffering excellent sample complexity and built-in invariances, intrinsic\ngeometry alone is invariant to isometric deformations, making it unsuitable for\nmany applications. To overcome this limitation, we propose several upgrades to\nGNNs to leverage extrinsic differential geometry properties of\nthree-dimensional surfaces, increasing its modeling power.\n  In particular, we propose to exploit the Dirac operator, whose spectrum\ndetects principal curvature directions --- this is in stark contrast with the\nclassical Laplace operator, which directly measures mean curvature. We coin the\nresulting models \\emph{Surface Networks (SN)}. We prove that these models\ndefine shape representations that are stable to deformation and to\ndiscretization, and we demonstrate the efficiency and versatility of SNs on two\nchallenging tasks: temporal prediction of mesh deformations under non-linear\ndynamics and generative models using a variational autoencoder framework with\nencoders/decoders given by SNs.","url_abs":"http://arxiv.org/abs/1705.10819v2","url_pdf":"http://arxiv.org/pdf/1705.10819v2.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":"surface-networks","repo_url":"https://github.com/jiangzhongshi/SurfaceNetworks","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"3d-geometry","task_name":"3D geometry"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1705.10819","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}