{"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/differential-geometry-in-neural-implicits","title":"Exploring Differential Geometry in Neural Implicits","arxiv_id":"2201.09263","date":"2022-01-23","proceeding":null,"authors":["Tiago Novello","Guilherme Schardong","Luiz Schirmer","Vinicius da Silva","Helio Lopes","Luiz Velho"],"abstract":"We introduce a neural implicit framework that exploits the differentiable properties of neural networks and the discrete geometry of point-sampled surfaces to approximate them as the level sets of neural implicit functions. To train a neural implicit function, we propose a loss functional that approximates a signed distance function, and allows terms with high-order derivatives, such as the alignment between the principal directions of curvature, to learn more geometric details. During training, we consider a non-uniform sampling strategy based on the curvatures of the point-sampled surface to prioritize points with more geometric details. This sampling implies faster learning while preserving geometric accuracy when compared with previous approaches. We also use the analytical derivatives of a neural implicit function to estimate the differential measures of the underlying point-sampled surface.","url_abs":"https://arxiv.org/abs/2201.09263v4","url_pdf":"https://arxiv.org/pdf/2201.09263v4.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":"differential-geometry-in-neural-implicits","repo_url":"https://github.com/dsilvavinicius/differential_geometry_in_neural_implicits","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2201.09263","atlas_url":"https://app.syntology.ai/?focus=2201.09263","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}