{"ID":2842609,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.08980","arxiv_id":"2511.08980","title":"A Finite Difference Approximation of Second Order Regularization of Neural-SDFs","abstract":"We introduce a finite-difference framework for curvature regularization in neural signed distance field (SDF) learning. Existing approaches enforce curvature priors using full Hessian information obtained via second-order automatic differentiation, which is accurate but computationally expensive. Others reduced this overhead by avoiding explicit Hessian assembly, but still required higher-order differentiation. In contrast, our method replaces these operations with lightweight finite-difference stencils that approximate second derivatives using the well known Taylor expansion with a truncation error of O(h^2), and can serve as drop-in replacements for Gaussian curvature and rank-deficiency losses. Experiments demonstrate that our finite-difference variants achieve reconstruction fidelity comparable to their automatic-differentiation counterparts, while reducing GPU memory usage and training time by up to a factor of two. Additional tests on sparse, incomplete, and non-CAD data confirm that the proposed formulation is robust and general, offering an efficient and scalable alternative for curvature-aware SDF learning.","short_abstract":"We introduce a finite-difference framework for curvature regularization in neural signed distance field (SDF) learning. Existing approaches enforce curvature priors using full Hessian information obtained via second-order automatic differentiation, which is accurate but computationally expensive. Others reduced this ov...","url_abs":"https://arxiv.org/abs/2511.08980","url_pdf":"https://arxiv.org/pdf/2511.08980v1","authors":"[\"Haotian Yin\",\"Aleksander Plocharski\",\"Michal Jan Wlodarczyk\",\"Przemyslaw Musialski\"]","published":"2025-11-12T04:56:08Z","proceeding":"cs.GR","tasks":"[\"cs.GR\",\"cs.CV\",\"cs.LG\"]","methods":"[]","has_code":false}