A Finite Difference Approximation of Second Order Regularization of Neural-SDFs

• URL: http://arxiv.org/abs/2511.08980v1
• Date: Thu, 13 Nov 2025 01:23:29 GMT
• Title: A Finite Difference Approximation of Second Order Regularization of Neural-SDFs
• Authors: Haotian Yin, Aleksander Plocharski, Michal Jan Wlodarczyk, Przemyslaw Musialski,
• Abstract summary: We introduce a finite-difference framework for curvature regularization in neural signed distance field (SDF) learning.<n> Experiments demonstrate that our finite-difference variants achieve reconstruction fidelity comparable to their automatic-differentiation counterparts.
• Score: 39.799207552858114
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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