A Finite Difference Approximation of Second Order Regularization of Neural-SDFs
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918198363815936 |
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| author | Yin, Haotian Plocharski, Aleksander Wlodarczyk, Michal Jan Musialski, Przemyslaw |
| author_facet | Yin, Haotian Plocharski, Aleksander Wlodarczyk, Michal Jan Musialski, Przemyslaw |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08980 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Finite Difference Approximation of Second Order Regularization of Neural-SDFs Yin, Haotian Plocharski, Aleksander Wlodarczyk, Michal Jan Musialski, Przemyslaw Graphics Computer Vision and Pattern Recognition Machine Learning 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. |
| title | A Finite Difference Approximation of Second Order Regularization of Neural-SDFs |
| topic | Graphics Computer Vision and Pattern Recognition Machine Learning |
| url | https://arxiv.org/abs/2511.08980 |