A Finite Difference Approximation of Second Order Regularization of Neural-SDFs
To address the high computational and memory overhead of curvature regularization in neural signed distance field (SDF) learning—stemming from reliance on second-order automatic differentiation—this paper proposes a lightweight finite-difference-based regularization framework. We introduce, for the first time, an O(h²)-accurate finite-difference stencil for explicit SDF curvature modeling, bypassing Hessian construction and second-order gradients entirely. The method enables plug-and-play approximations of both Gaussian curvature and rank-deficiency loss. Empirically, it matches the reconstruction accuracy of automatic-differentiation-based curvature regularization while reducing GPU memory consumption and training time by up to 50%. Moreover, it demonstrates strong robustness to sparse, incomplete, and non-CAD data. Our core contribution is achieving high-fidelity geometric regularization at the cost of only low-order differentiation, thereby significantly improving the efficiency and scalability of neural SDF learning.