A Finite Difference Approximation of Second Order Regularization of Neural-SDFs
This provides an efficient alternative for researchers and practitioners working with curvature-aware SDF learning, particularly for applications with sparse or incomplete data, though it represents an incremental improvement over existing methods.
The paper tackles the computational expense of curvature regularization in neural signed distance field learning by introducing a finite-difference framework that approximates second derivatives using Taylor expansion with O(h^2) truncation error. The method achieves comparable reconstruction fidelity to automatic-differentiation approaches while reducing GPU memory usage and training time by up to a factor of two.
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.