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

The introduction of a finite-difference framework for curvature regularization in neural signed distance field (SDF) learning marks a significant advancement in AI methodologies. Traditional approaches often rely on full Hessian information, which, while accurate, is computationally intensive. The new method, however, utilizes lightweight finite-difference stencils to approximate second derivatives, drastically reducing GPU memory usage and training time by up to 50%. Experiments have shown that this approach achieves reconstruction fidelity on par with automatic differentiation methods, confirming its effectiveness. Additionally, the robustness of the proposed formulation across various data types, including sparse and incomplete datasets, highlights its versatility and scalability. This innovation not only streamlines the learning process but also opens new avenues for efficient curvature-aware SDF learning, positioning it as a promising alternative in the rapidly evolving landscape …