Hermite Radial Basis Function for Surface Reconstruction via Differentiable Rendering

Recent advances in novel view synthesis have enabled differentiable rendering methods to reconstruct 3D scenes directly from images. Algorithms such as 3D Gaussian Splatting and RayGauss use local basis functions to represent radiance fields, enabling fast, high-quality rendering of realworld scenes. However, these methods lack an exact geometric representation of the scene. In this work, inspired by Hermite Radial Basis Function (HRBF) implicits, we introduce a global implicit function constructed from local RBFs and their derivatives to represent surfaces. The proposed formulation enables learning scene geometry through differentiable rendering of an implicit function. By leveraging local basis functions, it achieves both an efficient geometric representation and fast rendering, using a bounding volume hierarchy (BVH) to accelerate intersections with the local basis functions.