2DGH: 2D Gaussian-Hermite Splatting for High-quality Rendering and Better Geometry Features

2D Gaussian Splatting has recently emerged as a significant method in 3D reconstruction, enabling novel view synthesis and geometry reconstruction simultaneously. While the well-known Gaussian kernel is broadly used, its lack of anisotropy and deformation ability leads to dim and vague edges at object silhouettes, limiting the reconstruction quality of current Gaussian splatting methods. To enhance the representation power, we draw inspiration from quantum physics and propose to use the Gaussian-Hermite kernel as the new primitive in Gaussian splatting. The new kernel takes a unified mathematical form and extends the Gaussian function, which serves as the zero-rank special case in the updated general formulation. Our experiments demonstrate that the proposed Gaussian-Hermite kernel achieves improved performance over traditional Gaussian Splatting kernels on both geometry reconstruction and novel-view synthesis tasks. Specifically, on the DTU dataset, our method yields more accurate geometry reconstruction, while on datasets such as MipNeRF360 and our customized Detail dataset, it achieves better results in novel-view synthesis. These results highlight the potential of the Gaussian-Hermite kernel for high-quality 3D reconstruction and rendering.