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 term in the updated formulation. Our experiments demonstrate the extraordinary performance of Gaussian-Hermite kernel in both geometry reconstruction and novel-view synthesis tasks. The proposed kernel outperforms traditional Gaussian Splatting kernels, showcasing its potential for high-quality 3D reconstruction and rendering.
2D 高斯点云最近成为 3D 重建中的一种重要方法，能够同时实现新视图合成和几何重建。尽管广泛使用著名的高斯核，但其缺乏各向异性和变形能力，导致物体轮廓处边缘模糊，限制了当前高斯点云方法的重建质量。为了提升表示能力，我们从量子物理学中获得灵感，提出使用高斯-厄米特核作为高斯点云中的新原语。新核采用统一的数学形式，扩展了高斯函数，作为更新公式中的零阶项。我们的实验表明，高斯-厄米特核在几何重建和新视图合成任务中表现卓越。与传统高斯点云核相比，所提出的核展现了其在高质量 3D 重建和渲染中的潜力。