Recently, 3D Gaussian Splatting (3DGS) has attracted attention for its superior rendering quality and speed over Neural Radiance Fields (NeRF). To address 3DGS's limitations in surface representation, 2D Gaussian Splatting (2DGS) introduced disks as scene primitives to model and reconstruct geometries from multi-view images, offering view-consistent geometry. However, the disk's first-order linear approximation often leads to over-smoothed results. We propose Quadratic Gaussian Splatting (QGS), a novel method that replaces disks with quadric surfaces, enhancing geometric fitting, whose code will be open-sourced. QGS defines Gaussian distributions in non-Euclidean space, allowing primitives to capture more complex textures. As a second-order surface approximation, QGS also renders spatial curvature to guide the normal consistency term, to effectively reduce over-smoothing. Moreover, QGS is a generalized version of 2DGS that achieves more accurate and detailed reconstructions, as verified by experiments on DTU and TNT, demonstrating its effectiveness in surpassing current state-of-the-art methods in geometry reconstruction.
最近，3D 高斯投影（3D Gaussian Splatting, 3DGS）因其在渲染质量和速度上优于神经辐射场（Neural Radiance Fields, NeRF）而受到关注。为了解决 3DGS 在表面表示上的局限性，2D 高斯投影（2D Gaussian Splatting, 2DGS）引入了以圆盘为场景基元的方法，从多视角图像中建模和重建几何结构，提供视图一致的几何表示。然而，圆盘的线性一阶近似往往导致结果过于平滑。 我们提出了一种新方法 Quadratic Gaussian Splatting (QGS)，将圆盘替换为二次曲面，从而提升几何拟合能力，相关代码将开源。QGS 在非欧几里得空间中定义高斯分布，使得基元能够捕捉更复杂的纹理特征。作为二阶曲面近似方法，QGS 还能渲染空间曲率，引导法线一致性项，从而有效减少过度平滑。 此外，QGS 是 2DGS 的广义版本，能够实现更精确、更细致的重建。通过在 DTU 和 TNT 数据集上的实验验证，我们的方法在几何重建方面超越了当前最先进的方法，展现了其卓越的效果。