3D Gaussian Splatting (3DGS) has revolutionized fast novel view synthesis, yet its opacity-based formulation makes surface extraction fundamentally difficult. Unlike implicit methods built on Signed Distance Fields or occupancy, 3DGS lacks a global geometric field, forcing existing approaches to resort to heuristics such as TSDF fusion of blended depth maps. Inspired by the Objects as Volumes framework, we derive a principled occupancy field for Gaussian Splatting and show how it can be used to extract highly accurate watertight meshes of complex scenes. Our key contribution is to introduce a learnable oriented normal at each Gaussian element and to define an adapted attenuation formulation, which leads to closed-form expressions for both the normal and occupancy fields at arbitrary locations in space. We further introduce a novel consistency loss and a dedicated densification strategy to enforce Gaussians to wrap the entire surface by closing geometric holes, ensuring a complete shell of oriented primitives. We modify the differentiable rasterizer to output depth as an isosurface of our continuous model, and introduce Primal Adaptive Meshing for Region-of-Interest meshing at arbitrary resolution. We additionally expose fundamental biases in standard surface evaluation protocols and propose two more rigorous alternatives. Overall, our method Gaussian Wrapping sets a new state-of-the-art on DTU and Tanks and Temples, producing complete, watertight meshes at a fraction of the size of concurrent work-recovering thin structures such as the notoriously elusive bicycle spokes.

翻译：三维高斯泼溅（3D Gaussian Splatting, 3DGS）革新了快速新视角合成技术，但其基于不透明度的公式化表达使得曲面提取本质上困难重重。与基于符号距离场或占用的隐式方法不同，3DGS缺乏全局几何场，迫使现有方法采用诸如融合混合深度图的TSDF融合等启发式策略。受《物体即体素》框架启发，我们为高斯泼溅推导出原则性的占用场，并展示如何利用该场提取复杂场景的高精度水密网格。我们的核心贡献在于：为每个高斯单元引入可学习的定向法线，并定义修正的衰减公式，从而导出空间中任意位置处法线与占用场的闭式表达式。我们进一步引入新型一致性损失与专用致密化策略，迫使高斯体通过闭合几何孔洞包裹整个曲面，确保获得完整的定向基元外壳。通过修改可微分光栅化器输出连续模型等值面形式的深度，我们提出用于任意分辨率感兴趣区域网格化的原始自适应网格算法。此外，我们揭示了标准曲面评估协议中的根本偏差，并提出了两种更严谨的替代方案。总体而言，我们的方法——高斯包裹法（Gaussian Wrapping）在DTU和Tanks and Temples数据集上刷新了最优性能，能以远小于现有工作的数据量生成完整水密网格，并成功恢复诸如难以捕捉的自行车辐条等薄壁结构。