揭示3D高斯点阵在什么条件下能真实还原场景表面
When 3D Gaussian Splatting Recovers Real Surfaces
- 通过首次击中渲染模型分离几何与外观，建立数学分析框架
- 发现几何错位会将空间纹理转为高频角度信号，导致表面失真
- 实验证明：在真实数据上即使高阶球谐系数仍能保持表面一致
3D高斯点阵（3DGS）何时能恢复真实场景表面而非仅过拟合视图依赖的外观？我们基于首次击中渲染抽象，构建了一个数学框架，清晰分离几何与外观。证明几何错位会通过视差将空间纹理强制转化为高频角度信号。这确立了严格的可识别窗口：若角度容量受限，表面一致解在数学上占优；若无限制，相同图像可被错误的不透明海报式几何完美解释。合成压力测试实验验证此预测，显示海报失败恰发生在高角度容量时。相反，在标准采集协议下的真实数据集上，重建结果即便在高阶球谐度下仍保持表面一致性，符合丰富空间纹理使海报解超出测试角度容量范围的预测。
原文摘要 · Abstract (English)
When does 3D Gaussian Splatting (3DGS) recover the true scene surface rather than just overfitting view-dependent appearance? We answer this by developing a mathematical framework based on a first-hit rendering abstraction that cleanly isolates geometry from appearance. We prove that geometric misalignment forcefully converts spatial textures into high-frequency angular signals via parallax. This establishes a strict identifiability window: if angular capacity is bounded, surface-consistent solutions are mathematically preferred; if unrestricted, the same images can be perfectly explained by an incorrect, opaque billboard geometry. Experiments on synthetic stress tests confirm this prediction, showing billboard failures emerge precisely at high angular capacities. Conversely, in the real-world datasets we evaluate under standard capture protocols, reconstructions remain surface-consistent even at high SH degrees, which is consistent with the prediction that rich spatial texture can push billboard solutions outside the tested angular-capacity range.
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