当3D高斯溅射（3DGS）恢复真实表面时
When 3D Gaussian Splatting Recovers Real Surfaces
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中文总结 AI 辅助
该研究构建基于首击渲染抽象的数学框架，明确3D高斯溅射（3DGS）的可识别性窗口，经合成与真实数据集实验验证，揭示角容量对3DGS恢复真实表面的关键影响。
中文摘要 AI 辅助
3D高斯溅射（3DGS）何时能恢复真实场景表面，而非仅过拟合视角相关外观？我们通过开发基于首击渲染抽象的数学框架来回答此问题，该框架可清晰将几何与外观分离。我们证明几何错位会通过视差将空间纹理强制转换为高频角信号，这确立了严格的可识别性窗口：若角容量受限，表面一致解在数学上更受青睐；若角容量不受限，相同图像可被错误的不透明广告牌几何完美解释。合成压力测试实验证实了该预测，显示广告牌失效恰好出现在高角容量时。相反，在我们评估的采用标准采集协议的真实世界数据集上，即使在高SH阶下，重建仍保持表面一致性，这与“丰富空间纹理可将广告牌解决方案推至测试的角容量范围之外”的预测一致。
英文摘要
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.
发表机构
- School of EECS, Penn State（宾夕法尼亚州立大学电子工程与计算机科学学院）
机构由 AI 辅助整理，请以论文原文为准。
