动态3D高斯点云过拟合主因是变形不连贯，非参数量过多。
Incoherent Deformation, Not Capacity: Diagnosing and Mitigating Overfitting in Dynamic Gaussian Splatting
- 通过正则化高斯体形变场的平滑性，提升泛化能力。
- 在D-NeRF上使训练测试差距从6.18dB降至2.54dB，降幅超57%。
- 适合关注视频3D重建泛化性的研究者和工程师。
动态3D高斯点云方法在单目视频上训练视图的PSNR表现优异，但泛化能力差：在D-NeRF基准上平均训练-测试PSNR差距达6.18dB，个别场景高达11dB。我们发现两个关键因素：其一，分裂机制导致超过80%的差距——禁用分裂使高斯点数从44K降至3K，PSNR差距从6.18dB降至1.15dB；所有阈值消融实验中，差距与点数呈对数线性关系（r=0.995，置信区间[0.99,1.00]），暗示容量解释。其二，容量解释不完整：引入局部平滑性惩罚（弹性能量正则化，EER），在点云增加85%的情况下将差距减少40.8%；直接测量训练模型中的每点应变，EER使平均应变降低99.72%（中位数99.80%），且8/8场景下中位应变低于基线1%分位数水平。结合GAD（损失率感知密度阈值）与PTDrop（抖动加权丢弃），在相同λ下实现57%的差距缩减。该结论在不同形变架构（Deformable-3DGS）及真实单目视频（4 HyperNeRF场景）中均成立，验证了变形连贯性对泛化的决定性作用。
原文摘要 · Abstract (English)
Dynamic 3D Gaussian Splatting methods achieve strong training-view PSNR on monocular video but generalize poorly: on the D-NeRF benchmark we measure an average train-test PSNR gap of 6.18 dB, rising to 11 dB on individual scenes. We report two findings that together account for most of that gap. Finding 1 (the role of splitting). A systematic ablation of the Adaptive Density Control pipeline (split, clone, prune, frequency, threshold, schedule) shows that splitting is responsible for over 80% of the gap: disabling split collapses the cloud from 44K to 3K Gaussians and the gap from 6.18 dB to 1.15 dB. Across all threshold-varying ablations, gap is log-linear in count (r = 0.995, bootstrap 95% CI [0.99, 1.00]), which suggests a capacity-based explanation. Finding 2 (the role of deformation coherence). We show that the capacity explanation is incomplete. A local-smoothness penalty on the per-Gaussian deformation field -- Elastic Energy Regularization (EER) -- reduces the gap by 40.8% while growing the cloud by 85%. Measuring per-Gaussian strain directly on trained checkpoints, EER reduces mean strain by 99.72% (median 99.80%) across all 8 scenes; on 8/8 scenes the median Gaussian under EER is less strained than the 1st-percentile (best-behaved) Gaussian under baseline. Alongside EER, we evaluate two further regularizers: GAD, a loss-rate-aware densification threshold, and PTDrop, a jitter-weighted Gaussian dropout. GAD+EER reduces the gap by 48%; adding PTDrop and a soft growth cap reaches 57%. We confirm that coherence generalizes to (a) a different deformation architecture (Deformable-3DGS, +40.6% gap reduction at re-tuned lambda), and (b) real monocular video (4 HyperNeRF scenes, reducing the mean PSNR gap by 14.9% at the same lambda as D-NeRF, with near-zero quality cost). The overfitting in dynamic 3DGS is driven by incoherent deformation, not parameter count.
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