PH-Dropout: Practical Epistemic Uncertainty Quantification for View Synthesis

TL;DR

PH-Dropout (Post hoc Dropout), the first real-time and accurate method for epistemic uncertainty estimation that operates directly on pre-trained NeRF and GS models, is introduced.

Abstract

View synthesis using Neural Radiance Fields (NeRF) and Gaussian Splatting (GS) has demonstrated impressive fidelity in rendering real-world scenarios. However, practical methods for accurate and efficient epistemic Uncertainty Quantification (UQ) in view synthesis are lacking. Existing approaches for NeRF either introduce significant computational overhead (e.g., ``10x increase in training time" or ``10x repeated training") or are limited to specific uncertainty conditions or models. Notably, GS models lack any systematic approach for comprehensive epistemic UQ. This capability is crucial for improving the robustness and scalability of neural view synthesis, enabling active model updates, error estimation, and scalable ensemble modeling based on uncertainty. In this paper, we revisit NeRF and GS-based methods from a function approximation perspective, identifying key differences and connections in 3D representation learning. Building on these insights, we introduce PH-Dropout (Post hoc Dropout), the first real-time and accurate method for epistemic uncertainty estimation that operates directly on pre-trained NeRF and GS models. Extensive evaluations validate our theoretical findings and demonstrate the effectiveness of PH-Dropout.

Figures (11)

• Figure 1: Active Learning - $\overline{\sigma_{\text{max}}}$: PH-Dropout robustness to active learning is showed by a decreasing epistemic uncertainty at decreasing $\overline{\sigma_{\text{max}}}$, with increasing number of training views.
• Figure 1: Comparison of Bayes Rays and PH-Dropout on NeRFacto: Bayes Rays fails to correlate depth uncertainty with high prediction error on the LF dataset.
• Figure 2: Active Learning - $r_{\text{drop}}$: PH-Dropout robustness to active learning is showed by a decreasing epistemic uncertainty at increasing $r_{\text{drop}}$, with increasing number of training views.
• Figure 3: Correlation between PH-Dropout based epistemic uncertainty estimation and the actual RMSE, with 3DGS at bounded scenario (Blender drum). 8 training views.
• Figure 4: Correlation between PH-Dropout based epistemic uncertainty estimation and the actual RMSE, with 2DGS at unbounded scenario. 64 training views.

Theorems & Definitions (14)

• Theorem 3.1
• proof
• Lemma 4.1
• proof
• Theorem 4.2
• proof
• Theorem 4.3
• proof
• Theorem 4.4
• proof