[Paper Review] Density Uncertainty Quantification with NeRF-Ensembles: Impact of Data and Scene Constraints

Miriam Jäger, Steven Landgraf+1 more|arXiv (Cornell University)|Dec 22, 2023

Optical measurement and interference techniques4 citations

TL;DR

This paper proposes NeRF-Ensembles to quantify density uncertainty in Neural Radiance Fields, improving 3D reconstruction robustness and enabling post-processing artifact removal. By training multiple independently initialized NeRFs, the method estimates uncertainty via variance in density predictions, reducing noise and foggy artifacts while enhancing structural completeness through mean density outputs.

ABSTRACT

In the fields of computer graphics, computer vision and photogrammetry, Neural Radiance Fields (NeRFs) are a major topic driving current research and development. However, the quality of NeRF-generated 3D scene reconstructions and subsequent surface reconstructions, heavily relies on the network output, particularly the density. Regarding this critical aspect, we propose to utilize NeRF-Ensembles that provide a density uncertainty estimate alongside the mean density. We demonstrate that data constraints such as low-quality images and poses lead to a degradation of the training process, increased density uncertainty and decreased predicted density. Even with high-quality input data, the density uncertainty varies based on scene constraints such as acquisition constellations, occlusions and material properties. NeRF-Ensembles not only provide a tool for quantifying the uncertainty but exhibit two promising advantages: Enhanced robustness and artifact removal. Through the utilization of NeRF-Ensembles instead of single NeRFs, small outliers are removed, yielding a smoother output with improved completeness of structures. Furthermore, applying percentile-based thresholds on density uncertainty outliers proves to be effective for the removal of large (foggy) artifacts in post-processing. We conduct our methodology on 3 different datasets: (i) synthetic benchmark dataset, (ii) real benchmark dataset, (iii) real data under realistic recording conditions and sensors.

Motivation & Objective

• To investigate how data and scene constraints affect density uncertainty in NeRF-based 3D reconstructions.
• To evaluate the performance of NeRF-Ensembles in improving robustness and reducing artifacts compared to single NeRFs.
• To explore the use of density uncertainty for post-processing artifact removal, particularly foggy and ghostly artifacts.
• To identify key factors—such as image quality, pose accuracy, occlusions, and material properties—that influence training performance and uncertainty.
• To establish best practices for high-quality 3D reconstruction using NeRF-Ensembles with optimized data and acquisition conditions.

Proposed method

• Training a multi-member NeRF-Ensemble with randomly initialized, independent NeRFs to estimate density uncertainty via variance across ensemble members.
• Using the mean density across ensemble members to produce a more robust and complete 3D reconstruction, reducing small outliers and noise.
• Applying percentile-based thresholds on density uncertainty to identify and remove high-uncertainty voxels, effectively eliminating large (foggy) artifacts in post-processing.
• Evaluating the impact of data constraints by injecting image noise (σ_Im) and pose noise (σ_t, σ_R, σ_t,R) into input data to assess effects on PSNR and uncertainty.
• Analyzing scene constraints such as view coverage gaps, occlusions, and material properties (e.g., reflectivity) on uncertainty distribution in 3D space.
• Conducting experiments on three datasets: synthetic, real benchmark, and real-world data under realistic recording conditions to validate generalization.

Figure 1: Flowchart of the methodology: Input data are the images and corresponding camera poses. A NeRF-Ensemble with a total number of M members is trained. The NeRF-Ensemble provides an average network output with mean density values over all NeRFs in the ensemble and a corresponding density unce

Experimental results

Research questions

• RQ1 How do image noise and pose noise affect the training performance and density uncertainty of NeRFs?
• RQ2 How do scene-level constraints such as occlusions, poor view coverage, and reflective materials influence density uncertainty in NeRF reconstructions?
• RQ3 To what extent does using NeRF-Ensembles improve reconstruction robustness compared to single NeRFs?
• RQ4 Can density uncertainty quantification from NeRF-Ensembles effectively guide post-processing artifact removal?
• RQ5 What are the optimal data and acquisition conditions for minimizing density uncertainty and maximizing reconstruction quality?

Key findings

• Pose noise in translation (σ_t), rotation (σ_R), and their combination (σ_t,R) significantly degrades PSNR and increases density uncertainty, while image noise (σ_Im) reduces PSNR but does not necessarily increase uncertainty.
• Even with high-quality input data, density uncertainty increases in occluded or poorly covered regions due to acquisition constellations and material properties such as reflectivity.
• The mean density output from NeRF-Ensembles reduces small outliers and improves structural completeness, resulting in smoother and more complete reconstructions than single NeRFs.
• Percentile-based thresholding on density uncertainty effectively removes large (foggy) artifacts in post-processing, significantly improving visual quality and geometric fidelity.
• High-quality poses are more critical than non-noisy images for minimizing density uncertainty, highlighting the importance of accurate camera calibration in NeRF pipelines.
• The use of NeRF-Ensembles provides a reliable uncertainty quantification that enables both improved robustness and targeted artifact removal, justifying the additional training cost.