POp-GS: Next Best View in 3D-Gaussian Splatting with P-Optimality (2503.07819v2)

Abstract: In this paper, we present a novel algorithm for quantifying uncertainty and information gained within 3D Gaussian Splatting (3D-GS) through P-Optimality. While 3D-GS has proven to be a useful world model with high-quality rasterizations, it does not natively quantify uncertainty or information, posing a challenge for real-world applications such as 3D-GS SLAM. We propose to quantify information gain in 3D-GS by reformulating the problem through the lens of optimal experimental design, which is a classical solution widely used in literature. By restructuring information quantification of 3D-GS through optimal experimental design, we arrive at multiple solutions, of which T-Optimality and D-Optimality perform the best quantitatively and qualitatively as measured on two popular datasets. Additionally, we propose a block diagonal covariance approximation which provides a measure of correlation at the expense of a greater computation cost.

Overview of POp-GS: Next Best View in 3D-Gaussian Splatting with P-Optimality

The paper "POp-GS: Next Best View in 3D-Gaussian Splatting with P-Optimality" addresses the challenge of quantifying uncertainty in 3D Gaussian Splatting (3D-GS) models. While 3D-GS has garnered attention for its high-quality novel view synthesis through explicit world modeling, it inherently lacks mechanisms for uncertainty quantification. This deficiency is notable in applications involving active perception and online SLAM where understanding information gain and managing resource constraints are vital.

The authors introduce a method for quantifying uncertainty and information gain through the application of optimal experimental design, presenting T-Optimality and D-Optimality as particularly effective solutions. They further propose a block diagonal approximation to the 3D-GS uncertainty, offering a balance between accuracy and computational overhead.

Methodology

The authors commence by exploring the principles of Gaussian Splatting. 3D-GS models scenes using 3D ellipsoids defined by parameters such as position ($\mu$), scale ($S$), rotation ($R$), opacity ($\alpha$), and color (using spherical harmonics). These ellipsoids can be rendered to create 2D projections, which provide novel views of the scene. While traditional approaches have leveraged gradient descent for optimizing these parameters, uncertainty quantification remains underexplored.

The paper advances the field by utilizing optimal experimental design frameworks, particularly focusing on P-Optimality metrics. These metrics (notably D-Optimality and T-Optimality) provide measures of information gain based on the covariance matrix derived from the Hessian matrix of the system. The authors argue for using block diagonal approximation of the covariance matrix to capture parameter correlations more accurately. This approximation allows for more precise computation of information gain while managing the large memory requirements of storing full covariance matrices for complex models.

Numerical Results

Experiments conducted on the Mip-NeRF360 and Blender datasets demonstrate the superior performance of D-Optimality and T-Optimality approaches over existing methods, including FisherRF. The authors highlight that these approaches yield significant improvements in terms of PSNR, SSIM, and LPIPS metrics, especially in scenarios involving sparse observations (e.g., ten-view setups).

• In single view selection tasks with ten views, D-Optimality using block diagonal approximation achieved PSNR improvements as high as 25.41, outperforming FisherRF's 24.59 on the Blender dataset.
• Batch view selection tests also underscored the efficacy of P-optimal solutions, with D-Optimality demonstrating high SSIM and low LPIPS scores, indicating superior relayance of visual fidelity and perceptual accuracy.

Additionally, information quantification showed strong correlation with reconstruction error, reinforcing the validity of the proposed approach for effective uncertainty estimation.

Implications and Future Work

This work has immediate implications for robotic systems requiring efficient active perception strategies, offering tools for optimally selecting views that enhance model accuracy while conserving computational resources. The methodology proposed is advantageous for real-time applications such as autonomous navigation, robotic mapping, and complex scene understanding.

Future developments may explore enhancing the block diagonal approximation to encapsulate inter-ellipsoid dependencies or leveraging the opacity parameter more effectively. The application of these approaches could extend to multimodal systems where integration of additional sensory data might be beneficial.

The insight gained from this paper extends theoretical understanding of active perception through optimal experimental design while practical implementation for real-time SLAM and novel view synthesis systems in robotics remains promising. The increase in computational efficiency and prediction fidelity aligns closely with contemporary needs of AI-driven spatial awareness requiring robust, scalable solutions.