用P-最优性量化3D高斯点云的信息量，提升视觉定位可靠性
POp-GS: Next Best View in 3D-Gaussian Splatting with P-Optimality
- 基于最优实验设计重构信息度量方式，引入P-最优性框架
- 在两个数据集上验证，T-和D-最优性表现最佳，信息量化更准确
- 提出块对角协方差近似，捕捉特征相关性，适合高精度场景建模
本文提出一种新算法，通过P-最优性量化3D高斯点云（3D-GS）中的不确定性与信息增益。尽管3D-GS能生成高质量渲染结果，但其无法原生提供不确定性度量，限制了其在3D-GS SLAM等实际应用中的使用。我们从最优实验设计的角度重新构建信息量化问题，得到多种解法；其中T-最优性和D-最优性在两个主流数据集上的定量与定性评估中表现最优。此外，我们提出一种块对角协方差近似方法，在增加计算开销的前提下，提供了特征间相关性的度量。
原文摘要 · Abstract (English)
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.
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