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

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. Quantifying uncertainty in parameters of 3D-GS is necessary to understand the information gained from acquiring new images as in active perception, or identify redundant images which can be removed from memory due to resource constraints in online 3D-GS SLAM. We propose to quantify uncertainty and information gain in 3D-GS by reformulating the problem through the lens of optimal experimental design, which is a classical solution to measuring information gain. 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 approximation of the 3D-GS uncertainty, which provides a measure of correlation for computing more accurate information gain, at the expense of a greater computation cost.