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.

In this paper, we present a novel algorithm for probabilistically updating and rasterizing semantic maps within 3D Gaussian Splatting (3D-GS). Although previous methods have introduced algorithms which learn to rasterize features in 3D-GS for enhanced scene understanding, 3D-GS can fail without warning which presents a challenge for safety-critical robotic applications. To address this gap, we propose a method which advances the literature of continuous semantic mapping from voxels to ellipsoids, combining the precise structure of 3D-GS with the ability to quantify uncertainty of probabilistic robotic maps. Given a set of images, our algorithm performs a probabilistic semantic update directly on the 3D ellipsoids to obtain an expectation and variance through the use of conjugate priors. We also propose a probabilistic rasterization which returns per-pixel segmentation predictions with quantifiable uncertainty. We compare our method with similar probabilistic voxel-based methods to verify our extension to 3D ellipsoids, and perform ablation studies on uncertainty quantification and temporal smoothing.

We present a novel end-to-end algorithm (PoCo) for the indoor RGB-D place recognition task, aimed at identifying the most likely match for a given query frame within a reference database. The task presents inherent challenges attributed to the constrained field of view and limited range of perception sensors. We propose a new network architecture, which generalizes the recent Context of Clusters (CoCs) to extract global descriptors directly from the noisy point clouds through end-to-end learning. Moreover, we develop the architecture by integrating both color and geometric modalities into the point features to enhance the global descriptor representation. We conducted evaluations on public datasets ScanNet-PR and ARKit with 807 and 5047 scenarios, respectively. PoCo achieves SOTA performance: on ScanNet-PR, we achieve R@1 of 64.63%, a 5.7% improvement from the best-published result CGis (61.12%); on Arkit, we achieve R@1 of 45.12%, a 13.3% improvement from the best-published result CGis (39.82%). In addition, PoCo shows higher efficiency than CGis in inference time (1.75X-faster), and we demonstrate the effectiveness of PoCo in recognizing places within a real-world laboratory environment. Video: https://youtu.be/D8dObAeMiCw;