Current methods based on Neural Radiance Fields fail in the low data limit, particularly when training on incomplete scene data. Prior works augment training data only in next-best-view applications, which lead to hallucinations and model collapse with sparse data. In contrast, we propose adding a set of views during training by rejection sampling from a posterior uncertainty distribution, generated by combining a volumetric uncertainty estimator with spatial coverage. We validate our results on partially observed scenes; on average, our method performs 39.9% better with 87.5% less variability across established scene reconstruction benchmarks, as compared to state of the art baselines. We further demonstrate that augmenting the training set by sampling from any distribution leads to better, more consistent scene reconstruction in sparse environments. This work is foundational for robotic tasks where augmenting a dataset with informative data is critical in resource-constrained, a priori unknown environments. Videos and source code are available at https://murpheylab.github.iollow-data-nerfl

Ergodic search enables optimal exploration of an information distribution with guaranteed asymptotic coverage of the search space. However, current methods typically have exponential computational complexity and are limited to Euclidean space. We introduce a computationally efficient ergodic search method. Our contributions are two-fold as follows: First, we develop a kernel-based ergodic metric, generalizing it from Euclidean space to Lie groups. We prove this metric is consistent with the exact ergodic metric and ensures linear complexity. Second, we derive an iterative optimal control algorithm for trajectory optimization with the kernel metric. Numerical benchmarks show our method is two orders of magnitude faster than the state-of-the-art method. Finally, we demonstrate the proposed algorithm with a peg-in-hole insertion task. We formulate the problem as a coverage task in the space of SE(3) and use a 30-s-long human demonstration as the prior distribution for ergodic coverage. Ergodicity guarantees the asymptotic solution of the peg-in-hole problem so long as the solution resides within the prior information distribution, which is seen in the 100% success rate.