Data Augmentation for NeRFs in the Low Data Limit

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.io/low-data-nerf/.

Fast Ergodic Search with Kernel Functions

Ergodic search enables optimal exploration of an information distribution while guaranteeing the asymptotic coverage of the search space. However, current methods typically have exponential computation complexity in the search space dimension and are restricted to Euclidean space. We introduce a computationally efficient ergodic search method. Our contributions are two-fold. First, we develop a kernel-based ergodic metric and generalize it from Euclidean space to Lie groups. We formally prove the proposed metric is consistent with the standard ergodic metric while guaranteeing linear complexity in the search space dimension. Secondly, we derive the first-order optimality condition of the kernel ergodic metric for nonlinear systems, which enables efficient trajectory optimization. Comprehensive numerical benchmarks show that the proposed method is at least two orders of magnitude faster than the state-of-the-art algorithm. 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-second-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.