Current methods based on Neural Radiance Fields (NeRF) significantly lack the capacity to quantify uncertainty in their predictions, particularly on the unseen space including the occluded and outside scene content. This limitation hinders their extensive applications in robotics, where the reliability of model predictions has to be considered for tasks such as robotic exploration and planning in unknown environments. To address this, we propose a novel approach to estimate a 3D Uncertainty Field based on the learned incomplete scene geometry, which explicitly identifies these unseen regions. By considering the accumulated transmittance along each camera ray, our Uncertainty Field infers 2D pixel-wise uncertainty, exhibiting high values for rays directly casting towards occluded or outside the scene content. To quantify the uncertainty on the learned surface, we model a stochastic radiance field. Our experiments demonstrate that our approach is the only one that can explicitly reason about high uncertainty both on 3D unseen regions and its involved 2D rendered pixels, compared with recent methods. Furthermore, we illustrate that our designed uncertainty field is ideally suited for real-world robotics tasks, such as next-best-view selection.

We propose a Multi-Instance-Learning (MIL) approach for weakly-supervised learning problems, where a training set is formed by bags (sets of feature vectors or instances) and only labels at bag-level are provided. Specifically, we consider the Multi-Instance Dynamic-Ordinal-Regression (MI-DOR) setting, where the instance labels are naturally represented as ordinal variables and bags are structured as temporal sequences. To this end, we propose Multi-Instance Dynamic Ordinal Random Fields (MI-DORF). In this framework, we treat instance-labels as temporally-dependent latent variables in an Undirected Graphical Model. Different MIL assumptions are modelled via newly introduced high-order potentials relating bag and instance-labels within the energy function of the model. We also extend our framework to address the Partially-Observed MI-DOR problems, where a subset of instance labels are available during training. We show on the tasks of weakly-supervised facial behavior analysis, Facial Action Unit (DISFA dataset) and Pain (UNBC dataset) Intensity estimation, that the proposed framework outperforms alternative learning approaches. Furthermore, we show that MIDORF can be employed to reduce the data annotation efforts in this context by large-scale.