Manifold Sampling for Differentiable Uncertainty in Radiance Fields

Abstract: Radiance fields are powerful and, hence, popular models for representing the appearance of complex scenes. Yet, constructing them based on image observations gives rise to ambiguities and uncertainties. We propose a versatile approach for learning Gaussian radiance fields with explicit and fine-grained uncertainty estimates that impose only little additional cost compared to uncertainty-agnostic training. Our key observation is that uncertainties can be modeled as a low-dimensional manifold in the space of radiance field parameters that is highly amenable to Monte Carlo sampling. Importantly, our uncertainties are differentiable and, thus, allow for gradient-based optimization of subsequent captures that optimally reduce ambiguities. We demonstrate state-of-the-art performance on next-best-view planning tasks, including high-dimensional illumination planning for optimal radiance field relighting quality.