  This paper presents Neural Visibility Field (NVF), a novel uncertainty
quantification method for Neural Radiance Fields (NeRF) applied to active
mapping. Our key insight is that regions not visible in the training views lead
to inherently unreliable color predictions by NeRF at this region, resulting in
increased uncertainty in the synthesized views. To address this, we propose to
use Bayesian Networks to composite position-based field uncertainty into
ray-based uncertainty in camera observations. Consequently, NVF naturally
assigns higher uncertainty to unobserved regions, aiding robots to select the
most informative next viewpoints. Extensive evaluations show that NVF excels
not only in uncertainty quantification but also in scene reconstruction for
active mapping, outperforming existing methods.
