  Recently neural volumetric representations such as neural reflectance fields
have been widely applied to faithfully reproduce the appearance of real-world
objects and scenes under novel viewpoints and lighting conditions. However, it
remains challenging and time-consuming to render such representations under
complex lighting such as environment maps, which requires individual ray
marching towards each single light to calculate the transmittance at every
sampled point. In this paper, we propose a novel method based on precomputed
Neural Transmittance Functions to accelerate the rendering of neural
reflectance fields. Our neural transmittance functions enable us to efficiently
query the transmittance at an arbitrary point in space along an arbitrary ray
without tedious ray marching, which effectively reduces the time-complexity of
the rendering. We propose a novel formulation for the neural transmittance
function, and train it jointly with the neural reflectance fields on images
captured under collocated camera and light, while enforcing monotonicity.
Results on real and synthetic scenes demonstrate almost two order of magnitude
speedup for renderings under environment maps with minimal accuracy loss.
