  We present a new generic method for shadow-aware multi-view satellite
photogrammetry of Earth Observation scenes. Our proposed method, the Shadow
Neural Radiance Field (S-NeRF) follows recent advances in implicit volumetric
representation learning. For each scene, we train S-NeRF using very high
spatial resolution optical images taken from known viewing angles. The learning
requires no labels or shape priors: it is self-supervised by an image
reconstruction loss. To accommodate for changing light source conditions both
from a directional light source (the Sun) and a diffuse light source (the sky),
we extend the NeRF approach in two ways. First, direct illumination from the
Sun is modeled via a local light source visibility field. Second, indirect
illumination from a diffuse light source is learned as a non-local color field
as a function of the position of the Sun. Quantitatively, the combination of
these factors reduces the altitude and color errors in shaded areas, compared
to NeRF. The S-NeRF methodology not only performs novel view synthesis and full
3D shape estimation, it also enables shadow detection, albedo synthesis, and
transient object filtering, without any explicit shape supervision.
