  Most face relighting methods are able to handle diffuse shadows, but struggle
to handle hard shadows, such as those cast by the nose. Methods that propose
techniques for handling hard shadows often do not produce geometrically
consistent shadows since they do not directly leverage the estimated face
geometry while synthesizing them. We propose a novel differentiable algorithm
for synthesizing hard shadows based on ray tracing, which we incorporate into
training our face relighting model. Our proposed algorithm directly utilizes
the estimated face geometry to synthesize geometrically consistent hard
shadows. We demonstrate through quantitative and qualitative experiments on
Multi-PIE and FFHQ that our method produces more geometrically consistent
shadows than previous face relighting methods while also achieving
state-of-the-art face relighting performance under directional lighting. In
addition, we demonstrate that our differentiable hard shadow modeling improves
the quality of the estimated face geometry over diffuse shading models.
