  Neural radiance fields, or NeRF, represent a breakthrough in the field of
novel view synthesis and 3D modeling of complex scenes from multi-view image
collections. Numerous recent works have shown the importance of making NeRF
models more robust, by means of regularization, in order to train with possibly
inconsistent and/or very sparse data. In this work, we explore how differential
geometry can provide elegant regularization tools for robustly training
NeRF-like models, which are modified so as to represent continuous and
infinitely differentiable functions. In particular, we present a generic
framework for regularizing different types of NeRFs observations to improve the
performance in challenging conditions. We also show how the same formalism can
also be used to natively encourage the regularity of surfaces by means of
Gaussian or mean curvatures.
