Regularization of NeRFs using differential geometry

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.