Sampling strategy
GL-NeRF sample points at which the integral of volume density reaches the values of the roots of the Laguerre polynomials.
Volume rendering in neural radiance fields is inherently time-consuming due to the large number of MLP calls on the points sampled per ray. Previous works would address this issue by introducing new neural networks or data structures. In this work, We propose GL-NeRF, a new perspective of computing volume rendering with the Gauss-Laguerre quadrature. GL-NeRF significantly reduces the number of MLP calls needed for volume rendering, introducing no additional data structures or neural networks. The simple formulation makes adopting GL-NeRF in any NeRF model possible. In the paper, we first justify the use of the Gauss-Laguerre quadrature and then demonstrate this plug-and-play attribute by implementing it in two different NeRF models. We show that with a minimal drop in performance, GL-NeRF can significantly reduce the number of MLP calls, showing the potential to speed up any NeRF model.
GL-NeRF is built upon revisiting the volume rendering integral. By a simple change of variable, we found that it is a weighted integral w.r.t the color function and can be computed by the Gauss-Laguerre quadrature.
GL-NeRF sample points at which the integral of volume density reaches the values of the roots of the Laguerre polynomials.
In addition to the Stone-Weierstrass theorem, we empirically found that the color function can be approximated by polynomials.
GL-NeRF provides on-par results with baseline methods it's adopted on.
TensoRF is served as a baseline example while GL-NeRF is able to be plugged into ANY NeRF representation.