  Since being proposed, Neural Radiance Fields (NeRF) have achieved great
success in related tasks, mainly adopting the hierarchical volume sampling
(HVS) strategy for volume rendering. However, the HVS of NeRF approximates
distributions using piecewise constant functions, which provides a relatively
rough estimation. Based on the observation that a well-trained weight function
$w(t)$ and the $L_0$ distance between points and the surface have very high
similarity, we propose $L_0$-Sampler by incorporating the $L_0$ model into
$w(t)$ to guide the sampling process. Specifically, we propose to use piecewise
exponential functions rather than piecewise constant functions for
interpolation, which can not only approximate quasi-$L_0$ weight distributions
along rays quite well but also can be easily implemented with few lines of code
without additional computational burden. Stable performance improvements can be
achieved by applying $L_0$-Sampler to NeRF and its related tasks like 3D
reconstruction. Code is available at https://ustc3dv.github.io/L0-Sampler/ .
