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/ .

翻译：自提出以来，神经辐射场（NeRF）在相关任务中取得了巨大成功，其体渲染主要采用分层体采样（HVS）策略。然而，NeRF的HVS采用分段常数函数近似分布，这仅能提供较为粗糙的估计。基于良训练权重函数 $w(t)$ 与点到表面间的 $L_0$ 距离具有高度相似性的观测，我们提出 $L_0$-Sampler，将 $L_0$ 模型融入 $w(t)$ 以引导采样过程。具体而言，我们提出使用分段指数函数而非分段常数函数进行插值，该方法不仅能良好地近似沿射线的准$L_0$ 权重分布，而且可通过少量代码轻松实现且不增加额外计算负担。将 $L_0$-Sampler 应用于NeRF及其相关任务（如三维重建），可获得稳定的性能提升。代码开源地址：https://ustc3dv.github.io/L0-Sampler/ 。