In many recent works, multi-layer perceptions (MLPs) have been shown to be suitable for modeling complex spatially-varying functions including images and 3D scenes. Although the MLPs are able to represent complex scenes with unprecedented quality and memory footprint, this expressive power of the MLPs, however, comes at the cost of long training and inference times. On the other hand, bilinear/trilinear interpolation on regular grid based representations can give fast training and inference times, but cannot match the quality of MLPs without requiring significant additional memory. Hence, in this work, we investigate what is the smallest change to grid-based representations that allows for retaining the high fidelity result of MLPs while enabling fast reconstruction and rendering times. We introduce a surprisingly simple change that achieves this task -- simply allowing a fixed non-linearity (ReLU) on interpolated grid values. When combined with coarse to-fine optimization, we show that such an approach becomes competitive with the state-of-the-art. We report results on radiance fields, and occupancy fields, and compare against multiple existing alternatives. Code and data for the paper are available at https://geometry.cs.ucl.ac.uk/projects/2022/relu_fields.

翻译：在许多近期研究中，多层感知机已被证明适用于建模包含图像和三维场景在内的复杂空间变化函数。尽管MLP能够以前所未有的质量和内存占用表示复杂场景，但其表达能力的代价是冗长的训练和推理时间。另一方面，基于规则网格的双线性/三线性插值虽能实现快速训练与推理，但若未显著增加内存需求，其质量无法媲美MLP。因此，本文探究如何对网格表示进行最小改动，以在保持MLP高保真结果的同时实现快速重建与渲染。我们引入了一种出奇简洁的改变——在插值网格值上固定施加非线性（ReLU）。结合从粗到细的优化策略后，该方法可与现有最优技术相媲美。我们报告了在辐射场和占用场上的结果，并与多种现有方案进行了对比。论文代码与数据详见https://geometry.cs.ucl.ac.uk/projects/2022/relu_fields。