  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.
