  Neural radiance-density field methods have become increasingly popular for
the task of novel-view rendering. Their recent extension to hash-based
positional encoding ensures fast training and inference with visually pleasing
results. However, density-based methods struggle with recovering accurate
surface geometry. Hybrid methods alleviate this issue by optimizing the density
based on an underlying SDF. However, current SDF methods are overly smooth and
miss fine geometric details. In this work, we combine the strengths of these
two lines of work in a novel hash-based implicit surface representation. We
propose improvements to the two areas by replacing the voxel hash encoding with
a permutohedral lattice which optimizes faster, especially for higher
dimensions. We additionally propose a regularization scheme which is crucial
for recovering high-frequency geometric detail. We evaluate our method on
multiple datasets and show that we can recover geometric detail at the level of
pores and wrinkles while using only RGB images for supervision. Furthermore,
using sphere tracing we can render novel views at 30 fps on an RTX 3090. Code
is publicly available at: https://radualexandru.github.io/permuto_sdf
