View source for Instant Neural Graphics Primitives with a Multiresolution Hash Encoding


[https://nvlabs.github.io/instant-ngp/ Project Webpage]

Allows training a NeRF or other neural representation in seconds but optimizing features in a hash table.<br>
This is faster than an octree since it doesn't require pointer chasing while using less space than enumerating voxels.<br>
Furthermore, the size of the hash table allows control over the amount of detail.

==Method==
===Multi-resolution Hash Encoding===

# For each level/resolution
## Find which voxel we are in and get indices to the corners.
## Hash each corner and retrieve features (<math>\in \mathbb{R}^{F}</math>) from the hash map.
## Do trilienar interpolation to get an average feature.
# Concatenate features from all levels (<math display="inline">\in \mathbb{R}^{LF}</math>) along with auxiliary inputs (<math display="inline">\in \mathbb{R}^{E}</math>, e.g. view direction) to produce a feature vector <math display="inline">\mathbf{y} \in \mathbb{R}^{LF+E}</math>.
# Pass <math>\mathbf{y}</math> through your small feature decoding neural network.

===Levels===
For resolutions in <math>[N_{min}, N_{max}]</math>.
* Resolution at level l: <math>N_{l} = \lfloor N_{min} * b^{l} \rfloor</math>
* <math>b = \exp \left( \frac{\log N_{max} - \log N_{min} }{L-1} \right)</math>

===Hashing Function===
* Hash collisions are ignored.
* The hash function used is: <math>h(\mathbf{x}) = \left( \oplus_{i=1}^{d} x_i \pi_i \right) \mod T</math>
** <math display="inline">\oplus</math> is bitwise XOR.
** <math display="inline">\pi_i</math> are unique large primes.
** <math display="inline">T</math> is the size of the hash table.

==Experiments==
===Setup===
* RTX 3090
* MLP with two hidden layers with width of 64 neurons.
* Hash tables are stored using half-precision.

==References==
[[Category: Papers]]