Hash Encoding

Multiresolution hash encoding (Müller et al., SIGGRAPH 2022)

1. For $\mathbf{x}$, find the surrounding voxel at each of $L$ resolutions; hash its corner coordinates $(i,j,k)$ into $[0,T)$.
2. Look up $F$-dimensional feature vectors in the table ${\theta }_l$.
3. Linearly interpolate by the position of $\mathbf{x}$ in the voxel.
4. Concatenate all levels (+ auxiliary inputs).
5. Decode with a small MLP. Gradients flow back into the looked-up features.

Intuition

Memory is a fixed budget $T$ per level, independent of the grid resolution. Important locations claim slots through training; unimportant ones share slots harmlessly. Collisions are resolved implicitly by gradients and the multiresolution structure. No tree has to be built or rebuilt (unlike octrees). Training takes seconds.

Octree (NGLOD, NSVF)	Hash grid (Instant NGP)
explicit adaptive tree, memory only where the surface is	flat table of $T$ features per level, no spatial structure
construction, traversal, rebuilding during training	the hash is the address

Appears in

• Lecture 6.1, Instant NGP
• Lecture 7, Instant NGP: three pillars, NeRF in minutes

Related concepts

• Neural Field
• Voxel Grid