Our scene representation is a hybrid of primitive and volumetric model. (a) Primitive component. We explicitly allocate voxels primitives to cover different scene level-of-details under an Octree layout. Note that we do not replicate a traditional Octree data structure with parent-child pointers or linear Octree. We only keep voxels at the Octree leaf nodes without any ancestor nodes. (b) Volumetric component. Inside a voxel is a volumetric (trilinear) density field and a (constant) spherical harmonic field. We sample K points on the ray-voxel intersection segment to compute the intensity contribution from the voxel to the pixel with numerical integration.
Adaptive level-of-details is crucial to scalability and quality. Sparse voxels with uniform voxel size can not scale up.
We sort voxels by ray direction-dependent Morton order, which ensures correct primitive blending order with mathematical proof. Sorting by primtive centers like 3DGS can produce inaccurate rendering. The inaccurate sorting causes 3DGS popping artifact (see left video below) while we don't have this issue (right video).