Alpha Invariance: On Inverse Scaling Between Distance and Volume Density in Neural Radiance Fields

Scale-ambiguity in 3D scene dimensions leads to magnitude-ambiguity of volumetric densities in neural radiance fields, i.e., the densities double when scene size is halved, and vice versa. We call this property alpha invariance. For NeRFs to better maintain alpha invariance, we recommend 1) parameterizing both distance and volume densities in log space, and 2) a discretization-agnostic initialization strategy to guarantee high ray transmittance. We revisit a few popular radiance field models and find that these systems use various heuristics to deal with issues arising from scene scaling. We test their behaviors and show our recipe to be more robust. Visit our project page at https://pals.ttic.edu/p/alpha-invariance . * Equal contribution. Figure 1. A discretized view of volume rendering. Top: a ray is cut into intervals, each with a density i 0 and interval length di. Bottom: illustration of the weight given to the 3rd interval, computed through alpha compositing. The rendered color is obtained by weighting all the interval colors with their wis. If we scale each di by a constant k, scaling i by 1 k renders the identical color.