# Permutohedral Lattice

Physically based inverse rendering must separate materials from illumination, and the decomposition is ambiguous. Learned material predictions are usually added as auxiliary regularization losses, which change the objective and require rebalancing against photometric fitting. This work instead restricts the optimization space: multi-view material predictions are fused onto a mesh, a permutohedral lattice is built in the prior feature space, and surface points with similar predictions share material variables while the objective stays purely photometric. On Synthetic4Relight and TensoIR-Synthetic, relighting PSNR with two predictors is 1.5–2.5 dB above the strongest evaluated mesh-based baseline, and it beats a regularization loss using the same prior in controlled comparisons.

Physically based inverse rendering must separate materials from illumination, and the decomposition is ambiguous. Learned material predictions are usually added as auxiliary regularization losses, which change the objective and require rebalancing against photometric fitting. This work instead restricts the optimization space: multi-view material predictions are fused onto a mesh, a permutohedral lattice is built in the prior feature space, and surface points with similar predictions share material variables while the objective stays purely photometric. On Synthetic4Relight and TensoIR-Synthetic, relighting PSNR with two predictors is 1.5–2.5 dB above the strongest evaluated mesh-based baseline, and it beats a regularization loss using the same prior in controlled comparisons.