Algorithm 1 Forward Rendering and Gated Optimization in Lumina-4DGS

Require:  3D Gaussians $\mathrm{\Theta }=\{\mu ,\mathrm{\Sigma },c_{sh},\alpha \}$, Camera Pose $\mathbf{P}$, Time t, Image $I_{gt}$ Ensure:  Final Rendered Image $I_{final}$, Updated Parameters   1:Initialization: Global AE/AWB parameters (${\mathbf{a}}_t,{\mathbf{b}}_t$), Bilateral Grid ${\mathcal{G}}_t$, Threshold ${\tau }_t$   2://—Stage 1: Forward Rendering (Pixel-wise integration)—   3:for each ray r traversing sorted Gaussians do   4:   Calculate canonical color via Spherical Harmonics: $c_{canonical}=\mathrm{SH}2\mathrm{RGB}(c_{sh},r)$   5:   // Step A: Global AWB and AE Compensation   6:   Apply channel-wise gain (AWB) and global bias (AE):   7:      $c_{global}=exp\left({\mathbf{a}}_t\right)\odot c_{canonical}+{\mathbf{b}}_t$   8:   // Step B: Local Photometric Refinement   9:   Sample grid affine matrix ${\mathrm{\Gamma }}_t$ for spatial position $\mu$: 10:      ${\mathrm{\Gamma }}_t=\mathrm{Interpolate}({\mathcal{G}}_t,\mu )$ 11:   Apply local affine correction: 12:      $c_{local}={\mathrm{\Gamma }}_t\times {[c_{global},1]}^T$ 13:   // Step C: Volumetric Alpha Blending 14:   Accumulate transmittance $T_i$ and final color: 15:      $C_{final}\left(r\right)={\sum }_i{\alpha }_i{T}_i{c}_{local,i}$ 16:end for 17:Assemble pixels to form $I_{final}$ 18://—Stage 2: Object-Aware SSIM-Gated Optimization— 19:Render raw geometry image $I_{render}$ without exposure compensation 20:Calculate object-level structural reliability: $S={\mathrm{SSIM}}_{obj}(I_{render},I_{gt})$ 21:if $S>{\tau }_t$ then 22:   ${\mathcal{M}}_{gate}\leftarrow 1$    // Structure is reliable, unfreeze appearance 23:else 24:   ${\mathcal{M}}_{gate}\leftarrow 0$    // Structure is chaotic, freeze appearance 25:end if 26://—Stage 3: Gradient Modulation— 27:Compute total loss ${\mathcal{L}}_{total}$ (see Equation (20)) 28:Update Geometry: $\mathrm{\Theta }\leftarrow \mathrm{\Theta }-\eta {\nabla }_{\mathrm{\Theta }}{\mathcal{L}}_{total}$ 29:Update Exposure: ${\mathrm{\Theta }}_{exp}\leftarrow {\mathrm{\Theta }}_{exp}-\eta \left({\mathcal{M}}_{gate}·{\nabla }_{{\mathrm{\Theta }}_{exp}}{\mathcal{L}}_{total}\right)$ 30:return $I_{final}$