Only What Was Seen: Observation-Gram Compaction of View-Dependent Appearance in 3D Gaussian Splatting
Abstract: Most of the memory of a 3D Gaussian Splatting model holds spherical-harmonic colour coefficients, yet each Gaussian is seen only from the narrow cone of directions of the training cameras. We turn this into a distortion metric that other compressors can adopt: a per-Gaussian observation Gram matrix, accumulated from viewing directions and blending weights, is the exact first-order map from coefficient changes to squared image error and needs only the model and the camera poses. Under it, degree reduction becomes a closed-form projection that generalises truncation, degree allocation a Lagrangian rate-distortion problem, and vector quantisation the matrix-weighted Lloyd algorithm, of which Compressed3D's quantiser is the scalar case. Swapped into Compressed3D with everything else unchanged, the metric raises PSNR by +0.49 dB before fine-tuning, with SSIM and LPIPS following, and at matched rate still gains +0.32 dB without a single training image. A training-free stack built on the metric alone is 15% smaller than the image-free GSICO at equal quality on Mip-NeRF 360.