From Pixels to Compact Gaussians: Generalizable 2D Gaussian Image Representation via Error-Aware Graph Coarsening

Existing 2D Gaussian image representations often learn to place primitives from scratch or optimize them separately for each image. We observe that an image itself already provides an analytic starting point: each pixel supplies a Gaussian center and color, while its local structure tensor determines an anisotropic covariance. Rasterizing this dense field achieves approximately $25$–$30$ dB PSNR without training or per-image optimization. This high-fidelity but overcomplete initialization reframes compact Gaussian representation as a budget-constrained simplification problem. This overcomplete foundation shifts the core objective from synthesizing primitives to strategically pruning them under reconstruction feedback. To this end, we introduce Error-aware Pixel-Inductive Gaussians (EPIG), a bottom-up framework that alternates error-aware graph coarsening with reconstruction-driven refinement. A merging network selects neighboring primitives for moment-matched contraction, and a refinement network updates the survivors using the rendering residual. Repeating these steps yields a compact representation in a few feed-forward stages without test-time optimization. Across three budgets on DIV2K and zero-shot Kodak, EPIG improves PSNR over the evaluated feed-forward baselines.