Predicting Compression Gains Before Encoding: Attribute Models for 2D Gaussian Images

Gaussian image representations, which encode an image as a set of 2D Gaussians, have become a practical representation for image compression. Compressing this set involves two interlinked design choices: the spatial organization of the Gaussians and the probability model for their attributes. Such choices are typically made empirically, by building candidate coders and comparing total file size. A controlled study of lossless coding of quantized Gaussian sets shows that this practice can mislead: among the structures tested, a quadtree hierarchy codes positions most compactly, yet loses overall because of the attribute model paired with it. We therefore propose a predict-before-encoding protocol: it measures, on a selection split, whether the information a quadtree cell carries about each attribute outweighs the cost of learning a separate model per cell, and fixes the answer before any evaluation image is encoded. In a prospective study on GaussianImage representations, the predicted gain over conditioning every attribute, 1.414 bits per Gaussian, closely matches the realized gain of 1.361, and the protocol also correctly forecast the one comparison the chosen coder loses.