Analysis of Converged 3D Gaussian Splatting Solutions: Density Effects and Prediction Limit

TL;DR

This paper analyzes the structure and properties of 3D Gaussian Splatting solutions, revealing density-dependent patterns and fundamental limits in prediction, with implications for improving training and system design.

Contribution

It introduces the concept of Rendering-Optimal References (RORs), analyzes their statistical properties, and formalizes the density-stratification phenomenon affecting 3D Gaussian Splatting.

Findings

Stable mixture-structured scales and bimodal radiance patterns in RORs.

Density-dependent predictability of geometric and appearance parameters.

Visibility heterogeneity causes coupling between geometry and appearance in sparse regions.

Abstract

We investigate what structure emerges in 3D Gaussian Splatting (3DGS) solutions from standard multi-view optimization. We term these Rendering-Optimal References (RORs) and analyze their statistical properties, revealing stable patterns: mixture-structured scales and bimodal radiance across diverse scenes. To understand what determines these parameters, we apply learnability probes by training predictors to reconstruct RORs from point clouds without rendering supervision. Our analysis uncovers fundamental density-stratification. Dense regions exhibit geometry-correlated parameters amenable to render-free prediction, while sparse regions show systematic failure across architectures. We formalize this through variance decomposition, demonstrating that visibility heterogeneity creates covariance-dominated coupling between geometric and appearance parameters in sparse regions. This reveals the dual character of RORs: geometric primitives where point clouds suffice, and view synthesis primitives where multi-view constraints are essential. We provide density-aware strategies that improve training robustness and discuss architectural implications for systems that adaptively balance feed-forward prediction and rendering-based refinement.