Geometric Probing for Isotropic Optimization Manifold in Sparse-View 3D Gaussian Splatting

3D Gaussian Splatting (3DGS) achieves impressive rendering quality but degrades drastically under sparse views. Through optimization manifold analysis, we reveal that sparse supervision produces anisotropic loss surfaces where rendering quality collapses sharply along three geometric fragility axes: position shifts, rotation/scale ill-conditioning, and opacity instability. Guided by this analysis, we propose Stable 3DGS (StableGS), which steers optimization toward isotropic stability via geometric probing. Unlike the generic, uniform smoothing of methods like SAM, which cannot fit 3DGS, StableGS uses domain-specific geometric probes to target the splatting operator’s unique instabilities. Our approach comprises: (1) Attribute-Space Probing that varies each Gaussian’s attributes based on Hessian-informed sensitivity analysis to measure rendering fragility, then minimizes loss at probe points; (2) Viewpoint-Space Probing that samples geometrically critical poses and enforces consistency between base and probed configurations. StableGS significantly advances state-of-the-art (SOTA) performance across multiple benchmarks, achieving substantial improvements such as +0.64dB PSNR on DTU [14] with 74% anisotropy reduction in optimization manifold. Code is available at https://github.com/zyl123456aB/StableGS.