BA-GS: Bayesian Adaptive Gaussian Splatting for SFM-Free 3D Reconstruction

3D Gaussian Splatting (3DGS) has demonstrated exceptional performance in reconstruction and novel view synthesis tasks. However, its reliance on Structure-from-Motion preprocessing may lead to degraded performance under sparse-view scenarios. Recent works attempt to address this limitation by leveraging pre-trained image matching models to generate Gaussian primitives but overlook the probabilistic uncertainty embedded in both the initial primitive distribution and iterative position updates. This uncertainty can accumulate and degrade reconstruction fidelity. Hence, we propose BA-GS, a Bayesian framework that models both the global distribution and local uncertainty of Gaussian primitives. At global initialization, a Variational Bayesian Gaussian Mixture Model (VB-GMM) models the latent distribution of primitives, capturing region-wise density and gradient patterns. At local refinement, an Adaptive Kalman Filter refines each primitive's position by recursively fusing noisy gradient observations with spatial priors, dynamically adjusting its covariance according to local uncertainty. This hierarchical Bayesian formulation effectively bridges probabilistic distribution modeling and uncertainty-aware optimization, resulting in improved reconstruction quality under sparse-view conditions. Experiments across multiple benchmark datasets including Tanks and Temples, MVimgNet, and LLFF demonstrate that our method consistently outperforms existing approaches. By robustly handling initialization and optimization noise, our work paves the way for scalable 3D scene reconstruction from sparse image captures.