ProBA: Probabilistic Bundle Adjustment with the Bhattacharyya Coefficient

arXiv:2505.20858v2 Announce Type: replace Abstract: Classical Bundle Adjustment (BA) is fundamentally limited by its reliance on precise metric initialization and prior camera intrinsics. While modern dense matchers offer high-fidelity correspondences, traditional Structure-from-Motion (SfM) pipelines struggle to leverage them, as rigid track-building heuristics fail in the presence of their inherent noise. We present \textbf{ProBA (Probabilistic Bundle Adjustment)}, a probabilistic re-parameterization of the BA manifold that enables joint optimization of extrinsics, focal lengths, and geometry from a strict cold start. By replacing fragile point tracks with a flexible kinematic pose graph and representing landmarks as 3D Gaussians, our framework explicitly models spatial uncertainty through a unified Negative Log-Likelihood (NLL) objective. This volumetric formulation smooths the non-convex optimization landscape and naturally weights correspondences by their statistical confidence. To maintain global consistency, we optimize over a sparse view graph using an iterative, adaptive edge-weighting mechanism to prune erroneous topological links. Furthermore, we resolve mirror ambiguities inherent to prior-free SfM via a dual-hypothesis regularization strategy. Extensive evaluations show that our approach significantly expands the basin of attraction and achieves superior accuracy over both classical and learning-based baselines, providing a scalable foundation that greatly benefits SfM and SLAM robustness in unstructured environments.