ProBA: Probabilistic Bundle Adjustment with the Bhattacharyya Coefficient

TL;DR

ProBA introduces a probabilistic bundle adjustment framework that models spatial uncertainty and improves robustness in structure-from-motion and SLAM tasks, especially in noisy, unstructured environments.

Contribution

It presents a novel probabilistic re-parameterization of BA that jointly optimizes camera parameters and geometry from scratch, leveraging a Gaussian landmark representation and adaptive graph optimization.

Findings

Achieves superior accuracy over classical and learning-based methods.

Expands the basin of attraction, improving robustness in noisy conditions.

Provides a scalable framework for SfM and SLAM in unstructured environments.

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.