# ProBA: Probabilistic Bundle Adjustment with the Bhattacharyya Coefficient

arXiv: https://arxiv.org/abs/2505.20858 · HTML: https://mlsanity.com/paper/2505.20858/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 43 references that are in the map.
- First posted on arXiv 27 May 2025.

## Builds on (most cited first, 18 of 18)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [DUSt3R: Geometric 3D Vision Made Easy](https://mlsanity.com/paper/2312.14132/) (2023)
- [VGGT: Visual Geometry Grounded Transformer](https://mlsanity.com/paper/2503.11651/) (2025)
- [ORB-SLAM: a Versatile and Accurate Monocular SLAM System](https://mlsanity.com/paper/1502.00956/) (2015)
- [LoFTR: Detector-Free Local Feature Matching with Transformers](https://mlsanity.com/paper/2104.00680/) (2021)
- [Grounding Image Matching in 3D with MASt3R](https://mlsanity.com/paper/2406.09756/) (2024)
- [RoMa: Robust Dense Feature Matching](https://mlsanity.com/paper/2305.15404/) (2023)
- [TEASER: Fast and Certifiable Point Cloud Registration](https://mlsanity.com/paper/2001.07715/) (2020)
- [Image Matching across Wide Baselines: From Paper to Practice](https://mlsanity.com/paper/2003.01587/) (2020)
- [SPARF: Neural Radiance Fields from Sparse and Noisy Poses](https://mlsanity.com/paper/2211.11738/) (2022)
- [COLMAP-Free 3D Gaussian Splatting](https://mlsanity.com/paper/2312.07504/) (2023)
- [DKM: Dense Kernelized Feature Matching for Geometry Estimation](https://mlsanity.com/paper/2202.00667/) (2022)
- [MASt3R-SfM: a Fully-Integrated Solution for Unconstrained Structure-from-Motion](https://mlsanity.com/paper/2409.19152/) (2024)
- [A Survey of Structure from Motion](https://mlsanity.com/paper/1701.08493/) (2017)
- [Detector-Free Structure from Motion](https://mlsanity.com/paper/2306.15669/) (2023)
- [Power Variable Projection for Initialization-Free Large-Scale Bundle Adjustment](https://mlsanity.com/paper/2405.05079/) (2024)
- [Building Rome with Convex Optimization](https://mlsanity.com/paper/2502.04640/) (2025)

## Abstract (arXiv)

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 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.