# Power Variable Projection for Initialization-Free Large-Scale Bundle Adjustment

arXiv: https://arxiv.org/abs/2405.05079 · HTML: https://mlsanity.com/paper/2405.05079/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 27 references that are in the map.
- First posted on arXiv 8 May 2024.

## Builds on (most cited first, 5 of 5)

- [Stochastic Bundle Adjustment for Efficient and Scalable 3D Reconstruction](https://mlsanity.com/paper/2008.00446/) (2020)
- [Square Root Bundle Adjustment for Large-Scale Reconstruction](https://mlsanity.com/paper/2103.01843/) (2021)
- [MegBA: A GPU-Based Distributed Library for Large-Scale Bundle Adjustment](https://mlsanity.com/paper/2112.01349/) (2021)
- [A Game of Bundle Adjustment -- Learning Efficient Convergence](https://mlsanity.com/paper/2308.13270/) (2023)
- [Multidirectional Conjugate Gradients for Scalable Bundle Adjustment](https://mlsanity.com/paper/2110.04015/) (2021)

## Built on by (most cited first, 9 of 9)

- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)
- [Towards Initialization-free Calibrated Bundle Adjustment](https://mlsanity.com/paper/2506.23808/) (2025)
- [A Taxonomy of Structure from Motion Methods](https://mlsanity.com/paper/2505.15814/) (2025)
- [PRaDA: Projective Radial Distortion Averaging](https://mlsanity.com/paper/2504.16499/) (2025)
- [Sparse Variable Projection in Robotic Perception: Exploiting Separable Structure for Efficient Nonlinear Optimization](https://mlsanity.com/paper/2512.07969/) (2025)
- [ProBA: Probabilistic Bundle Adjustment with the Bhattacharyya Coefficient](https://mlsanity.com/paper/2505.20858/) (2025)
- [CSS-BA: Gate-Guided Column Space Search for Bundle Adjustment](https://mlsanity.com/paper/2607.15652/) (2026)
- [Initialization-Free Bundle Adjustment Revisited: A Controlled Experimental Study](https://mlsanity.com/paper/2608.18028/) (2026)
- [Triangulation-Free Bundle Adjustment with Graduated Non-Convexity for Camera Pose Refinement from Coarse Priors](https://mlsanity.com/paper/2608.21008/) (2026)

## Abstract (arXiv)

Most Bundle Adjustment (BA) solvers like the Levenberg-Marquardt algorithm require a good initialization. Instead, initialization-free BA remains a largely uncharted territory. The under-explored Variable Projection algorithm (VarPro) exhibits a wide convergence basin even without initialization. Coupled with object space error formulation, recent works have shown its ability to solve small-scale initialization-free bundle adjustment problem. To make such initialization-free BA approaches scalable, we introduce Power Variable Projection (PoVar), extending a recent inverse expansion method based on power series. Importantly, we link the power series expansion to Riemannian manifold optimization. This projective framework is crucial to solve large-scale bundle adjustment problems without initialization. Using the real-world BAL dataset, we experimentally demonstrate that our solver achieves state-of-the-art results in terms of speed and accuracy. To our knowledge, this work is the first to address the scalability of BA without initialization opening new venues for initialization-free structure-from-motion.