Welcome to the official page of the paper Power Variable Projection for Initialization-Free Large-Scale Bundle Adjustment (accepted at ECCV 2024). You can find a video presentation here.

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.

This implementation is built on RootBA. Please follow the same instructions to install the dependencies.

Build external libraries

Use the build script:

./scripts/build-external.sh

Build PoVar

Use the build script:

./scripts/build-rootba-povar.sh [BUILD_TYPE]

You can optionally pass the cmake BUILD_TYPE used to compile RootBA as the first argument. If you don't pass anything the default is Release. The cmake build folder is build, inside the project root. This build script will use ccache and ninja automaticaly if they are found on PATH.

You can download the BAL dataset on the Bundle Adjustment in the Large webpage. Before using our solver, we randomly initialize a projective camera model, with the option --create-dataset:

./bin/bal --input /venice/problem-89-110973-pre.txt --create-dataset

The randomized dataset is created in the new folder data_custom/ on the root.

In line with our paper, the stratified BA includes two steps.

(a) We propose four different solvers --solver-type-step-1 for the nonlinear separable optimization problem:

• POWER_VARPROJ: Variable projection with power series expansion (by default)
• POWER_BUNDLE_ADJUSTMENT: Levenberg-Marquardt with power series expansion (see PoBA https://arxiv.org/abs/2204.12834)
• PCG: Variable projection with preconditioned conjugate gradients
• CHOLESKY: Variable projection with Cholesky factorization

(b) We propose two different solvers --solver-type-step-2 for the projective refinement problem:

• RIPOBA: Riemannian manifold framework for Levenberg-Marquardt with power series (by default)
• RIPCG: Riemannian manifold framework for Levenberg-Marquardt with preconditioned conjugate gradients

The implementation uses double precision.

Once the random initialization has been done, you can run the two solvers in a row with, for instance:

./bin/bal --num-threads 4 --input /data_custom/problem-89-110973-pre.txt --solver-type-step-1 POWER_SCHUR_COMPLEMENT --solver-type-step-2 RIPOBA 

The command --help will provide some explanations about the different options. In particular, you can set, among others:

• --max-num-iterations-step-1, --max-num-iterations-step-2: maximum number of outer iterations for each step (by default, 50).
• --power-sc-iterations: maximum order of power series (by default, 20).
• --residual-robust-norm: NONE (by default), CAUCHY, HUBER.
• --alpha: weight of the affine part in pOSE formulation (by default, 0.1).

If you find our work useful in your research, please consider citing:

@inproceedings{weber2025power,
  title={Power Variable Projection for Initialization-Free Large-Scale Bundle Adjustment},
  author={Weber, Simon and Hong, Je Hyeong and Cremers, Daniel},
  booktitle={European Conference on Computer Vision},
  pages={111--126},
  year={2025},
  organization={Springer}
}

@inproceedings{weber2023power,
  title={Power bundle adjustment for large-scale 3d reconstruction},
  author={Weber, Simon and Demmel, Nikolaus and Chan, Tin Chon and Cremers, Daniel},
  booktitle={Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition},
  pages={281--289},
  year={2023}
}

The code of the RootBA project is licensed under a BSD 3-Clause License.

Parts of the code are derived from Ceres Solver. Please also consider licenses of used third-party libraries. See ACKNOWLEDGEMENTS.