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Computer Vision Group
TUM Department of Informatics
Technical University of Munich

Technical University of Munich



Square Root Bundle Adjustment for Large-Scale Reconstruction


We propose a new formulation for the bundle adjustment problem which relies on nullspace marginalization of landmark variables by QR decomposition. Our approach, which we call square root bundle adjustment, is algebraically equivalent to the commonly used Schur complement trick, improves the numeric stability of computations, and allows for solving large-scale bundle adjustment problems with single-precision floating-point numbers. We show in real-world experiments with the BAL datasets that even in single precision the proposed solver achieves on average equally accurate solutions compared to Schur complement solvers using double precision. It runs significantly faster, but can require larger amounts of memory on dense problems. The proposed formulation relies on simple linear algebra operations and opens the way for efficient implementations of bundle adjustment on hardware platforms optimized for single-precision linear algebra processing.


Open-Source Code

The code is available on https://github.com/NikolausDemmel/rootba

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Conference and Workshop Papers
[]Square Root Marginalization for Sliding-Window Bundle Adjustment (N Demmel, D Schubert, C Sommer, D Cremers and V Usenko), In IEEE International Conference on Computer Vision (ICCV), 2021. ([project page]) [bibtex] [arXiv:2109.02182] [pdf]
[]Square Root Bundle Adjustment for Large-Scale Reconstruction (N Demmel, C Sommer, D Cremers and V Usenko), In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2021. ([project page]) [bibtex] [arXiv:2103.01843] [pdf]
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In April 2022 Jürgen Sturm, Christian Kerl and Daniel Cremers were featured among the top 10 most influential scholars in robotics of the last decade.


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