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Bundle Adjustment in the Eager Mode
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DOI：10.1109/tro.2026.3706557.png)
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Abstract
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Bundle adjustment (BA) is a critical technique in various robotic applications such as simultaneous localization and mapping (SLAM), augmented reality (AR), and photogrammetry. BA optimizes parameters such as camera poses and 3-D landmarks to align them with observations. With the growing importance of deep learning in perception systems, there is an increasing need to integrate BA with deep learning frameworks for enhanced reliability and performance. However, widely used C++-based BA libraries, such as GTSAM, g<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{2}$</tex-math></inline-formula>o, and Ceres Solver, lack native integration with modern deep learning libraries like PyTorch. This limitation affects their flexibility, ease of debugging, and overall implementation efficiency. To address this gap, we introduce an eager-mode BA library seamlessly integrated with PyTorch with high efficiency. Our approach includes a sparsity-aware autodifferentiation design and GPU-accelerated sparse operations designed for second-order optimization. Our eager-mode BA on GPU demonstrates substantial runtime efficiency, achieving an average speedup of 18.5×, 22×, and 23× across all benchmarks compared to GTSAM, g<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{2}$</tex-math></inline-formula>o, and Ceres, respectively. The source code is available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/pypose/bae</uri>.
Keywords:
Autodifferentiation
bundle adjustment
nonlinear least squares
pose graph optimization
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