A novel algorithm for optimizing bundle adjustment in image sequence alignment

2024-11-10

arXiv.org

AI Summary

Bundle adjustment (BA) in cryo-electron tomography conventionally relies on the Levenberg–Marquardt (L-M) algorithm, which suffers from high sensitivity to initial estimates and slow convergence. Method: To address these limitations, this work introduces optimal control theory into the general nonlinear optimization framework of BA for the first time, proposing an Optimal Control-based Algorithm (OCA) featuring a bisection-based parameter update mechanism. OCA formulates BA as a joint state-control optimization problem, explicitly modeling both geometric parameters and auxiliary control variables to stabilize iterative updates. Contribution/Results: Experiments on synthetic and real cryo-tomographic data demonstrate that OCA achieves significantly faster convergence than L-M—particularly under poor initialization—thereby improving 3D structure reconstruction efficiency. The enhanced robustness and speed directly accelerate tilt-series image registration and downstream reconstruction pipelines.

Technology Category

• Search and Optimization: Algorithm Configuration
• Machine Learning: Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Algorithmic accountability and transparency on the web
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

The Bundle Adjustment (BA) model is commonly optimized using a nonlinear least squares method, with the Levenberg-Marquardt (L-M) algorithm being a typical choice. However, despite the L-M algorithm's effectiveness, its sensitivity to initial conditions often results in slower convergence when applied to poorly conditioned datasets, motivating the exploration of alternative optimization strategies. This paper introduces a novel algorithm for optimizing the BA model in the context of image sequence alignment for cryo-electron tomography, utilizing optimal control theory to directly optimize general nonlinear functions. The proposed Optimal Control Algorithm (OCA) exhibits superior convergence rates and effectively mitigates the oscillatory behavior frequently observed in L-M algorithm. Extensive experiments on both synthetic and real-world datasets were conducted to evaluate the algorithm's performance. The results demonstrate that the OCA achieves faster convergence compared to the L-M algorithm. Moreover, the incorporation of a bisection-based update procedure significantly enhances the OCA's performance, particularly in poorly initialized datasets. These findings indicate that the OCA can substantially improve the efficiency of 3D reconstructions in cryo-electron tomography.

Problem

• Optimizing bundle adjustment for image sequence alignment
• Improving convergence in poorly conditioned datasets
• Enhancing 3D reconstruction efficiency in cryo-electron tomography

Innovation

• Uses optimal control theory for optimization
• Introduces bisection-based update procedure
• Improves convergence in poorly initialized datasets