A novel algorithm for optimizing bundle adjustment in image sequence alignment

TL;DR

This paper presents a new optimal control-based algorithm for bundle adjustment in image sequence alignment, demonstrating faster convergence and better robustness than traditional Levenberg-Marquardt methods, especially in challenging datasets.

Contribution

The paper introduces the Optimal Control Algorithm (OCA), a novel method that improves convergence speed and robustness in bundle adjustment for cryo-electron tomography.

Findings

OCA converges faster than L-M algorithm.

Incorporating bisection-based updates enhances performance.

OCA is effective on synthetic and real datasets.

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.