北京大学学报自然科学版 ›› 2020, Vol. 56 ›› Issue (6): 1013-1019.DOI: 10.13209/j.0479-8023.2020.098

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基于BFGS修正的高斯牛顿光束法平差解算方法

赵帅华1, 李言言2, 曹健1,†, 曹喜信1   

  1. 1. 北京大学软件与微电子学院, 北京 102600 2. 德国慕尼黑工业大学, 慕尼黑 80333
  • 收稿日期:2019-12-10 修回日期:2020-02-04 出版日期:2020-11-20 发布日期:2020-11-20
  • 通讯作者: 曹健, E-mail: caojian(at)ss.pku.edu.cn
  • 基金资助:
    国家重点研发计划(2018YFE0203801)资助

A BFGS-Corrected Gauss-Newton Solver for Bundle Adjustment

ZHAO Shuaihua1, LI Yanyan2, CAO Jian1,†, CAO Xixin1   

  1. 1. School of Software and Microelectronics, Peking University, Beijing 102600 2. Technische Universität München, Munich 80333
  • Received:2019-12-10 Revised:2020-02-04 Online:2020-11-20 Published:2020-11-20
  • Contact: CAO Jian, E-mail: caojian(at)ss.pku.edu.cn

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摘要：

针对高斯牛顿(Gauss-Newton, GN)方法求解光束法平差模型时对初值准确度要求高、应用场景受限的问题, 提出基于拟牛顿法BFGS (Broyden-Fletcher-Goldfarb-Shanno)修正的高斯牛顿算法——BFGS-GN 法。当高斯牛顿法的信息矩阵失去正定性后, 使用BFGS算法对法方程进行补充修正, 可从根本上消除高斯牛顿方法对初值敏感的数学缺陷。在数据集上的实验结果表明, BFGS-GN算法对不同类型的初值具有鲁棒性, 在初值较好的情况下, 所提方法与高斯牛顿法具有相同的精度和迭代效率; 在初值较差的情况下, 高斯牛顿方法
因发散而失效, BFGS-GN算法仍可以收敛到较高的精度。

关键词: 光束法平差, 高斯牛顿, BFGS 算法, 初值鲁棒

Abstract:

Aiming at the problem that the Gauss-Newton (GN) method is sensitive to the initial information matrix in the Bundle Adjustment (BA) model, which leads to limited application scenarios, the paper proposes a novel method BFGS-GN using BFGS (Broyden-Fletcher-Goldfarb-Shanno) algorithm to improve the traditional Gauss-Newton method. When the information matrix of the Gauss-Newton method loses positive definiteness, BFGS algorithm can be used to modify the normal equations, which fundamentally eliminates the mathematical defect that the Gauss-Newton method is sensitive to initial values. Experimental results demonstrate that proposed method is robust to different types of initials. The same accuracy and the number of iterations as GN can be obtained when the initial values are good. As for bad inputs, GN-based BA method cannot work but BFGS-GN can converge to a minimum.

Key words: bundle adjustment, Gauss-Newton, BFGS algorithm, initial value robustness

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