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<p>This study proposes a novel alternating optimization algorithm for bundle adjustment, a critical process in structure from motion methods. We introduce the inverse depth of each three-dimensional (3D) point as an augmented independent variable and develop a low-order polynomial error metric. Theoretically, the error can be adjusted to align closely with the re-projection error since it essentially acts as a re-weighted re-projection error. We decouple the bundle adjustment problem by breaking it down into three separate tasks: estimating the camera’s pose, determining the 3D structure, and optionally estimating the camera’s intrinsic parameter. Each task can be handled independently, either by camera or by point, allowing for easy distribution of computation. Camera pose estimation is a case of the absolute orientation problem, which can be globally solved in closed form. A linearization scheme is proposed for 3D point estimation, which allows the computation of the update direction and line search in closed form. Our algorithm proves to be efficient, reliable, and accurate, as demonstrated by experimental results that confirm its superiority over recent alternatives.</p>

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Alternating optimization for bundle adjustment with closed form solutions

  • 期刊论文

  • 发表日期：

    2025年5月15日

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  • Chengzhe Meng,
  • Yiwen Jiang,
  • Weiwei Xu

摘要

This study proposes a novel alternating optimization algorithm for bundle adjustment, a critical process in structure from motion methods. We introduce the inverse depth of each three-dimensional (3D) point as an augmented independent variable and develop a low-order polynomial error metric. Theoretically, the error can be adjusted to align closely with the re-projection error since it essentially acts as a re-weighted re-projection error. We decouple the bundle adjustment problem by breaking it down into three separate tasks: estimating the camera’s pose, determining the 3D structure, and optionally estimating the camera’s intrinsic parameter. Each task can be handled independently, either by camera or by point, allowing for easy distribution of computation. Camera pose estimation is a case of the absolute orientation problem, which can be globally solved in closed form. A linearization scheme is proposed for 3D point estimation, which allows the computation of the update direction and line search in closed form. Our algorithm proves to be efficient, reliable, and accurate, as demonstrated by experimental results that confirm its superiority over recent alternatives.