仅用单目相机重建运动点3D轨迹，解决观测条件差时的误差问题。
3D Trajectory Reconstruction of Moving Points Based on a Monocular Camera
- 用时间多项式表示点运动，结合岭估计改善病态问题。
- 实测与仿真验证方法在误差大、距离远时仍保持高精度。
- 自动确定多项式阶数，适合工程中低质量视频追踪场景。
点目标的运动测量是摄影测量中的基础问题，广泛应用于各类工程领域。仅凭单目相机图像，若无先验假设，则无法实现点的3D运动重建。在观测条件受限（如观测不足、距离远、平台观测误差大）的情况下，最小二乘估计会面临病态问题。本文提出一种基于单目相机的运动点3D轨迹重建算法。点的运动采用时间多项式表示，引入岭估计以缓解因观测条件差导致的病态问题。进一步提出一种自动确定时间多项式阶数的算法，并定义了时间多项式的可重构性，用于定量描述重建精度。模拟与真实实验结果表明，该方法具有可行性、高精度和高效性。
原文摘要 · Abstract (English)
The motion measurement of point targets constitutes a fundamental problem in photogrammetry, with extensive applications across various engineering domains. Reconstructing a point's 3D motion just from the images captured by only a monocular camera is unfeasible without prior assumptions. Under limited observation conditions such as insufficient observations, long distance, and high observation error of platform, the least squares estimation faces the issue of ill-conditioning. This paper presents an algorithm for reconstructing 3D trajectories of moving points using a monocular camera. The motion of the points is represented through temporal polynomials. Ridge estimation is introduced to mitigate the issues of ill-conditioning caused by limited observation conditions. Then, an automatic algorithm for determining the order of the temporal polynomials is proposed. Furthermore, the definition of reconstructability for temporal polynomials is proposed to describe the reconstruction accuracy quantitatively. The simulated and real-world experimental results demonstrate the feasibility, accuracy, and efficiency of the proposed method.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。