3D Trajectory Reconstruction of Moving Points Based on a Monocular Camera
This addresses a fundamental photogrammetry problem for engineering applications, but it is incremental as it builds on existing methods with specific improvements.
The paper tackled the problem of reconstructing 3D trajectories of moving points from monocular camera images under limited observation conditions, using temporal polynomials and ridge estimation to mitigate ill-conditioning, with results demonstrating feasibility, accuracy, and efficiency in simulations and real-world experiments.
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.