# 3D Trajectory Reconstruction of Moving Points Based on a Monocular Camera

arXiv: https://arxiv.org/abs/2502.19689 · HTML: https://mlsanity.com/paper/2502.19689/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 57 references that are in the map.
- First posted on arXiv 27 Feb 2025.

## Builds on (most cited first, 3 of 3)

- [Triangulation: Why Optimize?](https://mlsanity.com/paper/1907.11917/) (2019)
- [Camera Calibration using a Collimator System](https://mlsanity.com/paper/2409.20034/) (2024)
- [GTT-Net: Learned Generalized Trajectory Triangulation](https://mlsanity.com/paper/2109.03408/) (2021)

## Built on by (most cited first, 2 of 2)

- [Spiking Neural Networks with Temporal Attention-Guided Adaptive Fusion for imbalanced Multi-modal Learning](https://mlsanity.com/paper/2505.14535/) (2025)
- [Trajectory Optimization in Single and Dual-UAV Bearing-Only Target Localization](https://mlsanity.com/paper/2606.09188/) (2026)

## Abstract (arXiv)

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.