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

TL;DR

This paper introduces a novel algorithm for reconstructing 3D trajectories of moving points from monocular camera images, addressing challenges like ill-conditioning and limited observations with polynomial motion modeling and ridge estimation.

Contribution

It proposes a new method combining temporal polynomial representation, ridge estimation, and an automatic polynomial order selection for accurate 3D trajectory reconstruction from monocular images.

Findings

Demonstrates high accuracy in simulated and real-world tests.

Shows robustness under limited observation conditions.

Achieves efficient 3D trajectory reconstruction.

Abstract

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.