Object trajectory estimation in the dashcam videos with ego-motion

In this work, we propose a straightforward and practical object trajectory estimation method for dashboard camera (dashcam) videos with ego-motion. When an object detaches or is launched from a preceding vehicle, its motion under gravity follows a parabolic trajectory in 3D camera coordinates. However, conventional 2D image-plane methods, such as polynomial or exponential models, often yield inaccurate results because they neglect the camera's ego-motion and lack a rigorous physical foundation. To address this, we derive a projection-based model from the 3D parabolic trajectory by incorporating the longitudinal translation of the dashcam into the projection process. We then estimate trajectory parameters using least-squares optimization, resulting in a practical and physically grounded estimation approach. Quantitative evaluation on real-world forensic case studies demonstrated that the proposed model fits the observed data closely, achieving an average Root Mean Square Error of 6.64 pixels. These results suggest that our approach can assist forensic analysts in interpreting object motion in traffic accident investigations.