a new approach to estimate motion and structure of a moving rigid object in a 3d space with a single hand-held camera

Classical sfm (structure from motion) algorithms are widely used to estimate the three-dimensional structure of a stationary scene with a moving camera. however, when there are moving objects in the scene, if the equation of the moving object is unknown, the approach fails. this paper first demonstrates that when the frame rate is high enough and the object movement is continuous in time, meaning that acceleration is limited, a simple linear model can be effectively used to estimate the motion. this theory is first mathematically proven in a closed-form expression and then optimized by a nonlinear function applicable for our problem. the algorithm is evaluated both on synthesized and real data from hopkins dataset.