• Jian Zhou, Yang Shang, Xiaohu Zhang, and Wenxian Yu.
• Shanghai Key Laboratory of Navigation and Location Based Services, Shanghai Jiao Tong University, Shanghai 200240, China. zhou_jian_1980@foxmail.com.
• Sensors (Basel). 2015 Mar 9; 15 (3): 5666-86.

AbstractWe propose a monocular trajectory intersection method to solve the problem that a monocular moving camera cannot be used for three-dimensional reconstruction of a moving object point. The necessary and sufficient condition of when this method has the unique solution is provided. An extended application of the method is to not only achieve the reconstruction of the 3D trajectory, but also to capture the orientation of the moving object, which would not be obtained by PnP problem methods due to lack of features. It is a breakthrough improvement that develops the intersection measurement from the traditional "point intersection" to "trajectory intersection" in videometrics. The trajectory of the object point can be obtained by using only linear equations without any initial value or iteration; the orientation of the object with poor conditions can also be calculated. The required condition for the existence of definite solution of this method is derived from equivalence relations of the orders of the moving trajectory equations of the object, which specifies the applicable conditions of the method. Simulation and experimental results show that it not only applies to objects moving along a straight line, or a conic and another simple trajectory, but also provides good result for more complicated trajectories, making it widely applicable.

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