The Derivation of Matrix Transformation from Pixel Coordinates to Real-World Coordinates for Vehicle Trajectory Tracking

Lately, the issue of coordinate transformation has gained interest from surveyors, GIS experts, remote-sensing practitioners and especially many researchers in transportation studies. In transportation studies, coordinate transformation is important for modelling vehicle trajectories. The trajectory of a vehicle can be obtained through traffic data. Traffic data are commonly collected from a video camera fixed at an elevated position to record traffic flow. In order to display the data coordinates as if they were taken from a top-view angle, coordinate transformation is needed. The most widely applied methods of coordinate transformation are generally being developed. Mostly, existing methods have complex computation and a large number of parameters. Naturally, complex transformations with a large number of parameters (sometimes with high-order terms that are not linear) are more accurate but introduce more distortions and deformations into the data. In this paper, a novel coordinate transformation for mapping the coordinates between video images and the real world based on a mathematical approach is proposed. The proposed coordinate transformation method was written using a matrix equation. This matrix transformation is a function of several parameters, i.e. the camera's pixels, the camera's height from the ground, and the actual width and length of the road recorded on camera. Experiments were designed to verify the proposed method, which was applied to vehicle movement tracking. The results showed that the proposed matrix transformation can correctly transform pixel coordinates to real-world coordinates with a simpler calculation and fewer parameters than existing methods.