Single camera 6-dof object tracking using spatial resection based techniques

Abstract. Photogrammetric methods and advanced algorithms are widely used for tracking objects in camera image sequences in various sectors, such as motion analysis, industrial inspection, monitoring of environmental processes, or analyzing impact events or explosions. The use of multi camera stereo photogrammetry systems is a common approach to track objects in 3D. Nevertheless, single camera based solutions may be particularly valuable in scenarios where only one camera can be used due to constraints such as cost limitations, synchronization requirements, or spatial observation conditions. This will especially be the case, if powerful high-speed cameras are being employed. 
This paper presents a photogrammetric approach based on spatial resection principles for using a single camera for 3D object tracking. The method utilizes direct computation of velocity and acceleration as well as rotation parameters of a moving object in 3D space, allowing for the determination of the object’s position and trajectory from image sequences captured by a single high-speed camera. The method is derived from the inverse spatial resection, where a stationary camera observes a moving object of known geometry and the apparent changes of the six camera exterior orientation parameters obtained from spatial resection are transferred into 6-dof object motion parameters. In our developed spatial resection based object tracking method, 12 unknown parameters are calculated. Different from conventional spatial resection, these 12 parameters are the first and second derivatives of the 6 exterior orientation parameters (three linear translations plus three angular orientation elements) over time. The approach is implemented in a way that these 12 motion parameters can be determined directly from an arbitrary number of images (at least three) of an image sequence, thus significantly enhancing precision and reliability. 
The method has undergone rigorous testing and validation using both simulated data as well as real data obtained in a civil engineering impact monitoring experiment observed by a high-speed camera. In addition to explaining the methodology, the paper presents the results of these validation tests.