Motion capture from dynamic orthographic cameras

We present an extension to the scaled orthographic camera model. It deals with dynamic cameras looking at far away objects. The camera is allowed to change focal length and translate and rotate in 3D. The model we derive says that this motion can be treated as scaling, translation and rotation in a 2D image plane. It is exactly valid in the limit where the distance between the camera and its target goes to infinity. We show two applications of this model to motion capture applications at large distances, i.e. outside a studio, using the affine factorization algorithm. The model is used to motivate theoretically why the factorization can be carried out in a single batch step, when having both dynamic cameras and a dynamic object. Furthermore, the model is used to motivate how the position of the object can be reconstructed by measuring the virtual 2D motion of the cameras. For testing we use videos from a real football game and reconstruct the 3D motion of a footballer as he scores a goal.