Static multi-camera factorization using rigid motion

TL;DR: An approach to calibrate a static camera network where no correspondences between different camera views are required and this solution can be used as an initial guess for iterative optimization schemes which make use of the strong algebraic structure contained in the data.

Abstract: Camera networks have gained increased importance in recent years. Previous approaches mostly used point correspondences between different camera views to calibrate such systems. However, it is often difficult or even impossible to establish such correspondences. In this paper, we therefore present an approach to calibrate a static camera network where no correspondences between different camera views are required. Each camera tracks its own set of feature points on a commonly observed moving rigid object and these 2D feature trajectories are then fed into our algorithm. By assuming the cameras can be well approximated with an affine camera model, we show that the projection of any feature point trajectory onto any affine camera axis is restricted to a 13-dimensional subspace. This observation enables the computation of the camera calibration matrices, the coordinates of the tracked feature points, and the rigid motion of the object with a non-iterative trilinear factorization approach. This solution can then be used as an initial guess for iterative optimization schemes which make use of the strong algebraic structure contained in the data. Our new approach can handle extreme configurations, e.g. a camera in a camera network tracking only one single feature point. The applicability of our algorithm is evaluated with synthetic and real world data.