Pointing Angle Characterization of Optical Axes in a Multi-Camera System

Abstract

Geometric camera calibration is critical for many Computer Vision applications. This process characterizes intrinsic and extrinsic parameters of the camera. Intrinsic parameters typically include the camera’s center point and focal length. Extrinsic parameters describe the orientation of the camera with respect to a common coordinate system. A common method, developed by Zhang, computes these parameters given multiple poses of a dimensionally-known calibration target; using an optimization algorithm to transform the target’s 3D world points to the corresponding 2D points imaged on the camera sensor (Zhang, 1998). In this report, the author proposes an alternative method for computing camera pointing angle (rotational extrinsic parameters Rx/Ry) which strives to serve as a ground-truth for systems requiring accuracy less than 2 arcmin (2σ). Dubbed the Camera Centration Method, this approach utilizes a collimated light source whose beam is split and redirected in a predictable manner to each camera of a Multi-Camera-System (MCS). The common light source and known beam path serve as a bridge to identify the position of each camera with respect to the other. Given each camera’s intrinsic parameters, its orientation with respect to the incoming collimated laser source, and the sensor pixel activated by that source, the author shows that one can compute camera pointing angle of the left and right cameras with respect to the center. The proposed method is finally estimated to have a measurement uncertainty of 5.85 arcmin, an order of magnitude larger than the desired 0.1 – 0.25 arcmin uncertainty. In the Discussion Section, the author recommends improvements, which are outside the scope of this project, that reduce the estimated measurement uncertainty to 2.33 arcmin according to a first-order analysis. While the Camera Centration Method cannot replace the Zhang Method, the author concludes that it has the potential to serve as a ground truth for extrinsic rotation parameters, Rx/Ry, where the system accuracy spec is greater than ±46 arcmin (2σ).