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Efficient calibration of a multi-camera measurement system using a target with known dynamics

Aykın, Murat Deniz
Multi camera measurement systems are widely used to extract information about the 3D configuration or “state” of one or more real world objects. Camera calibration is the process of pre-determining all the remaining optical and geometric parameters of the measurement system which are either static or slowly varying. For a single camera, this consist of the internal parameters of the camera device optics and construction while for a multiple camera system, it also includes the geometric positioning of the individual cameras, namely “external” parameters. The calibration is a necessary step before any actual state measurements can be made from the system. In this thesis, such a multi-camera state measurement system and in particular the problem of procedurally effective and high performance calibration of such a system is considered. This thesis presents a novel calibration algorithm which uses the known dynamics of a ballistically thrown target object and employs the Extended Kalman Filter (EKF) to calibrate the multi-camera system. The state-space representation of the target state is augmented with the unknown calibration parameters which are assumed to be static or slowly varying with respect to the state. This results in a “super-state” vector. The EKF algorithm is used to recursively estimate this super-state hence resulting in the estimates of the static camera parameters. It is demonstrated by both simulation studies as well as actual experiments that when the ballistic path of the target is processed by the improved versions of the EKF algorithm, the camera calibration parameter estimates asymptotically converge to their actual values. Since the image frames of the target trajectory can be acquired first and then processed off-line, subsequent improvements of the EKF algorithm include repeated and bidirectional versions where the same calibration images are repeatedly used. Repeated EKF (R-EKF) provides convergence with a limited number of image frames when the initial target state is accurately provided while its bidirectional version (RB-EKF) improves calibration accuracy by also estimating the initial target state. The primary contribution of the approach is that it provides a fast calibration procedure where there is no need for any standard or custom made calibration target plates covering the majority of camera field-of-view. Also, human assistance is minimized since all frame data is processed automatically and assistance is limited to making the target throws. The speed of convergence and accuracy of the results promise a field-applicable calibration procedure.