Stratified calibration and group synchronized focal length estimation for structure from motion algorithms

Çalışkan, Akın
The estimation of unknown calibration parameters of the cameras without using any calibration pattern is critical for the performance of the 3D computer vision applications such as structure from motion, pose estimation, visual odometry, and it is still an open problem for the researchers. In this thesis, our contribution is two folded. First of all, we propose a novel stratified approach for estimating both the focal length and the radial distortion of a camera from given 2D point correspondences without knowing any calibration information, such as the focal length of a camera. We as- sume that the images share the same intrinsic parameters and we further assume that the optical image centers are known. Our method progresses first by showing that the distortion on the point coordinates can be removed without the knowledge of the true focal length by enforcing the epipolar geometry constraint. Next, by using the distortion free correspondences, we estimate the true focal length of the camera by enforcing the trace constraint. Secondly, we utilize the idea of estimation of calibration parameters from two cameras, and propose method for estimation of focal lengths of all cameras, which can be all different, used in structure from motion pipeline. The relation of focal lengths between two adjacent cameras are defined from a trace constraint, and this is followed by using the group synchronization method for all cameras in a dataset to estimate unknown focal lengths. In this step a novel energy function is proposed together with global optimum solution. The optimal solution for this function gives the resultant focal lengths with an error which can be handled by bundle adjustment stage of structure from motion algorithms, even if very limited number of focal lengths are available. In both contributions, our methods are quite easy to implement compared to other methods in the literature and we demonstrate their accuracy and robustness against noise on synthetically generated data sets. Furthermore, we perform experiments for the accuracy of our first method on real image pairs by comparing our results against a method that uses a calibration pattern, and for the accuracy and complexity of the second method on real data sets used in structure from motion pipelines