Linear Six-Point Algorithm of Camera Self-Calibration and 3D Reconstruction from Single-View

Camera self-calibration and 3D reconstruction plays an important role in robot vision system. In single-view vision system, the number of independent parameter to be estimated is equal to 11. Every 2D point can provide 2 DOF. This means that it is theoretically possible for a single-view vision to self-calibrate and 3D reconstruction by using at least 6 points. But, how to realize it is still an open problem. This is just the problem to be answered in this paper. By means of projecting the digital 3D shape matrix of the target in the single-view to the null space of its 3D model shape matrix, a new algorithm to linearly and exactly self-calibrate the camera and reconstruct the 3D pose of the target from its at least six un-calibrated feature points and its model shape is developed. The computation in the suggested algorithm applies null subspace projection and some of QR decompositions. Although the algorithm needs only 6 points, more points are encouraged to enhance the estimation precision and robustness of the algorithm. 18 points is more supported as optimal selection. The theoretical analysis and the experiments have demonstrated that the suggested algorithm is fast, exact, efficient and rather robust against noise