Direct relative orientation with four independent constraints

Relative orientation based on the coplanarity condition is one of the most important procedures in photogrammetry and computer vision. The conventional relative orientation model has five independent parameters if interior orientation parameters are known. The model of direct relative orientation contains nine unknowns to establish the linear transformation geometry, so there must be four independent constraints among the nine unknowns. To eliminate the influence of over parameterization of the conventional direct relative orientation model, a new relative orientation model with four independent constraints is proposed in this paper. The constraints are derived from the inherent orthogonal property of the rotation matrix of the right image of a stereo pair. These constraints are completely new as compared with the known literature. The proposed approach can find the optimal solution under least squares criteria. Experimental results show that the proposed approach is superior to the conventional model of direct relative orientation, especially at low altitude and close range photogrammetric applications.