Motion and Structure from Two Perspective Views: Algorithms, Error Analysis, and Error Estimation

This paper deals with estimating motion parameters and the structure of the scene from point (or feature) correspondences between two perspective views. First, a new algorithm is presented that gives a closed-form solution for motion parameters and the structure of the scene. The algorithm exploits redundancy in the data to obtain more reliable estimates in the presence of noise. Then, an approach is introduced to estimating the errors in the motion parameters computed by the algorithm. Specifically, standard deviation of the error is estimated in terms of the variance of the errors in the image coordinates of the corresponding points. The estimated errors indicate the reliability of the solution as well as any degeneracy or near degeneracy that causes the failure of the motion estimation algorithm. The presented approach to error estimation applies to a wide variety of problems that involve leastsquares optimization or pseudoinverse. Finally, the relationships between errors and the parameters of motion and imaging system are analyzed. The results of the analysis show , among other things, that the errors are very sensitive to the translation direction and the range of field of view. Simulations are conducted to demonstrate the performance of the algorithms, error estimation, as well as the relationships between the errors and the parameters of motion and imaging systems. The algorithms are tested on images of real world scenes with point correspondences computed automatically.