We propose a method for the recovery of projective structure and motion by the factorization of the rank 1 matrix containing the images of all points in all views. In our method, the unknowns are the 3D motion and relative depths of the set of points, not their 3D positions. The coordinates of the points along the camera plane are given by their image positions in the first frame. The knowledge of the coordinates along the camera plane enables us to solve the SFM problem by iteratively factorizing the rank 1 matrix. This simplifies the decomposition compared with the SVD (Singular Value Decomposition). Experiments with both simulated and real data show that the method is efficient for the recovery of projective structure and motion.

This paper proposes a linear algorithm for metric reconstruction from projective reconstruction. Metric reconstruction problem is equivalent to estimating the projective transformation matrix that converts projective reconstruction to Euclidean reconstruction. We build a quadratic form from dual absolute conic projection equation with respect to the elements of the transformation matrix. The matrix of quadratic form of rank 2 is then eigen-decomposed to produce a linear estimate. The algorithm is applied to three different sets of real data and the results show a feasibility of the algorithm. Additionally, our comparison of results of the linear algorithm to results of bundle adjustment, applied to sets of synthetic image data having Gaussian image noise, shows reasonable error ranges.