Camera motion parameter recovery under perspective projection

We present a very simple solution of the motion recovery problem using the displacement map produced by a camera moving in a stationary environment under the perspective projection assumption. If the motion equations hold exactly (ideal case), the solution is derived immediately from the singular value decomposition (SVD) of a linear system matrix. In the ideal case the rank of the matrix indicates whether there is a zero or non-zero translation component in the camera motion. In practice the motion equations do not hold exactly. We speculate that the solution vector is a linear combination of the 3 smallest but non-zero eigenvalue eigenvectors. Then we find the 3 combination coefficients so that the solution obeys an equal number of problem constraints. The speculation turns out to yield good results for small noise situations but degrades fast as the noise power increases