Spectral Criterion for Estimating the Relative Camera Pose

A method for estimating the relative position and orientation of a camera from corresponding image points is presented, in which the translation is eliminated from the optimization while the rotation is estimated using a spectral criterion based on the consistency of epipolar plane normals. For each point pair, a symmetric rank-1 matrix is constructed from the cross product of normalized bearing directions, and the smallest eigenvalue of the sum of these matrices is minimized over R ∈ SO(3). The translation direction is then recovered as the eigenvector associated with the minimal eigenvalue. A smooth approximation to the smallest eigenvalue via the log-sum-exp function is introduced, and iterative robust weights are employed. The implementation relies on automatic differentiation. Experiments on real data confirm the high reliability of the estimates.