Iterative projective reconstruction from multiple views
We propose an iterative method for the recovery of the projective structure and motion from multiple images. It has been recently noted that by scaling the measurement matrix by the true projective depths, recovery of the structure and motion is possible by factorization. The reliable determination of the projective depths is crucial to the success of this approach. The previous approach recovers these projective depths using pairwise constraints among images. We first discuss a few important drawbacks with this approach. We then propose an iterative method where we simultaneously recover both the projective depths as well as the structure and motion that avoids some of these drawbacks by utilizing all of the available data uniformly. The new approach makes use of a subspace constraint on the projections of a 3D point onto an arbitrary number of images. The projective depths are readily determined by solving a generalized eigenvalue problem derived from the subspace constraint. We also formulate a dual subspace constraint on all the points in a given image, which can be used for verifying the projective geometry of a scene or object that was modeled. We prove the monotonic convergence of the iterative scheme to a local maximum. We show the robustness of the approach on both synthetic and real data despite large perspective distortions and varying initializations.