Carnegie Mellon University
file.pdf (620.45 kB)

Iterative Projective Reconstruction From Multiple Views

Download (620.45 kB)
journal contribution
posted on 2000-01-01, 00:00 authored by Shyjan Mahamud, Martial Hebert
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.


Publisher Statement

"©2000 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE." "This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder."



Usage metrics



    Ref. manager