It is known that the problem of multiview reconstruction can be solved in two steps: first estimate camera rotations and then translations using them. This paper presents new robust techniques for both of these steps. (i) Given pairwise relative rotations, global camera rotations are estimated linearly in least squares. (ii) Camera translations are estimated using a standard technique based on Second Order Cone Programming. Robustness is achieved by using only a subset of points according to a new criterion that diminishes the risk of chosing a mismatch. It is shown that only four points chosen in a special way are sufficient to represent a pairwise reconstruction almost equally as all points. This leads to a significant speedup. In image sets with repetitive or similar structures, non-existent epipolar geometries may be found. Due to them, some rotations and consequently translations may be estimated incorrectly. It is shown that iterative removal of pairwise reconstructions with the largest residual and reregistration removes most non-existent epipolar geometries. The performance of the proposed method is demonstrated on difficult wide base-line image sets.

A technique for building consistent 3D reconstructions from many views based on fitting a low rank matrix to a matrix with missing data is presented. Rank-four submatrices of minimal, or slightly larger, size are sampled and spans of their columns are combined to constrain a basis of the fitted matrix. The error minimized is expressed in terms of the original subspaces which leads to a better resistance to noise compared to previous methods. More than 90% of the missing data can be handled while finding an acceptable solution efficiently. Applications to 3D reconstruction using both affine and perspective camera models are shown. For the perspective model, a new linear method based on logarithms of positive depths from chirality is introduced to make the depths consistent with an overdetermined set of epipolar geometries. Results are shown for scenes and sequences of various types. Many images in open and closed sequences in narrow and wide base-line setups are reconstructed with reprojection errors around one pixel. It is shown that reconstructed cameras can be used to obtain dense reconstructions from epipolarly aligned images.

This paper proposes a method for line reconstruction from many perspective images by factorization of a matrix containing line correspondences. No point correspondences are used. We formulate the reconstruction from line correspondences in the language of Plucker line coordinates. The reconstruction is posed as the factorization of 3m /spl times/ n matrix S into the product S = QL of 3m /spl times/ 6 projection matrix Q and 6 /spl times/ n line matrix L, both satisfying Klein identities. The matrix S contains coordinates of lines detected in perspective images. Similarly to reconstruction from point correspondences in perspective images, the matrix S has to be properly rescaled before it can be factorized. We propose a scaling of image line coordinates based on trifocal tensors that are analogical to the scaling proposed by Sturm and Triggs (1996) for points. We propose an SVD based factorization enforcing Klein identities on Q and L in a noise-free situation. We show experiments on real data that suggest that a good reconstruction may be obtained even if data is noisy and the identities are not enforced exactly. We also discuss an extension of the method for images with occlusions.