Considers the problem of upgrading a 3D structure known only up to an unknown affine transformation to a scaled Euclidean structure by imposing only known or hypothesized orthogonality relations between structure elements. This seemingly simple problem is confounded by the facts that (i) the structure elements assumed to be orthogonal are corrupted by measurement noise, (ii) that the angle measure is not linear in the errors, and (iii) that the assumption of orthogonality may in some cases be unfounded. Assuming normal errors on the structure, we make the following contributions. We show that for all but the shortest direction vectors the distribution of their inner product is indeed well described by a normal distribution, and we give an unbiased estimator of its mean and its variance. Using this distribution we give a likelihood ratio test of the hypothesis of K>5 mutually consistent orthogonality relations, and a maximum likelihood estimator of the absolute conic based on the same relations, thus providing optimal rectification of the structure. We also provide simple means of computing these in a short succession of linear steps, and assess the validity of that approach.

In this paper we specialize the projective unifocal, bifocal, and trifocal tensors to the affine case, and show how the tensors obtained relate to the registered tensors encountered in previous work. This enables us to obtain an affine specialization of known projective relations connecting points and lines across two or three views. In the simpler case of affine cameras we give neccessary and sufficient constraints on the components of the trifocal tensor together with a simple geometric interpretation. Finally, we show how the estimation of the tensors from point correspondences is achieved through factorization, and discuss the estimation from line correspondences.

This paper describes methods for tracking using point and line features in affine views to provide fundamental invariance to changes of focal length. It first demonstrates how an earlier method of transfer-based tracking using spatio-temporal matching of point features in a stereo active head is indeed zoom-invariant. In order to also make use of lines the paper then illustrates how the affine tri- and quadrifocal tensors may be applied to tracking with zoom in monocular and stereo systems respectively. The usefulness of the tensors is evident from their ability to transfer a fixation point in two uncalibrated images into novel views. Whereas the trifocal tensor is already familiar and in common use for matching and reconstruction we believe this to be the first practical application of a quadrifocal tensor. We develop expressions for affine tri- and quadrifocal tensors, and using novel affine specializations of existing projective algorithms we show how computation of the tensors is faster simpler and more stable. Experiments on real images are presented.