The 8-point algorithm is a well known method for solving the relative orientation and scene reconstruction problem for calibrated cameras. In that algorithm, a matrix, called the fundamental matrix of the two calibrated cameras is computed using 8 or more point correspondences between the pair of images. The relative orientation of the two cameras may be computed from the fundamental matrix. In...

We consider the high-dimensional inference problem where the signal is a low-rank symmetric matrix which is corrupted by an additive Gaussian noise. Given a probabilistic model for the low-rank matrix, we compute the limit in the large dimension setting for the mutual information between the signal and the observations, as well as the matrix minimum mean square error, while the rank of the sign...

A self-contained review is given of the matrix model of M-theory. The introductory part of the review is intended to be accessible to the general reader. M-theory is an eleven-dimensional quantum theory of gravity which is believed to underlie all superstring theories. This is the only candidate at present for a theory of fundamental physics which reconciles gravity and quantum field theory in ...

The theory of partial differential equations has evolved in close concurrence with specific examples coming from physics. A prominent case in the history of science was the propagation of light in crystals investigated by such great physicists as Huygens, Fresnel, Biot, Brewster and Laplace. In particular, the prediction of conical refraction in biaxial crystals by Hamilton in 1832 and its expe...

A new method is presented for computing the fundamental matrix from point correspondences: its singular value decomposition (SVD) is optimized by the Levenberg-Marquard (LM) method. The search is initialized by optimal correction of unconstrained ML. There is no need for tentative 3-D reconstruction. The accuracy achieves the theoretical bound (the KCR lower bound).

The estimation of fundamental matrix from two-view images has been an important topic of research in 3D computer vision. In this paper, we present an improved robust algorithm for fundamental matrix estimation via modification of the RANSAC algorithm. The proposed algorithm is based on constructing a voting array for all the point correspondence pairs to record the consistency votes for each po...

In this paper, we propose a robust method to estimate the fundamental matrix in the presence of outliers. The new method uses random minimum subsets as a search engine to find inliers. The fundamental matrix is computed from a minimum subset and subsequently evaluated over the entire data set by means of the same measure, namely minimization of 2D reprojection error. A mixture model of Gaussian...

In recent work the authors proposed a wide-ranging method for estimating parameters that constrain image feature locations and satisfy a constraint not involving image data. The present work illustrates the use of the method with experiments concerning estimation of the fundamental matrix. Results are given for both synthetic and real images. It is demonstrated that the method gives results com...

Estimating the fundamental matrix from a pair of stereo images is one of the central problems in stereo vision. Typically, this estimation is based on a sparse set of point correspondences that has been obtained by a matching of characteristic image features. In this paper, however, we propose a completely different strategy: Motivated by the high precision of recent variational methods for com...

We present a geometric approach for the analysis of dynamic scenes containing multiple rigidly moving objects seen in two perspective views. Our approach exploits the algebraic and geometric properties of the so-called multibody epipolar constraint and its associated multibody fundamental matrix, which are natural generalizations of the epipolar constraint and of the fundamental matrix to multi...