The epipolar geometry is a key point in computer vision and the fundamental matrix estimation the unique way to compute it. This article surveys several methods of fundamental matrix estimation. All the different methods have been programmed and their accuracy analysed using synthetic and real images. A discussion justified with experimental results is given and the code is available in Interne...

The normalized eight-point algorithm is broadly used for the computation of the fundamental matrix between two images given a set of correspondences. However, it performs poorly for low-size datasets due to the way in which the rank-two constraint is imposed on the fundamental matrix. We propose two new algorithms to enforce the rank-two constraint on the fundamental matrix in closed form. The ...

Scene geometry can be inferred from point correspondences between two images. The inference process includes the selection of a model. Four models are considered: background (or null), collineation, affine fundamental matrix and fundamental matrix. It is shown how Minimum Description Length (MDL) can be used to compare the different models. The main result is that there is little reason for pre...

The geometry of two uncalibrated views obtained with a parabolic catadioptric device is the subject of this paper. We introduce the notion of circle space, a natural representation of line images, and the set of incidence preserving transformations on this circle space which happens to equal the Lorentz group. In this space, there is a bilinear constraint on transformed image coordinates in two...

Epipolar geometry is a key point in computer vision and the fundamental matrix estimation is the only way to compute it. This article is a fresh look in the subject that overview classic and latest presented methods of fundamental matrix estimation which have been classified into linear methods, iterative methods and robust methods. All of these methods have been programmed and their accuracy a...

This paper deals with the analysis of the uncertainty of the fundamental matrix. The basic idea is to compute the fundamental matrix and its uncertainty at the same time. We give two diierent methods. The rst one is a statistical approach. As in all statistical methods the precision of the results depends on the number of analyzed samples. This means that we can always improve our results if we...

Scene geometry can be inferred from point correspondences between two images. The inference process includes the selection of a model. Four models are considered: background (or null), collineation, affine fundamental matrix and fundamental matrix. It is shown how Minimum Description Length (MDL) can be used to compare the different models. The main result is that there is little reason for pre...

This paper describes a new algorithm for visual control of an uncalibrated 3 DOF joint system, using two weakly calibrated fixed cameras. The algorithm estimates on-line the Image Jacobian, a matrix which linearly relates joint velocity and image feature velocity. In our experiments we prove that by using the fundamental matrix, robustness of the estimation in the presence of noise is significa...

We revisit the bilinear matching constraint between two perspective views of a 3D scene. Our objective is to represent the constraint in the same manner and form as the trilinear constraint among three views. The motivation is to establish a common terminology that bridges between the fundamental matrix F (associated with the bilinear constraint) and the trifocal tensor T jk i (associated with ...

Matrix string theory is equivalent to type IIA superstring theory in the light-cone gauge, together with extra degrees of freedom representing D-brane states. It is therefore the appropriate framework in which to study systems of multiple fundamental strings expanding into higher-dimensional D-branes. Starting from Matrix theory in a weakly curved background, we construct the linear couplings o...