Non-Linear Estimation of the Fundamental Matrix With Minimal Parameters

International audienceThe purpose of this paper is to give a very simple method for nonlinearly estimating the fundamental matrix using the minimum number of seven parameters. Instead of minimally parameterizing it, we rather update what we call its orthonormal representation, which is based on its singular value decomposition. We show how this method can be used for efficient bundle adjustment of point features seen in two views. Experiments on simulated and real data show that this implementation performs better than others in terms of computational cost, i.e., convergence is faster, although methods based on minimal parameters are more likely to fall into local minima than methods based on redundant parameters

Triangulation projective contrainte par multi-coplanarité

http://www.irit.fr/ACTIVITES/ORASIS2001/images/docs/bartoli.ps.gzInternational audienceCet article traite du problème de la reconstruction et de l'estimation du mouvement entre les caméras à partir de deux vues d'une scène rigide. Plus particulièrement, nous traitons le cas où la scène contient des plans, c'est-à-dire des ensembles de points coplanaires ou multi-coplanaires (points sur plusieurs plans), qui constituent des contraintes géométriques très fortes. La plupart des travaux existants ne les exploitent que d'une manière sous-optimale. Une approche typique est d'estimer une reconstruction isolée de points, d'ajuster des plans et éventuellement de corriger la position 3D des points afin de les rendre coplanaires. Dans cet article, nous présentons une méthode permettant d'estimer de façon conjointe et optimale (au sens du maximum de vraisemblance) la structure de la scène et le mouvement entre les caméras : le résultat est une structure minimisant l'erreur de reprojection tout en satisfaisant exactement les contraintes géométriques. Pour ce faire, la structure est paramétrée de façon minimale par des entités 2D ou 3D. Des résultats expérimentaux montrent que les résultats de reconstruction obtenus sont de qualité supérieure à ceux d'autres méthodes, notamment celles basées sur une reconstruction individuelle de points, ceci même dans les cas où les plans de la scène sont imparfaits

3-D Reconstruction of Urban Scenes from Sequences of Images

In this paper, we address the problem of the recovery of the Euclidean geometry of a scene from a sequence of images without any prior knowledge either about the parameters of the cameras, or about the motion of the camera(s). We do not require any knowledge of the absolute coordinates of some control points in the scene to achieve this goal. Using various computer vision tools, we establish correspondences between images and recover the epipolar geometry of the set of images, from which we show how to compute the complete set of perspective projection matrices for each camera position. These being known, we proceed to reconstruct the scene. This reconstruction is defined up to an unknown projective transformation (i.e. is parameterized with 15 arbitrary parameters). Next we show how to go from this reconstruction to a more constrained class of reconstructions, defined up to an unknown affine transformation (i.e. parameterized with 12 arbitrary parameters) by exploiting known geometr..

Generalised epipolar constraints

The frontier of a curved surface is the envelope of contour generators showing the boundary, at least locally, of the visible region swept out under viewer motion. In general, the outlines of curved surfaces (apparent contours) from different viewpoints are generated by different contour generators on the surface and hence do not provide a constraint on viewer motion. Frontier points, however, have projections which correspond to a real point on the surface and can be used to constrain viewer motion by the epipolar constraint. We show how to recover viewer motion from frontier points and generalise the ordinary epipolar constraint to deal with points, curves and apparent contours of surfaces. This is done for both continuous and discrete motion, known or unknown orientation, calibrated and uncalibrated, perspective, weak perspective and orthographic cameras. Results of an iterative scheme to recover the epipolar line structure from real image sequences using only the outlines of curved surfaces, is presented. A statistical evaluation is performed to estimate the stability of the solution. It is also shown how the full motion of the camera from a sequence of images can be obtained from the relative motion between image pairs

Automatic visual recognition using parallel machines

Invariant features and quick matching algorithms are two major concerns in the area of automatic visual recognition. The former reduces the size of an established model database, and the latter shortens the computation time. This dissertation, will discussed both line invariants under perspective projection and parallel implementation of a dynamic programming technique for shape recognition. The feasibility of using parallel machines can be demonstrated through the dramatically reduced time complexity. In this dissertation, our algorithms are implemented on the AP1000 MIMD parallel machines. For processing an object with a features, the time complexity of the proposed parallel algorithm is O(n), while that of a uniprocessor is O(n2). The two applications, one for shape matching and the other for chain-code extraction, are used in order to demonstrate the usefulness of our methods. Invariants from four general lines under perspective projection are also discussed in here. In contrast to the approach which uses the epipolar geometry, we investigate the invariants under isotropy subgroups. Theoretically speaking, two independent invariants can be found for four general lines in 3D space. In practice, we show how to obtain these two invariants from the projective images of four general lines without the need of camera calibration. A projective invariant recognition system based on a hypothesis-generation-testing scheme is run on the hypercube parallel architecture. Object recognition is achieved by matching the scene projective invariants to the model projective invariants, called transfer. Then a hypothesis-generation-testing scheme is implemented on the hypercube parallel architecture