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ABSTRACT: The 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.
IEEE Transactions on Pattern Analysis and Machine Intelligence 04/2004; · 4.91 Impact Factor
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ABSTRACT: We address the problem of camera motion and structure reconstruction from line correspondences across multiple views, from initialization to final bundle adjustment. One of the main difficulties when dealing with line features is their algebraic representation. First, we consider the triangulation problem. Based on Plucker coordinates to represent the lines, we propose a maximum likelihood algorithm, relying on linearising the Plucker constraint, and on a Plucker correction procedure to compute the closest Plucker coordinates to a given 6-vector. Second, we consider the bundle adjustment problem. Previous overparameterizations of 3D lines induce gauge freedoms and/or internal consistency constraints. We propose the orthonormal representation, which allows handy nonlinear optimization of 3D lines using the minimum 4 parameters, within an unconstrained nonlinear optimizer. We compare our algorithms to existing ones on simulated and real data.
Computer Vision, 2003. Proceedings. Ninth IEEE International Conference on; 11/2003
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ABSTRACT: We address the problem of aligning two reconstructions of lines and cameras in projective, affine, metric or Euclidean space. We propose several 3D (three-dimensional) and image-related linear algorithms. The result can be used to initialize the nonlinear minimization of several proposed error functions, as well as the maximum likelihood estimator that we derive. We evaluate and compare our algorithms to existing ones using simulated and real data.
Computer Vision and Pattern Recognition, 2003. Proceedings. 2003 IEEE Computer Society Conference on; 07/2003
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ABSTRACT: We address the problem of constructing mosaics from video sequences taken by rotating cameras. In particular we investigate the widespread case where the scene is not only static but may also contain large dynamic areas, induced by moving or deforming objects. Most of the existing techniques fail to produce reliable results on such video sequences. For such alignment purposes, two classes of techniques may be used: feature-based and direct methods. We derive both of them in a unified statistical manner and propose an integrated framework to construct what we call motion panoramas, based on a mixed feature-based and direct approach. Experimental results are provided on large image sequences. In particular we consider sport videos where the moving and deforming athlete is visible in every frame of the sequence, thereby making the alignment task tricky.
Motion and Video Computing, 2002. Proceedings. Workshop on; 01/2003
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ABSTRACT: This paper is about the problem of structure and motion recovery from two views of a rigid scene. Especially, we deal with the case of scenes containing planes, i.e. there are sets of coplanar points. Coplanarity is a strong constraint for both structure recovery and motion estimation. Most existing works do only exploit one of the two aspects, or, if both, then in a sub-optimal manner. A typical example is to estimate motion (epipolar geometry) using raw point correspondences, to perform a 3D reconstruction and then to fit planes and maybe correct 3D point positions to make them coplanar. In this paper we present an approach to estimate camera motion and piecewise planar structure simultaneously and optimally: the result is the estimation of camera motion and 3D structure, that minimizes reprojection error while satisfying the piecewise planarity. The estimation problem is minimally parameterized using 2D entities-epipoles, epipolar transformation, plane homographies and image points-subsequently deriving the corresponding 3D entities is trivial. Experimental results show that the reconstruction is of clearly superior quality compared to traditional methods based only on points, even if the scene is not perfectly piecewise planar
3-D Digital Imaging and Modeling, 2001. Proceedings. Third International Conference on; 02/2001
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ABSTRACT: In this paper, we address the problem of structure and motion recovery from two views of a scene containing planes, i.e, sets of coplanar points. Most of the existing works do only exploit this constraint in a sub-optimal manner We propose to parameterize the structure of such scenes with planes and points on planes and derive the MLE (Maximum Likelihood Estimator) using a minimal parameterization based on 2D entities. The result is the estimation of camera motion and 3D structure in projective space, that minimizes reprojection error while satisfying the piecewise planarity. We propose a quasi-linear estimator that provides reliable initialization values for plane equations. Experimental results show that the reconstruction is of clearly superior quality compared to traditional methods based only on points, even if the scene is not perfectly piecewise planar
Computer Vision, 2001. ICCV 2001. Proceedings. Eighth IEEE International Conference on; 02/2001
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ABSTRACT: We study the problem of aligning two 3D line reconstructions expressed in Plucker line coordinates. We introduce the 6×6 3D line motion matrix that acts on Plucker coordinates in projective, affine or Euclidean space. We characterize its algebraic properties and its relation to the usual 4×4 point motion matrix, and propose various methods for estimating 3D motion from line correspondences, based on image-related and 3D cost functions. We assess the quality of the different estimation methods using simulated data and real images.
Computer Vision and Pattern Recognition, 2001. CVPR 2001. Proceedings of the 2001 IEEE Computer Society Conference on; 02/2001
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A. Bartoli
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ABSTRACT: In this paper, we investigate the problem of the automatic creation of 3D models of man-made environments that we represent as collections of textured planes. A typical approach is to automatically compute a sparse feature reconstruction and to manually give their plane-memberships as well as the delineation of the planes. Textures are then extracted from the images while optimizing the model, typically the disparity between marked and predicted edges. We propose a means to automatically estimate the model of the scene, in terms of the number of planes and their parameters from a point feature reconstruction. The method is based on random sampling of reconstructed points to generate plane hypotheses. Each of these is then evaluated using a measure of approximate photoconsistency while recovering the corresponding plane delineation. We then compute the maximum likelihood estimate of all scene parameters, i.e. the set of planes and reconstructed points as well as relative camera pose, with respect to actual images. The approach is validated on simulated data and real images.
Computer Vision and Pattern Recognition, 2001. CVPR 2001. Proceedings of the 2001 IEEE Computer Society Conference on; 02/2001
