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Exploiting loops in the graph of trifocal tensors for calibrating a network of cameras
 In ECCV (2
, 2010
"... Abstract. A technique for calibrating a network of perspective cameras based on their graph of trifocal tensors is presented. After estimating a set of reliable epipolar geometries, a parameterization of the graph of trifocal tensors is proposed in which each trifocal tensor is encoded by a 4vector ..."
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Abstract. A technique for calibrating a network of perspective cameras based on their graph of trifocal tensors is presented. After estimating a set of reliable epipolar geometries, a parameterization of the graph of trifocal tensors is proposed in which each trifocal tensor is encoded by a 4vector. The strength of this parameterization is that the homographies relating two adjacent trifocal tensors, as well as the projection matrices depend linearly on the parameters. A method for estimating these parameters in a global way benefiting from loops in the graph is developed. Experiments carried out on several real datasets demonstrate the efficiency of the proposed approach in distributing errors over the whole set of cameras. 1
Making Minimal Solvers Fast
"... In this paper we propose methods for speeding up minimal solvers based on Gröbner bases and action matrix eigenvalue computations. Almost all existing Gröbner basis solvers spend most time in the eigenvalue computation. We present two methods which speed up this phase of Gröbner basis solvers: (1) a ..."
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In this paper we propose methods for speeding up minimal solvers based on Gröbner bases and action matrix eigenvalue computations. Almost all existing Gröbner basis solvers spend most time in the eigenvalue computation. We present two methods which speed up this phase of Gröbner basis solvers: (1) a method based on a modified FGLM algorithm for transforming Gröbner bases which results in a singlevariable polynomial followed by direct calculation of its roots using Sturmsequences and, for larger problems, (2) fast calculation of the characteristic polynomial of an action matrix, again solved using Sturmsequences. We enhanced the FGLM method by replacing time consuming polynomial division performed in standard FGLM algorithm with efficient matrixvector multiplication and we show how this method is related to the characteristic polynomial method. Our approaches allow computing roots only in some feasible interval and in desired precision. Proposed methods can significantly speedup many existing solvers. We demonstrate them on three important minimal computer vision problems. 1 1.
Robust focal length estimation by voting in multiview
"... scene reconstruction ..."
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Onesided Radial Fundamental Matrix Estimation
"... For modern consumer cameras often approximate calibration data is available, making applications such as 3D reconstruction or photo registration easier as compared to the pure uncalibrated setting. In this paper we address the setting with calibrateduncalibrated image pairs: for one image intrinsi ..."
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For modern consumer cameras often approximate calibration data is available, making applications such as 3D reconstruction or photo registration easier as compared to the pure uncalibrated setting. In this paper we address the setting with calibrateduncalibrated image pairs: for one image intrinsic parameters are assumed to be known, whereas the second view has unknown distortion and calibration parameters. This situation arises e.g. when one would like to register archive imagery to recently taken photos. A commonly adopted strategy for determining epipolar geometry is based on feature matching and minimal solvers inside a RANSAC framework. However, only very few existing solutions apply to the calibrateduncalibrated setting. We propose a simple and numerically stable twostep scheme to first estimate radial distortion parameters and subsequently the focal length using novel solvers. We demonstrate the performance on synthetic and real datasets. 1
Optimizing the Viewing Graph for StructurefromMotion
"... The viewing graph represents a set of views that are related by pairwise relative geometries. In the context of StructurefromMotion (SfM), the viewing graph is the input to the incremental or global estimation pipeline. Much effort has been put towards developing robust algorithms to overcome po ..."
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The viewing graph represents a set of views that are related by pairwise relative geometries. In the context of StructurefromMotion (SfM), the viewing graph is the input to the incremental or global estimation pipeline. Much effort has been put towards developing robust algorithms to overcome potentially inaccurate relative geometries in the viewing graph during SfM. In this paper, we take a fundamentally different approach to SfM and instead focus on improving the quality of the viewing graph before applying SfM. Our main contribution is a novel optimization that improves the quality of the relative geometries in the viewing graph by enforcing loop consistency constraints with the epipolar point transfer. We show that this optimization greatly improves the accuracy of relative poses in the viewing graph and removes the need for filtering steps or robust algorithms typically used in global SfM methods. In addition, the optimized viewing graph can be used to efficiently calibrate cameras at scale. We combine our viewing graph optimization and focal length calibration into a global SfM pipeline that is more efficient than existing approaches. To our knowledge, ours is the first global SfM pipeline capable of handling uncalibrated image sets. 1.
Noname manuscript No. (will be inserted by the editor) On Camera Calibration with Linear Programming and Loop Constraint
"... Abstract A technique for calibrating a network of perspective cameras based on their graph of trifocal tensors is presented. After estimating a set of reliable epipolar geometries, a parameterization of the graph of trifocal tensors is proposed in which each trifocal tensor is linearly encoded by ..."
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Abstract A technique for calibrating a network of perspective cameras based on their graph of trifocal tensors is presented. After estimating a set of reliable epipolar geometries, a parameterization of the graph of trifocal tensors is proposed in which each trifocal tensor is linearly encoded by a 4vector. The strength of this parameterization is that the homographies relating two adjacent trifocal tensors, as well as the projection matrices depend linearly on the parameters. Two methods for estimating these parameters in a global way taking into account loops in the graph are developed. Both methods are based on sequential linear programming: the first relies on a locally linear approximation of the polynomials involved in the loop constraints whereas the second uses alternating minimization. Both methods have the advantage of being nonincremental and of uniformly distributing the error across all the cameras. Experiments carried out on several real data sets demonstrate the accuracy of the proposed approach and its efficiency in distributing errors over the whole set of cameras. Keywords structure from motion · camera calibration · sequential linear programming
Minimal Solvers for Relative Pose with a Single Unknown Radial Distortion
"... In this paper, we study the problems of estimating relative pose between two cameras in the presence of radial distortion. Specifically, we consider minimal problems where one of the cameras has no or known radial distortion. There are three useful cases for this setup with a single unknown distor ..."
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In this paper, we study the problems of estimating relative pose between two cameras in the presence of radial distortion. Specifically, we consider minimal problems where one of the cameras has no or known radial distortion. There are three useful cases for this setup with a single unknown distortion: (i) fundamental matrix estimation where the two cameras are uncalibrated, (ii) essential matrix estimation for a partially calibrated camera pair, (iii) essential matrix estimation for one calibrated camera and one camera with unknown focal length. We study the parameterization of these three problems and derive fast polynomial solvers based on Gröbner basis methods. We demonstrate the numerical stability of the solvers on synthetic data. The minimal solvers have also been applied to real imagery with convincing results1. 1.