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M.: Pose estimation with radial distortion and unknown focal length
 In: Computer Vision and Pattern Recognition
, 2009
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Cited by 19 (0 self)
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Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profitmaking activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal? Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.
Optimal Estimation of Vanishing Points in a Manhattan World
"... In this paper, we present an analytical method for computing the globally optimal estimates of orthogonal vanishing points in a “Manhattan world ” with a calibrated camera. We formulate this as constrained leastsquares problem whose optimality conditions form a multivariate polynomial system. We so ..."
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In this paper, we present an analytical method for computing the globally optimal estimates of orthogonal vanishing points in a “Manhattan world ” with a calibrated camera. We formulate this as constrained leastsquares problem whose optimality conditions form a multivariate polynomial system. We solve this system analytically to compute all the critical points of the leastsquares cost function, and hence the global minimum, i.e., the globally optimal estimate for the orthogonal vanishing points. The same optimal estimator is used in conjunction with RANSAC to generate orthogonalvanishingpoint hypotheses (from triplets of lines) and thus classify lines into parallel and mutually orthogonal groups. The proposed method is validated experimentally on the York Urban Database. 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.
Singlybordered blockdiagonal form for minimal problem solvers
 IN ACCV’14, 2014. 8
, 2014
"... The Gröbner basis method for solving systems of polynomial equations became very popular in the computer vision community as it helps to nd fast and numerically stable solutions to difficult problems. In this paper, we present a method that potentially signicantly speeds up Grobner basis solvers. We ..."
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Cited by 2 (2 self)
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The Gröbner basis method for solving systems of polynomial equations became very popular in the computer vision community as it helps to nd fast and numerically stable solutions to difficult problems. In this paper, we present a method that potentially signicantly speeds up Grobner basis solvers. We show that the elimination template matrices used in these solvers are usually quite sparse and that by permuting the rows and columns they can be transformed into matrices with nice blockdiagonal structure known as the singlybordered blockdiagonal (SBBD) form. The diagonal blocks of the SBBD matrices constitute independent subproblems and can therefore be solved, i.e. eliminated or factored, independently. The computational time can be further reduced on a parallel computer by distributing these blocks to different processors for parallel computation. The speedup is visible also for serial processing since we perform O(n³) GaussJordan eliminations on smaller (usually two, approximately n 2 n
Centre for Mathematical Sciences
"... This paper presents a solution to panoramic image stitching of two images with coinciding optical centers, but unknown focal length and radial distortion. The algorithm operates with a minimal set of corresponding points (three) which means that it is well suited for use in any RANSAC style algorith ..."
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This paper presents a solution to panoramic image stitching of two images with coinciding optical centers, but unknown focal length and radial distortion. The algorithm operates with a minimal set of corresponding points (three) which means that it is well suited for use in any RANSAC style algorithm for simultaneous estimation of geometry and outlier rejection. Compared to a previous method for this problem, we are able to guarantee that the right solution is found in all cases. The solution is obtained by solving a small system of polynomial equations. The proposed algorithm has been integrated in a complete multi image stitching system and we evaluate its performance on real images with lens distortion. We demonstrate both quantitative and qualitative improvements compared to state of the art methods. 1
Analytical LeastSquares Solution for 3D LidarCamera Calibration
"... Abstract This paper addresses the problem of estimating the intrinsic parameters of the 3D Velodyne lidar while at the same time computing its extrinsic calibration with respect to a rigidly connected camera. Existing approaches to solve this nonlinear estimation problem are based on iterative minim ..."
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Abstract This paper addresses the problem of estimating the intrinsic parameters of the 3D Velodyne lidar while at the same time computing its extrinsic calibration with respect to a rigidly connected camera. Existing approaches to solve this nonlinear estimation problem are based on iterative minimization of nonlinear cost functions. In such cases, the accuracy of the resulting solution hinges on the availability of a precise initial estimate, which is often not available. In order to address this issue, we divide the problem into two leastsquares subproblems, and analytically solve each one to determine a precise initial estimate for the unknown parameters. We further increase the accuracy of these initial estimates by iteratively minimizing a batch nonlinear leastsquares cost function. In addition, we provide the minimal observability conditions, under which, it is possible to accurately estimate the unknown parameters. Experimental results consisting of photorealistic 3D reconstruction of indoor and outdoor scenes are used to assess the validity of our approach. 1 Introduction and Related Work As demonstrated in the DARPA Urban Challenge, commercially available highspeed
Numerically Stable Optimization of Polynomial Solvers for Minimal Problems
"... Abstract. Numerous geometric problems in computer vision involve the solution of systems of polynomial equations. This is particularly true for so called minimal problems, but also for finding stationary points for overdetermined problems. The stateoftheart is based on the use of numerical linear ..."
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Abstract. Numerous geometric problems in computer vision involve the solution of systems of polynomial equations. This is particularly true for so called minimal problems, but also for finding stationary points for overdetermined problems. The stateoftheart is based on the use of numerical linear algebra on the large but sparse coefficient matrix that represents the original equations multiplied with a set of monomials. The key observation in this paper is that the speed and numerical stability of the solver depends heavily on (i) what multiplication monomials are used and (ii) the set of so called permissible monomials from which numerical linear algebra routines choose the basis of a certain quotient ring. In the paper we show that optimizing with respect to these two factors can give both significant improvements to numerical stability as compared to the state of the art, as well as highly compact solvers, while still retaining numerical stability. The methods are validated on several minimal problems that have previously been shown to be challenging. 1
Springer NetherlandsCamera Resectioning from a Box
"... This paper has been peerreviewed but does not include the final publisher proofcorrections or journal pagination. Citation for the published paper: ..."
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This paper has been peerreviewed but does not include the final publisher proofcorrections or journal pagination. Citation for the published paper:
An Analytical LeastSquares Solution to the Line Scan LIDARCamera Extrinsic Calibration Problem
"... Abstract — In this paper, we present an elegant solution to the 2D LIDARcamera extrinsic calibration problem. Specifically, we develop a simple method for establishing correspondences between a linescan (2D) LIDAR and a camera using a small calibration target that only contains a straight line. Mo ..."
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Abstract — In this paper, we present an elegant solution to the 2D LIDARcamera extrinsic calibration problem. Specifically, we develop a simple method for establishing correspondences between a linescan (2D) LIDAR and a camera using a small calibration target that only contains a straight line. Moreover, we formulate the nonlinear leastsquares problem for finding the unknown 6 degreeoffreedom (dof) transformation between the two sensors, and solve it analytically to determine its global minimum. Additionally, we examine the conditions under which the unknown transformation becomes unobservable, which can be used for avoiding illconditioned configurations. Finally, we present extensive simulation and experimental results for assessing the performance of the proposed algorithm as compared to alternative analytical approaches. I. INTRODUCTION AND RELATED WORK