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A Practical Rank-Constrained Eight-Point Algorithm for Fundamental Matrix Estimation

Yinqiang Zheng, Shigeki Sugimoto, Masatoshi Okutomi
2013 2013 IEEE Conference on Computer Vision and Pattern Recognition  
Due to its simplicity, the eight-point algorithm has been widely used in fundamental matrix estimation.  ...  In this work, we present a new rank-2 constrained eight-point algorithm, which directly incorporates the rank-2 constraint in the minimization process.  ...  Overview of Our Work In this work, we propose a new rank-2 constrained eightpoint algorithm for fundamental matrix estimation.  ... 
doi:10.1109/cvpr.2013.203 dblp:conf/cvpr/ZhengSO13 fatcat:7kb5dkoekjgavh3sne3nydwgbe

Rank-Constrained Fundamental Matrix Estimation by Polynomial Global Optimization Versus the Eight-Point Algorithm

Florian Bugarin, Adrien Bartoli, Didier Henrion, Jean-Bernard Lasserre, Jean-José Orteu, Thierry Sentenac
2014 Journal of Mathematical Imaging and Vision  
The fundamental matrix can be estimated from point matches. The current gold standard is to bootstrap the eight-point algorithm and two-view projective bundle adjustment.  ...  The eight-point algorithm first computes a simple linear least squares solution by minimizing an algebraic cost and then projects the result to the closest rank-deficient matrix.  ...  They all illustrate practical cases for which our initialization method allows bundle adjustment to reach a better local minimum than the eight-point algorithm.  ... 
doi:10.1007/s10851-014-0545-9 fatcat:fbud4kmg7jbwlb35clicx44kgq

Rank-constrained fundamental matrix estimation by polynomial global optimization versus the eight-point algorithm [article]

Florian Bugarin, Didier Henrion (LAAS, CTU/FEE), Jean-Bernard Lasserre, Thierry Sentenac
2014 arXiv   pre-print
The fundamental matrix can be estimated from point matches. The current gold standard is to bootstrap the eight-point algorithm and two-view projective bundle adjustment.  ...  The eight-point algorithm first computes a simple linear least squares solution by minimizing an algebraic cost and then projects the result to the closest rank-deficient matrix.  ...  They all illustrate practical cases for which our initialization method allows bundle adjustment to reach a better local minimum than the eight-point algorithm.  ... 
arXiv:1403.4806v1 fatcat:rl2yswfnpnflvhgdjaf5njl3ie

Singular Vector Methods for Fundamental Matrix Computation [chapter]

Ferran Espuny, Pascal Monasse
2014 Lecture Notes in Computer Science  
The normalized eight-point algorithm is broadly used for the computation of the fundamental matrix between two images given a set of correspondences.  ...  We propose two new algorithms to enforce the rank-two constraint on the fundamental matrix in closed form.  ...  The normalized eight-point algorithm introduced by Hartley [9] allows computing in closed form an estimate of the fundamental matrix given at least eight correspondences between two images.  ... 
doi:10.1007/978-3-642-53842-1_25 fatcat:3qs5hl57vbduxp7oppef65tx5i

A new approach to robust fundamental matrix estimation using an analytic objective function and adjusted gradient projection

Cuibing Du, Zongqing Lu, Jing-Hao Xue, Qingmin Liao, Xudong Jiang, Jenq-Neng Hwang
2019 Eleventh International Conference on Digital Image Processing (ICDIP 2019)  
problem of robust fundamental matrix estimation from corrupted correspondences.  ...  A new approach to robust fundamental matrix estimation using an analytic objective function and adjusted gradient projection," ABSTRACT In this paper we propose a new approach to tackling the challenging  ...  , LMEDS [9] and MLESAC [19] , an approximate fundamental matrix is obtained by a linear method like the eight-point algorithm [6] from a set of sample points, and repeating this can attain a set  ... 
doi:10.1117/12.2539648 fatcat:mbviukwojnbhpns5aw77wmf26e

A convex optimization approach to robust fundamental matrix estimation

Y. Cheng, J. A. Lopez, O. Camps, M. Sznaier
2015 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)  
This paper considers the problem of estimating the fundamental matrix from corrupted point correspondences.  ...  A general nonconvex framework is proposed that explicitly takes into account the rank-2 constraint on the fundamental matrix and the presence of noise and outliers.  ...  For all these methods, the number of iterations was set to 500, and in each iteration the fundamental matrix was calculated using the eight-point algorithm.  ... 
doi:10.1109/cvpr.2015.7298829 dblp:conf/cvpr/ChengLCS15 fatcat:iiu3r3pt2zfjvamvn64widorrq

Simultaneously Estimating the Fundamental Matrix and Homographies

Pei Chen, D. Suter
2009 IEEE Transactions on robotics  
The estimation of the fundamental matrix (FM) and/or one or more homographies between two views is of great interest for a number of computer vision and robotics tasks.  ...  We propose a solution method in which the Sampson error for the FM and homographies is minimized by the Levenberg-Marquardt (LM) algorithm.  ...  ., for providing the images and data of the Corridor sequence.  ... 
doi:10.1109/tro.2009.2030224 fatcat:juy45aofcvgivmtcre62wxwnjm

Clustering Assisted Fundamental Matrix Estimation [article]

Hao Wu, Yi Wan
2015 arXiv   pre-print
for fundamental matrix estimation.  ...  In this paper we propose a new method for fundamental matrix estimation that makes use of clustering a group of 4D vectors.  ...  The fundamental matrix F is a 3*3 matrix with rank 2.  ... 
arXiv:1504.03409v1 fatcat:szc2slvocredthf4avk752it7e

Multi-View Geometry for Camera Networks [chapter]

Richard J. Radke
2009 Multi-Camera Networks  
We also discuss feature detection and matching, and describe basic estimation algorithms for the most common problems that arise in multiview geometry.  ...  This chapter introduces the basics of multiview geometry in computer vision, including image formation and camera matrices, epipolar geometry and the fundamental matrix, projective transformations, and  ...  is called the normalized eight-point algorithm.  ... 
doi:10.1016/b978-0-12-374633-7.00003-3 fatcat:ibjqnv5pnfa3rm4lsagllgdbfa

Imaging Monocular Vision Localization and Application in Smart Home

Gao Junchai, Yan Keding, Han Bing
2017 International Journal of Smart Home  
A initial localization estimation is based on the simplified plane motion model with corresponding points projecting in two viewpoint images of a 3D point, and nonlinear optimization localization estimation  ...  simplified essential matrix is modeled for plane motion.  ...  m Fm   (5) It is a condition that all corresponding points are satisfied, from the formula (5) fundamental matrix F can be solved with all corresponding points of landmarks, which is a 33  matrix,  ... 
doi:10.14257/ijsh.2017.11.2.01 fatcat:rlnmv6fnbvg6bcx4b7phjjpp3m

One-dimensional dense disparity estimation for three-dimensional reconstruction

L. Oisel, E. Memin, L. Morin, F. Galpin
2003 IEEE Transactions on Image Processing  
The dense field estimation modelized within a robust framework is constrained by the epipolar geometry.  ...  A two-dimensional (2-D) triangular mesh model of the scene is calculated using a two-step algorithm mixing sparse matching and dense motion estimation approaches.  ...  The fundamental matrix is first estimated from eight matches: three of them are selected to perform a projective change of basis to constraint the matrix to be of rank 2.  ... 
doi:10.1109/tip.2003.815257 pmid:18237982 fatcat:76e3kp544rcqnefqdgivad7pyu

Algebraic Characterization of Essential Matrices and Their Averaging in Multiview Settings

Yoni Kasten, Amnon Geifman, Meirav Galun, Ronen Basri
2019 2019 IEEE/CVF International Conference on Computer Vision (ICCV)  
A common approach to essential matrix averaging is to separately solve for camera orientations and subsequently for camera positions.  ...  We next use these conditions to formulate essential matrix averaging as a constrained optimization problem, allowing us to recover a consistent set of essential matrices given a (possibly partial) set  ...  Acknowledgment This research was supported in part by the Minerva foundation with funding from the Federal German Ministry for Education and Research.  ... 
doi:10.1109/iccv.2019.00599 dblp:conf/iccv/KastenGGB19 fatcat:obqxt5plvfe5fehcsxucmhqke4

Revisiting hartley's normalized eight-point algorithm

W. Chojnacki, M.J. Brooks, A. van den Hengel, D. Gawley
2003 IEEE Transactions on Pattern Analysis and Machine Intelligence  
Hartley's eight-point algorithm has maintained an important place in computer vision, notably as a means of providing an initial value of the fundamental matrix for use in iterative estimation methods.  ...  In this paper, a novel explanation is given for the improvement in performance of the eight-point algorithm that results from using normalized data.  ...  INTRODUCTION IN a landmark paper, Longuet-Higgins [1] proposed the eight-point algorithm-a simple direct method for computation of the essential matrix.  ... 
doi:10.1109/tpami.2003.1227992 fatcat:7a3qr6ifafarzmiubpocyblmmy

Three-dimensional structure calculation: achieving accuracy without calibration

B. Boufama, A. Habed
2004 Image and Vision Computing  
Mainly, we describe a three-step procedure in which we jointly use the simplified form of the Kruppa's equations, a normalization of pixel coordinates and the eight-point algorithm to recover the three-dimensional  ...  One might suggest to place the scene even closer to the camera, for instance at © P © ¬ « , however, this will cause a lot of points to be projected outside the image frame. was placed at about P P ª ©  ...  Improved Eight-Point Algorithm One recent method for calculating the fundamental matrix F [7] has shown that with minor transformations on the image coordinates, the calculated using the Eight-Point  ... 
doi:10.1016/j.imavis.2004.03.015 fatcat:4hl43tpvojd33lyny4icr22mt4

A ROBUST METHOD FOR FUNDAMENTAL MATRIX ESTIMATION WITH RADIAL DISTORTION

J.-S. Xue, X.-N. Chen, H. Yi
2018 The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences  
We propose a novel robust method for radial fundamental matrix estimation.  ...  The estimation result of radial fundamental matrix could be served as the initialization for structure from motion.  ...  point for the fundamental matrix estimation.  ... 
doi:10.5194/isprs-archives-xlii-3-2029-2018 fatcat:2a7zoakg2jh6nhuijc6e6tpu5e
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