15.2.6 Fundamental Matrix Computation and Use

Ganapathy, S.,
Decomposition of Transformation Matrices for Robot Vision,
PRL(2), 1984, pp. 401-412. BibRef 8400
Earlier: CRA84(130-139). BibRef

Luong, Q.T., Faugeras, O.D.,
Self-Calibration of a Moving Camera from Point Correspondences and Fundamental Matrices,
IJCV(22), No. 3, March/April 1997, pp. 261-289.
WWW Version. 9706
See also Stability Analysis of the Fundamental Matrix, A. BibRef

Luong, Q.T., Faugeras, O.D.,
An Optimization Framework for Efficient Self-Calibration and Motion Determination,
ICPR94(A:248-252).
IEEE DOI Link BibRef 9400

Luong, Q.T., and Faugeras, O.D.,
Determining the Fundamental Matrix with Planes: Instability and New Algorithms,
CVPR93(489-494).
IEEE Abstract. BibRef 9300
Earlier:
Self-Calibration of a Camera Using Multiple Images,
ICPR92(I:9-12).
IEEE DOI Link Camera calibration for initially uncalibrated stereo images. Other methods are unstable when the points close to planar. BibRef

Faugeras, O.D., Luong, Q.T., Maybank, S.J.,
Camera Self-Calibration: Theory and Experiments,
ECCV92(321-334).
Springer DOI Link BibRef 9200

Luong, Q.T., Faugeras, O.D.,
The Fundamental Matrix: Theory, Algorithms, and Stability Analysis,
IJCV(17), No. 1, January 1996, pp. 43-75.
Springer DOI Link
Postscript Version. BibRef 9601
Earlier:
A Stability Analysis of the Fundamental Matrix,
ECCV94(A:577-588).
Springer DOI Link Fundamental Matrix. See also Self-Calibration of a Moving Camera from Point Correspondences and Fundamental Matrices. BibRef

Luong, Q.T., Deriche, R., Faugeras, O.D., and Papadopoulo, T.,
On Determining the Fundamental Matrix: Analysis of Different Methods and Experimental Results,
INRIATR RR-1894, 1993.
HTML Version. BibRef 9300

Csurka, G., Zeller, C., Zhang, Z.Y., Faugeras, O.D.,
Characterizing the Uncertainty of the Fundamental Matrix,
CVIU(68), No. 1, October 1997, pp. 18-36.
WWW Version. 9710
BibRef

Hartley, R.I.,
Kruppa's Equations Derived from the Fundamental Matrix,
PAMI(19), No. 2, February 1997, pp. 133-135.
IEEE Abstract.
IEEE DOI Link 9703
BibRef

See also Theory of Self-Calibration of a Moving Camera, A. See also Zur Ermittlung eines Objektes aus zwei Perspektiven mit innerer Orientierung.

Hartley, R.I.[Richard I.],
Minimizing Algebraic Error in Geometric Estimation Problems,
ICCV98(469-476).
IEEE DOI Link BibRef 9800
And: DARPA97(631-638). BibRef

Torr, P.H.S.[Philip H.S.], Zisserman, A.[Andrew], Maybank, S.J.[Stephen J.],
Robust Detection of Degenerate Configurations while Estimating the Fundamental Matrix,
CVIU(71), No. 3, September 1998, pp. 312-333.
WWW Version. BibRef 9809
Earlier:
Robust Detection of Degenerate Configurations for the Fundamental Matrix,
ICCV95(1037-1042).
IEEE DOI Link
IEEE DOI Link BibRef

Bober, M., Georgis, N., Kittler, J.V.,
On Accurate and Robust Estimation of Fundamental Matrix,
CVIU(72), No. 1, October 1998, pp. 39-53.
WWW Version. BibRef 9810
Earlier: BMVC96(Poster Session 2). 9608
University of Surrey See also Robust Motion Analysis. BibRef

Brandt, S.[Sami], Heikkonen, J.[Jukka],
A Bayesian weighting principle for the fundamental matrix estimation,
PRL(21), No. 12, November 2000, pp. 1081-1092. 0011
BibRef
And:
Optimal Method for the Affine F-Matrix and Its Uncertainty Estimation in the Sense of both Noise and Outliers,
ICCV01(II: 166-173).
IEEE DOI Link 0106
BibRef

Chen, Z.Z.[Ze-Zhi], Wu, C.K.[Cheng-Ke], Shen, P.[Peiyi], Liu, Y.[Yong], Quan, L.[Long],
A robust algorithm to estimate the fundamental matrix,
PRL(21), No. 9, August 2000, pp. 851-861. 0008
See also new image rectification algorithm, A. BibRef

Zhang, Z.Y.[Zheng-You], Xu, G.[Gang],
Unified Theory of Uncalibrated Stereo for Both Perspective and Affine Cameras,
JMIV(9), No. 3, November 1998, pp. 213-229.
WWW Version. BibRef 9811
Earlier:
A General expression of the Fundamental Matrix for Both Projective and Affine Cameras,
IJCAI97(1502-1507). See also Motion and Structure from Two Perspective Views: From Essential Parameters to Euclidean Motion Through the Fundamental Matrix. BibRef

Zhang, Z.Y.[Zheng-You], Loop, C.[Charles],
Estimating the Fundamental Matrix by Transforming Image Points in Projective Space,
CVIU(82), No. 2, May 2001, pp. 174-180.
WWW Version. 0108
BibRef
Earlier: A2, A1:
Computing Rectifying Homographies for Stereo Vision,
CVPR99(I: 125-131).
IEEE Abstract.
IEEE DOI Link Once you know the mapping, apply the rectification to the images so they line up. BibRef

Zhang, Z.Y.[Zheng-You], Loop, C.[Charles],
System and method for rectifying images of three dimensional objects,
US_Patent6,608,923, Aug 19, 2003
WWW Version. BibRef 0308

Chesi, G.[Graziano], Garulli, A., Vicino, A., Cipolla, R.,
Estimating the Fundamental Matrix via Constrained Least-Squares: A Convex Approach,
PAMI(24), No. 3, March 2002, pp. 397-401.
IEEE Abstract.
IEEE DOI Link 0202
BibRef
Earlier:
On the Estimation of the Fundamental Matrix: A Convex Approach to Constrained Least-Squares,
ECCV00(I: 236-250).
WWW Version. 0003
BibRef

Armangué, X.[Xavier], Salvi, J.[Joaquim],
Overall view regarding fundamental matrix estimation,
IVC(21), No. 2, February 2003, pp. 205-220.
WWW Version. 0301
BibRef

Chojnacki, W.[Wojciech], Brooks, M.J.[Michael J.], van den Hengel, A.J.[Anton J.], Gawley, D.[Darren],
A new constrained parameter estimator for computer vision applications,
IVC(22), No. 2, 1 February 2004, pp. 85-91.
WWW Version. 0402
BibRef
Earlier: A3, A2, A1, A4:
A New Constrained Parameter Estimator: Experiments in Fundamental Matrix Computation,
BMVC02(Computer Vision Tools). 0208
BibRef
Earlier: A1, A2, A3, A4:
A Fast MLE-Based Method for Estimating the Fundamental Matrix,
ICIP01(II: 189-192).
IEEE Abstract. 0108
BibRef

Integrate constraints from other than image data, e.g. for calibration. See also 3-D Interpretation of Optical-Flow by Renormalization. See also Determining the Egomotion of an Uncalibrated Camera from Instantaneous Optical Flow. See also Rationalising the Renormalisation Method of Kanatani.

Chojnacki, W.[Wojciech], Hill, R.[Rhys], van den Hengel, A.J.[Anton J.], Brooks, M.J.[Michael J.],
Multi-projective Parameter Estimation for Sets of Homogeneous Matrices,
DICTA09(119-124).
IEEE DOI Link 0912
BibRef

Chojnacki, W.[Wojciech], Szpak, Z.L.[Zygmunt L.], Brooks, M.J.[Michael J.], van den Hengel, A.[Anton],
Multiple Homography Estimation with Full Consistency Constraints,
DICTA10(480-485).
IEEE DOI Link 1012
BibRef

Eriksson, A.P.[Anders P.], van den Hengel, A.J.[Anton J.],
Optimization on the manifold of multiple homographies,
Subspace09(242-249).
IEEE DOI Link 0910
Enforce constraint that homographies for planes lie in a 4D subspace. BibRef

Torr, P.H.S., Fitzgibbon, A.W.,
Invariant Fitting of Two View Geometry,
PAMI(26), No. 5, May 2004, pp. 648-650.
IEEE Abstract. 0404
BibRef
Earlier: A2, A1: BMVC03(xx-yy).
HTML Version. 0409
Extension of See also Fitting Conic Sections to Scattered Data. and See also Fitting Conic Sections to Very Scattered Data: An Iterarive Refinement of the Bookstein Algorithm. for fitting Conics to determine the epipolar geometry to get the Essential Matrix or Fundamental Matrix. BibRef

Seo, J.K.[Jung-Kak], Hong, H.K.[Hyun-Ki], Jho, C.W.[Cheung-Woon], Choi, M.H.[Min-Hyung],
Two quantitative measures of inlier distributions for precise fundamental matrix estimation,
PRL(25), No. 6, 19 April 2004, pp. 733-741.
WWW Version. 0405
BibRef

Sagüés, C., Murillo, A.C., Escudero, F., Guerrero, J.J.,
From lines to epipoles through planes in two views,
PR(39), No. 3, March 2006, pp. 384-393.
WWW Version. 0601
Fundamental matrix using line matches when planar structure is assumed. BibRef

Zhong, H.X., Pang, Y.J., Feng, Y.P.,
A new approach to estimating fundamental matrix,
IVC(24), No. 1, 1 January 2006, pp. 56-60.
WWW Version. 0602
BibRef

Lehmann, S., Bradley, A.P.[Andrew P.], Vaughan, I., Williams, J., Kootsookos, P.J., Clarkson, L.,
Correspondence-Free Determination of the Affine Fundamental Matrix,
PAMI(29), No. 1, January 2007, pp. 82-97.
IEEE DOI Link 0701
Typically errors in matching dealt with using robust methods. Transmorm to a frequency domain task -- match lines in frequency (reasonable model for Orthographic cameras). BibRef

Helmke, U.[Uwe], Hüper, K.[Knut], Lee, P.Y.[Pei Yean], Moore, J.[John],
Essential Matrix Estimation Using Gauss-Newton Iterations on a Manifold,
IJCV(74), No. 2, August 2007, pp. 117-136.
Springer DOI Link 0705
Estimate the essential matrix from point correspondences between a stereo image pair, assuming that the internal camera parameters are known. BibRef

Kanatani, K.[Kenichi], Sugaya, Y.[Yasuyuki],
High Accuracy Fundamental Matrix Computation and Its Performance Evaluation,
IEICE(E90-D), No. 2, February 2007, pp. 579-585.
WWW Version. 0702
BibRef
Earlier: BMVC06(I:217).
PDF Version. 0609
See also Statistical Optimization for Geometric Fitting: Theoretical Accuracy Bound and High Order Error Analysis. BibRef

Kanatani, K.[Kenichi], Sugaya, Y.[Yasuyuki],
Compact Fundamental Matrix Computation,
PSIVT09(179-190).
Springer DOI Link 0901
BibRef

Sugaya, Y.[Yasuyuki], Kanatani, K.[Kenichi],
High Accuracy Computation of Rank-Constrained Fundamental Matrix,
BMVC07(xx-yy).
PDF Version. 0709
BibRef
And:
Highest Accuracy Fundamental Matrix Computation,
ACCV07(II: 311-321).
Springer DOI Link 0711
BibRef

Kim, J.S.[Jun-Sik], Kanade, T.[Takeo],
Degeneracy of the Linear Seventeen-Point Algorithm for Generalized Essential Matrix,
JMIV(37), No. 1, May 2010, pp. xx-yy.
Springer DOI Link 1003
BibRef

Datta, A.[Ankur], Kim, J.S.[Jun-Sik], Kanade, T.[Takeo],
Accurate camera calibration using iterative refinement of control points,
VS09(1201-1208).
IEEE DOI Link 0910
BibRef

Wu, H.H.P., Chang, S.H.,
Fundamental matrix of planar catadioptric stereo systems,
IET-CV(4), No. 2, June 2010, pp. 85-104.
WWW Version. 1007
BibRef

Chen, P.,
Why not use the Levenberg-Marquardt method for fundamental matrix estimation?,
IET-CV(4), No. 4, December 2010, pp. 286-294.
WWW Version. 1011
Maybe LM is not as bad as previously thought for computation of fundamental matrix. BibRef

Fathy, M.E.[Mohammed E.], Hussein, A.S.[Ashraf S.], Tolba, M.F.[Mohammed F.],
Fundamental matrix estimation: A study of error criteria,
PRL(32), No. 2, 15 January 2011, pp. 383-391.
Elsevier DOI Link
WWW Version. 1101
BibRef
Earlier:
Simple, Fast and Accurate Estimation of the Fundamental Matrix Using the Extended Eight-point Schemes,
BMVC10(xx-yy).
HTML Version. 1009
Fundamental matrix; Epipolar geometry; Structure and motion BibRef

Zhang, Y.J.[Yong-Jun], Huang, X.[Xu], Hu, X.Y.[Xiang-Yun], Wan, F.Q.[Fang-Qi], Lin, L.[Liwen],
Direct relative orientation with four independent constraints,
PandRS(66), No. 6, November 2011, pp. 809-817.
Elsevier DOI Link
WWW Version. 1112
Direct relative orientation; Essential matrix; Constraint; Accuracy analysis; Least squares adjustment BibRef

Tegolo, D.[Domenico], Bellavia, F.[Fabio],
noRANSAC for fundamental matrix estimation,
BMVC11(xx-yy).
HTML Version. 1110
BibRef

Zheng, Y.Q.[Yin-Qiang], Sugimoto, S.[Shigeki], Okutomi, M.[Masatoshi],
A branch and contract algorithm for globally optimal fundamental matrix estimation,
CVPR11(2953-2960).
IEEE DOI Link 1106
BibRef

Zhou, H.Y.[Hui-Yu], Schaefer, G.[Gerald],
Robust estimation of the fundamental matrix,
ICIP10(4233-4236).
IEEE DOI Link 1009
BibRef

Fakih, A., Zelek, J.S.,
Determination of the essential matrix using discrete and differential matching constraints,
CIIP09(110-115).
IEEE DOI Link 0903
BibRef

Skarbek, W.[Wladyslaw], Tomaszewski, M.[Michal],
Epipolar Angular Factorisation of Essential Matrix for Camera Pose Calibration,
MIRAGE09(401-412).
Springer DOI Link 0905
BibRef

Sukumar, S.R.[Sreenivas R.], Bozdogan, H.[Hamparsum], Page, D.L.[David L.], Koschan, A.F.[Andreas F.], Abidi, M.A.[Mongi A.],
On handling uncertainty in the fundamental matrix for scene and motion adaptive pose recovery,
CVPR08(1-8).
IEEE DOI Link 0806
BibRef

Den Hollander, R., Hanjalic, A.,
A Combined RANSAC-Hough Transform Algorithm for Fundamental Matrix Estimation,
BMVC07(xx-yy).
PDF Version. 0709
BibRef

Sur, F.[Frederic], Noury, N.[Nicolas], Berger, M.O.[Marie-Odile],
Computing the Uncertainty of the 8 point Algorithm for Fundamental Matrix Estimation,
BMVC08(xx-yy).
PDF Version. 0809
BibRef
Earlier: A2, A1, A3:
Fundamental Matrix Estimation Without Prior Match,
ICIP07(I: 513-516).
IEEE DOI Link 0709
BibRef

Sheikh, Y.[Yaser], Hakeem, A.[Asaad], Shah, M.[Mubarak],
On the Direct Estimation of the Fundamental Matrix,
CVPR07(1-7).
IEEE DOI Link 0706
BibRef

Fan, X.D.[Xiao-Dong], Vidal, R.[René],
The Space of Multibody Fundamental Matrices: Rank, Geometry and Projection,
WDV06(1-17).
Springer DOI Link 0705
BibRef

Levi, N., Werman, M.,
The viewing graph,
CVPR03(I: 518-522).
IEEE Abstract. 0307
Given N views, and some inter-view matricies, which others can we compute. BibRef

Li, Q.[Qi], Li, T.[Tao], Zhu, S.H.[Sheng-Huo], Kambhamettu, C.,
How well can wavelet denoising improve the accuracy of computing fundamental matrices?,
Motion02(247-252).
IEEE Abstract. 0303
BibRef

Salvi, J., Armangué, X., Pagés, J.,
A Survey Addressing the Fundamental Matrix Estimation Problem,
ICIP01(II: 209-212).
IEEE Abstract. 0108
Survey, Fundamental Matrix. BibRef

Lourakis, M.I.A.[Manolis I.A.], and Deriche, R.[Rachid],
Camera Self-Calibration Using the Singular Value Decomposition of the Fundamental Matrix,
ACCV00(I: 403-408). SVD
Postscript Version. 0001
BibRef
And:
Camera Self-Calibration Using the Singular Value Decomposition of the Fundamental Matrix: From Point Correspondences to 3D Measurements,
INRIARR-3748, August 1999.
HTML Version.
Postscript Version.
PDF Version. BibRef

Lourakis, M.I.A.[Manolis I.A.], and Deriche, R.[Rachid],
Camera Self-Calibration Using the Kruppa Equations and the SVD of the Fundamental Matrix: The Case of Varying Intrinsic Parameters,
INRIARR-3911, March 2000.
HTML Version.
Postscript Version.
PDF Version. BibRef 0003

Isgrò, F.[Francesco], Trucco, E.[Emanuele],
A General Rank-2 Parameterization of the Fundamental Matrix,
ICPR00(Vol I: 868-871).
IEEE DOI Link 0009
BibRef

Li, F., Brady, J.M., Wiles, C.,
Fast Computation of the Fundamental Matrix for an Active Stereo Vision System,
ECCV96(I:157-166).
Springer DOI Link BibRef 9600

Chapter on Active Vision, Camera Calibration, Mobile Robots, Navigation, Road Following continues in
Camera Calibration -- Lens Distortion, Aberration, Radial Distortion, Internal Parameters .