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. IEEE Top Reference. 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. 9710

WWW Version. BibRef

Hartley, R.I.,
Kruppa's Equations Derived from the Fundamental Matrix,
PAMI(19), No. 2, February 1997, pp. 133-135.
IEEE Abstract. IEEE Top Reference.
WWW Version. 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
WWW Version. 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 Top Reference.
WWW Version. 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 Top Reference.
WWW Version. 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. IEEE Top Reference. 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.

Torr, P.H.S., Fitzgibbon, A.W.,
Invariant Fitting of Two View Geometry,
PAMI(26), No. 5, May 2004, pp. 648-650.
IEEE Abstract. IEEE Top Reference. 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

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

Mainberger, M.[Markus], Bruhn, A.[Andrés], Weickert, J.[Joachim],
Is Dense Optic Flow Useful to Compute the Fundamental Matrix?,
ICIAR08(xx-yy).
Springer 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. IEEE Top Reference. 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. IEEE Top Reference. 0303
BibRef

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