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).
WWW Version. 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).
WWW Version. 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).
WWW Version. 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.
Postscript Version. BibRef 9601
Earlier:
A Stability Analysis of the Fundamental Matrix,
ECCV94(A:577-588).
WWW Version. 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).
WWW Version. 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).
WWW Version.
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). 9608University 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).
WWW Version. 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

Zhang, Z.Y.[Zheng-You], Xu, G.[Gang],
A General expression of the Fundamental Matrix for Both Projective and Affine Cameras,
IJCAI97(1502-1507). BibRef 9700

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

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.

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. 0409Extension 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. 0601Fundamental 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.
WWW Version. 0701Typically 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.
WWW Version. 0705Estimate the essential matrix from point correspondences between a stereo image pair, assuming that the internal camera parameters are known. BibRef

Noury, N.[Nicolas], Sur, F.[Frederic], Berger, M.O.[Marie-Odile],
Fundamental Matrix Estimation Without Prior Match,
ICIP07(I: 513-516).
WWW Version. 0709 BibRef

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

Fan, X.D.[Xiao-Dong], Vidal, R.[René],
The Space of Multibody Fundamental Matrices: Rank, Geometry and Projection,
WDV06(1-17).
WWW Version. 0705 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).
WWW Version. 0711 BibRef
Earlier: A2, A1:
High Accuracy Fundamental Matrix Computation and Its Performance Evaluation,
BMVC06(I:217).
PDF Version. 0609 BibRef

Levi, N., Werman, M.,
The viewing graph,
CVPR03(I: 518-522).
IEEE Abstract. IEEE Top Reference. 0307Given 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).
WWW Version.
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).
WWW Version. BibRef 9600

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