A Case Against Epipolar Geometry

We discuss briefly a number of areas where epipolar geometry is currently central in carrying out visual tasks. In contrast we demonstrate configurations for which 3D projective invariants can be computed from perspective stereo pairs, but epipolar geometry (and full projective structure) cannot. We catalogue a number of these configurations which generally involve isotropies under the 3D projective group, and investigate the connection with camera calibration. Examples are given of the invariants recovered from real images. We also indicate other areas where a strong reliance on epipolar geometry should be avoided, in particular for image transfer.

[1]  Patrick Gros,et al.  Présentation de la théorie des invariants sous une forme utilisable en vision par ordinateur , 1991 .

[2]  P. Beardsley,et al.  Affine and Projective Structure from Motion , 1992 .

[3]  Rajiv Gupta,et al.  Stereo from uncalibrated cameras , 1992, Proceedings 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[4]  H. C. Longuet-Higgins,et al.  A computer algorithm for reconstructing a scene from two projections , 1981, Nature.

[5]  J. G. Semple,et al.  Algebraic Projective Geometry , 1953 .

[6]  Thomas S. Huang,et al.  Theory of Reconstruction from Image Motion , 1992 .

[7]  Roger Mohr,et al.  Projective Geometry and Computer Vision , 1993, Handbook of Pattern Recognition and Computer Vision.

[8]  B Williamson.  The cloning revolution meets human genetics , 1981, Nature.

[9]  Thierry Viéville,et al.  Canonic Representations for the Geometries of Multiple Projective Views , 1994, ECCV.

[10]  Quang-Tuan Luong.  Matrice fondamentale et autocalibration en vision par ordinateur , 1992 .

[11]  S. Maybank.  The projective geometry of ambiguous surfaces , 1990, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[12]  Thomas Buchanan.  The twisted cubic and camera calibration , 1988, Comput. Vis. Graph. Image Process..

[13]  Amnon Shashua,et al.  Trilinearity in Visual Recognition by Alignment , 1994, ECCV.

[14]  S. Maybank.  Properties of essential matrices , 1990, Int. J. Imaging Syst. Technol..

[15]  Andrew Zisserman,et al.  Geometric invariance in computer vision , 1992 .

[16]  Olivier D. Faugeras,et al.  Motion from point matches: multiplicity of solutions , 1988, Geometry and Robotics.

[17]  Olivier D. Faugeras,et al.  What can be seen in three dimensions with an uncalibrated stereo rig , 1992, ECCV.

[18]  O. D. Faugeras,et al.  Camera Self-Calibration: Theory and Experiments , 1992, ECCV.

[19]  Andrew Zisserman,et al.  Motion From Point Matches Using Affine Epipolar Geometry , 1994, ECCV.

[20]  Long Quan,et al.  Towards structure from motion for linear features through reference points , 1991, Proceedings of the IEEE Workshop on Visual Motion.

[21]  Richard Szeliski,et al.  Recovering 3D Shape and Motion from Image Streams Using Nonlinear Least Squares , 1994, J. Vis. Commun. Image Represent..

[22]  Philip H. S. Torr,et al.  Stochastic Motion Clustering , 1994, ECCV.