A Guided Tour Through Multiview Relations

The aim of this paper is to give the non-specialist reader a comprehensible and intuitive introduction to multiview relations. It focusses on the geometric interpretation of the different image relationships, but also presents a concise mathematical formalism which allows to derive the algebraic expressions explicitly in an elementary and uniform manner. Special attention has been paid both to these multiview constraints as geometric incidence relations between image features (i.e. points and lines) in different views as well as to their use for image transfer. Moreover, an attempt has been made to provide sufficient pointers to the literature where the interested reader may find additional information on particular subjects as well as alternative viewpoints and mathematical formalisms.

[1]  Amnon Shashua,et al.  Algebraic Functions For Recognition , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

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

[3]  Andrew Zisserman,et al.  Robust computation and parametrization of multiple view relations , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[4]  Andrew Zisserman,et al.  Robust parameterization and computation of the trifocal tensor , 1997, Image Vis. Comput..

[5]  Amnon Shashua,et al.  Novel View Synthesis by Cascading Trilinear Tensors , 1998, IEEE Trans. Vis. Comput. Graph..

[6]  Amnon Shashua,et al.  Novel view synthesis in tensor space , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[7]  G. Sandini,et al.  Computer Vision — ECCV'92 , 1992, Lecture Notes in Computer Science.

[8]  Nassir Navab,et al.  Relative affine structure: theory and application to 3D reconstruction from perspective views , 1994, 1994 Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[9]  Amnon Shashua,et al.  Unifying two-view and three-view geometry , 1997 .

[10]  O. Faugeras,et al.  About the correspondences of points between N images , 1995, Proceedings IEEE Workshop on Representation of Visual Scenes (In Conjunction with ICCV'95).

[11]  Thierry Viéville,et al.  Canonical Representations for the Geometries of Multiple Projective Views , 1996, Comput. Vis. Image Underst..

[12]  Richard I. Hartley,et al.  A linear method for reconstruction from lines and points , 1995, Proceedings of IEEE International Conference on Computer Vision.

[13]  Minas E. Spetsakis A linear algorithm for point and line-based structure from motion , 1992, CVGIP Image Underst..

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

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

[16]  Richard I. Hartley,et al.  In defence of the 8-point algorithm , 1995, Proceedings of IEEE International Conference on Computer Vision.

[17]  Olivier D. Faugeras,et al.  On the geometry and algebra of the point and line correspondences between N images , 1995, Proceedings of IEEE International Conference on Computer Vision.

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

[19]  Amnon Shashua,et al.  Trilinear Tensor: The Fundamental Construct of Multiple-view Geometry and Its Applications , 1997, AFPAC.

[20]  Jan-Olof Eklundh,et al.  Computer Vision — ECCV '94 , 1994, Lecture Notes in Computer Science.

[21]  Andrew W. Fitzgibbon,et al.  Automatic Camera Recovery for Closed or Open Image Sequences , 1998, ECCV.

[22]  Bernd Neumann,et al.  Computer Vision — ECCV’98 , 1998, Lecture Notes in Computer Science.

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

[24]  Michael Werman,et al.  The study of 3D-from-2D using elimination , 1995, Proceedings of IEEE International Conference on Computer Vision.

[25]  B. Triggs The Geometry of Projective Reconstruction I: Matching Constraints and the Joint Image , 1995 .

[26]  Amnon Shashua,et al.  Ambiguity in reconstruction from images of six points , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[27]  B. Triggs A New Approach to Geometric Fitting , 1996 .

[28]  Olivier D. Faugeras,et al.  A nonlinear method for estimating the projective geometry of 3 views , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[29]  Amnon Shashua,et al.  The Rank 4 Constraint in Multiple (>=3) View Geometry , 1996, ECCV.

[30]  Narendra Ahuja,et al.  Motion and Structure from Line Correspondences; Closed-Form Solution, Uniqueness, and Optimization , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[31]  A. Heyden,et al.  Algebraic properties of multilinear constraints , 1997 .

[32]  Roberto Cipolla,et al.  Computer Vision — ECCV '96 , 1996, Lecture Notes in Computer Science.

[33]  Olivier D. Faugeras,et al.  The critical sets of lines for camera displacement estimation: A mixed Euclidean-projective and constructive approach , 1993, 1993 (4th) International Conference on Computer Vision.

[34]  Paul A. Beardsley,et al.  3D Model Acquisition from Extended Image Sequences , 1996, ECCV.

[35]  O. Faugeras Three-dimensional computer vision: a geometric viewpoint , 1993 .

[36]  Richard I. Hartley,et al.  Estimation of Relative Camera Positions for Uncalibrated Cameras , 1992, ECCV.

[37]  Amnon Shashua Multiple-View Geometry and Photometry , 1995, ACCV.

[38]  Richard I. Hartley,et al.  Projective reconstruction from line correspondences , 1994, 1994 Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[39]  Amnon Shashua,et al.  Projective Structure from Uncalibrated Images: Structure From Motion and Recognition , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[40]  Amnon Shashua,et al.  On Degeneracy of Linear Reconstruction From Three Views: Linear Line Complex and Applications , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[41]  Michael Werman,et al.  Trilinearity of three perspective views and its associated tensor , 1995, Proceedings of IEEE International Conference on Computer Vision.

[42]  Anders Heyden,et al.  A Common Framework for Multiple View Tensors , 1998, ECCV.

[43]  Olivier D. Faugeras,et al.  A New Characterization of the Trifocal Tensor , 1998, ECCV.

[44]  Bill Triggs,et al.  Matching constraints and the joint image , 1995, Proceedings of IEEE International Conference on Computer Vision.

[45]  Anders Heyden,et al.  Algebraic Varieties in Multiple View Geometry , 1996, ECCV.

[46]  Richard I. Hartley,et al.  Minimizing algebraic error in geometric estimation problems , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[47]  Richard I. Hartley,et al.  Computation of the Quadrifocal Tensor , 1998, ECCV.