Duality, Rigidity and Planar Parallax

We investigate the geometry of two views of seven points, four of which are coplanar, and the geometry of three views of six points, four of which are coplanar. We prove that the two are dual, and that the fundamental geometric constraints in each case are encapsulated by a planar homology. The work unifies a number of previously diverse results related to planar parallax, duality and planar homologies.

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

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

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

[4]  Amnon Shashua,et al.  On Geomatric and Algebraic Aspects of 3D Affine and Projective Structures from Perspective 2D Views , 1993, Applications of Invariance in Computer Vision.

[5]  Harpreet S. Sawhney Simplifying motion and structure analysis using planar parallax and image warping , 1994, Proceedings of 12th International Conference on Pattern Recognition.

[6]  Harpreet S. Sawhney Motion video analysis using planar parallax , 1994, Electronic Imaging.

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

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

[9]  A. Shashua,et al.  Shape tensors for efficient and learnable indexing , 1995, Proceedings IEEE Workshop on Representation of Visual Scenes (In Conjunction with ICCV'95).

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

[11]  Michal Irani,et al.  Representation of scenes from collections of images , 1995, Proceedings IEEE Workshop on Representation of Visual Scenes (In Conjunction with ICCV'95).

[12]  Luc Van Gool,et al.  Grouping and invariants using planar homologies , 1995 .

[13]  Stefan Carlsson,et al.  Duality of reconstruction and positioning from projective views , 1995, Proceedings IEEE Workshop on Representation of Visual Scenes (In Conjunction with ICCV'95).

[14]  Michael Werman,et al.  Duality of Multi-Point and Multi-Frame Geometry: Fundamental Shape Matrices and Tensors , 1996, ECCV.

[15]  P. Anandan,et al.  Parallax Geometry of Pairs of Points for 3D Scene Analysis , 1996, ECCV.

[16]  Ian D. Reid,et al.  A plane measuring device , 1999, Image Vis. Comput..