On Projection Matrices

Projection matrices from projective spaces P to P have long been used in multiple-view geometry to model the perspective projection created by the pin-hole camera. In this work we introduce higher-dimensional mappings P ! P, k = 4; 5; 6 for the representation of various applications in which the world we view is no longer rigid. We also describe the multi-view constraints from these new projection matrices and methods for extracting the (nonrigid) structure and motion for each application.

[1]  Lior Wolf,et al.  Homography Tensors: On Algebraic Entities that Represent Three Views of Static or Moving Planar Points , 2000, ECCV.

[2]  Andrew W. Fitzgibbon,et al.  Multibody Structure and Motion: 3-D Reconstruction of Independently Moving Objects , 2000, ECCV.

[3]  Amnon Shashua,et al.  Trajectory Triangulation: 3D Reconstruction of Moving Points from a Monocular Image Sequence , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[4]  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.

[5]  Charles R. Dyer,et al.  Interpolating view and scene motion by dynamic view morphing , 1999, Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149).

[6]  S. P. Mudur,et al.  Three-dimensional computer vision: a geometric viewpoint , 1993 .

[7]  Gian-Carlo Rota,et al.  On the Exterior Calculus of Invariant Theory , 1985 .

[8]  Amnon Shashua,et al.  On the synthesis of dynamic scenes from reference views , 2000, Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662).

[9]  Takeo Kanade,et al.  An Iterative Image Registration Technique with an Application to Stereo Vision , 1981, IJCAI.