Threading Fundamental Matrices

We present a new function that operates on Fundamental matrices across a sequence of views. The operation, we call “threading”, connects two consecutive Fundamental matrices using the Trilinear tensor as the connecting thread. The threading operation guarantees that consecutive camera matrices are consistent with a unique 3D model, without ever recovering a 3D model. Applications include recovery of camera ego-motion from a sequence of views, image stabilization (plane stabilization) across a sequence, and multi-view image-based rendering.

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

[2]  Anders Heyden,et al.  Reconstruction from image sequences by means of relative depths , 1995, Proceedings of IEEE International Conference on Computer Vision.

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

[4]  Lihi Zelnik-Manor,et al.  Multi-frame alignment of planes , 1999, Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149).

[5]  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.

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

[7]  Amnon Shashua,et al.  Model-Based Brightness Constraints: On Direct Estimation of Structure and Motion , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[8]  Gerald Sommer,et al.  Algebraic Frames for the Perception-Action Cycle , 2000, Lecture Notes in Computer Science.

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

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

[11]  Peter F. Sturm,et al.  A Factorization Based Algorithm for Multi-Image Projective Structure and Motion , 1996, ECCV.

[12]  Nassir Navab,et al.  Relative Affine Structure: Canonical Model for 3D From 2D Geometry and Applications , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[13]  E SpetsakisMinas,et al.  Structure from motion using line correspondences , 1990 .

[14]  O. Faugeras Stratification of three-dimensional vision: projective, affine, and metric representations , 1995 .

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

[16]  H. Damasio,et al.  IEEE Transactions on Pattern Analysis and Machine Intelligence: Special Issue on Perceptual Organization in Computer Vision , 1998 .

[17]  Amnon Shashua,et al.  Tensor Embedding of the Fundamental Matrix , 1998, SMILE.

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

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

[20]  Reinhard Koch,et al.  3D Structure from Multiple Images of Large-Scale Environments , 1998, Lecture Notes in Computer Science.

[21]  Amnon Shashua,et al.  Robust recovery of camera rotation from three frames , 1996, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[22]  Carlo Tomasi,et al.  Good features to track , 1994, 1994 Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

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

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

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

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

[27]  Michal Irani,et al.  Recovery of ego-motion using image stabilization , 1994, 1994 Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.