Structure from motion using line correspondences
International Journal of Computer Vision
Motion and Structure from Line Correspondences; Closed-Form Solution, Uniqueness, and Optimization
IEEE Transactions on Pattern Analysis and Machine Intelligence
Canonic representations for the geometries of multiple projective views
ECCV '94 Proceedings of the third European conference on Computer vision (vol. 1)
Relative Affine Structure: Canonical Model for 3D From 2D Geometry and Applications
IEEE Transactions on Pattern Analysis and Machine Intelligence
Lines and Points in Three Views and the Trifocal Tensor
International Journal of Computer Vision
Novel View Synthesis by Cascading Trilinear Tensors
IEEE Transactions on Visualization and Computer Graphics
Algebraic Functions For Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Hierarchical Model-Based Motion Estimation
ECCV '92 Proceedings of the Second European Conference on Computer Vision
From Reference Frames to Reference Planes: Multi-View Parallax Geometry and Applications
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume II - Volume II
On Degeneracy of Linear Reconstruction from Three Views: Linear Line Complex and Applications
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume II - Volume II
Duality, Rigidity and Planar Parallax
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume II - Volume II
The Rank 4 Constraint in Multiple (=3) View Geometry
ECCV '96 Proceedings of the 4th European Conference on Computer Vision-Volume II - Volume II
Threading Fundamental Matrices
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume I - Volume I
Trilinear Tensor: The Fundamental Construct of Multiple-view Geometry and Its Applications
AFPAC '97 Proceedings of the International Workshop on Algebraic Frames for the Perception-Action Cycle
Model-based brightness constraints: on direct estimation of structure and motion
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
Reconstruction from image sequences by means of relative depths
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
On the geometry and algebra of the point and line correspondences between N images
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Trilinearity of three perspective views and its associated tensor
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Matching constraints and the joint image
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
A Nonlinear Method for Estimating the Projective Geometry of 3 Views
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
An iterative image registration technique with an application to stereo vision
IJCAI'81 Proceedings of the 7th international joint conference on Artificial intelligence - Volume 2
A Minimal Set of Constraints for the Trivocal Tensor
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part I
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We revisit the bilinear matching constraint between two perspective views of a 3D scene. Our objective is to represent the constraint in the same manner and form as the trilinear constraint among three views. The motivation is to establish a common terminology that bridges between the fundamental matrix F (associated with the bilinear constraint) and the trifocal tensor Τijk (associated with the trilinearities). By achieving this goal we can unify both the properties and the techniques introduced in the past for working with multiple views for geometric applications. Doing that we introduce a 3 × 3 × 3 tensor Fijk, we call the bifocal tensor, that represents the bilinear constraint. The bifocal and trifocal tensors share the same form and share the same contraction properties. By close inspection of the contractions of the bifocal tensor into matrices we show that one can represent the family of rank-2 homography matrices by [δ]×F where ffi is a free vector. We then discuss four applications of the new representation: (i) Quasi-metric viewing of projective data, (ii) triangulation, (iii) view synthesis, and (iv) recovery of camera ego-motion from a stream of views.