Structure from motion using line correspondences
International Journal of Computer Vision
Lines and Points in Three Views and the Trifocal Tensor
International Journal of Computer Vision
On Degeneracy of Linear Reconstruction From Three Views: Linear Line Complex and Applications
IEEE Transactions on Pattern Analysis and Machine Intelligence
Algebraic Functions For Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computation of the Quadrifocal Tensor
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume I - Volume I
A Common Framework for Multiple View Tensors
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume I - Volume I
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
The study of 3D-from-2D using elimination
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
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part I
Revisiting Single-View Shape Tensors: Theory and Applications
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Egomotion Estimation Using Assorted Features
International Journal of Computer Vision
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The quadrifocal tensor which connects image measurements along 4 views is not yet well understood as its counterparts the fundamental matrix and the trifocal tensor. This paper establishes the structure of the tensor as an "epipole-homography" pairing Qijkl = v′j Hikl - v″k Hijl + v‴l Hijk where v′, v″, v‴ are the epipoles in views 2,3,4, H is the "homography tensor" the 3-view analogue of the homography matrix, and the indices i, j, k, l are attached to views 1,2,3,4 respectively -- i.e., Hikl is the homography tensor of views 1,3,4. In the course of deriving the structure Qijkl we show that Linear Line Complex (LLC) mappings are the basic building block in the process.We also introduce a complete break-down of the tensor slices: 3×3×3 slices are homography tensors, and 3×3 slices are LLC mappings. Furthermore, we present a closed-form formula of the quadrifocal tensor described by the trifocal tensor and fundamental matrix, and also show how to recover projection matrices from the quadrifocal tensor. We also describe the form of the 51 non-linear constraints a quadrifocal tensor must adhere to.