Lines and Points in Three Views and the Trifocal Tensor
International Journal of Computer Vision
Image-based view synthesis by combining trilinear tensors and learning techniques
VRST '97 Proceedings of the ACM symposium on Virtual reality software and technology
Dual Computation of Projective Shape and Camera Positions from Multiple Images
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
Reduced Multilinear Constraints: Theory and Experiments
International Journal of Computer Vision
3D Photography Using Shadows in Dual-Space Geometry
International Journal of Computer Vision
Model-Based Brightness Constraints: On Direct Estimation of Structure and Motion
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Linear Algorithm for Computing the Homography from Conics in Correspondence
Journal of Mathematical Imaging and Vision
Minimal Projective Reconstruction Including Missing Data
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Geometric Approach for the Theory and Applications of 3D Projective Invariants
Journal of Mathematical Imaging and Vision
Novel View Synthesis by Cascading Trilinear Tensors
IEEE Transactions on Visualization and Computer Graphics
A Minimal Set of Constraints for the Trivocal Tensor
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part I
On the Reprojection of 3D and 2D Scenes Without Explicit Model Selection
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part I
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part I
On the Structure and Properties of the Quadrifocal Tensor
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part I
Plane+Parallax, Tensors and Factorization
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part I
On Calibration and Reconstruction from Planar Curves
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part I
Tensor Embedding of the Fundamental Matrix
SMILE'98 Proceedings of the European Workshop on 3D Structure from Multiple Images of Large-Scale Environments
Revisiting Single-View Shape Tensors: Theory and Applications
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Shape tensors for efficient and learnable indexing
VSR '95 Proceedings of the IEEE Workshop on Representation of Visual Scenes
Duality of reconstruction and positioning from projective views
VSR '95 Proceedings of the IEEE Workshop on Representation of Visual Scenes
Video Augmentation by Image-Based Rendering Under the Perspective Camera Model
ICPR '98 Proceedings of the 14th International Conference on Pattern Recognition-Volume 2 - Volume 2
A 3D Shape Constraint on Video
IEEE Transactions on Pattern Analysis and Machine Intelligence
A matter of notation: Several uses of the Kronecker product in 3D computer vision
Pattern Recognition Letters
Multiple View Geometry under Projective Projection in Space-Time
IEICE - Transactions on Information and Systems
Virtual view specification and synthesis for free viewpoint television
IEEE Transactions on Circuits and Systems for Video Technology
Geometric and radiometric modeling of 3D scenes
ICME'09 Proceedings of the 2009 IEEE international conference on Multimedia and Expo
Visual control through the trifocal tensor for nonholonomic robots
Robotics and Autonomous Systems
Point matching constraints in two and three views
Proceedings of the 29th DAGM conference on Pattern recognition
Single-view matching constraints
ISVC'07 Proceedings of the 3rd international conference on Advances in visual computing - Volume Part II
PSIVT'07 Proceedings of the 2nd Pacific Rim conference on Advances in image and video technology
Predicting corresponding region in a third view using discrete epipolar lines
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Multiple view geometry in the space-time
ACCV'06 Proceedings of the 7th Asian conference on Computer Vision - Volume Part II
A survey of methods for volumetric scene reconstruction from photographs
VG'01 Proceedings of the 2001 Eurographics conference on Volume Graphics
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It has been established that certain trilinear forms of three perspective views give rise to a tensor of 27 intrinsic coefficients. We show in this paper that a permutation of the the trilinear coefficients produces three homography matrices (projective transformations of planes) of three distinct intrinsic planes, respectively. This, in turn, yields the result that 3D invariants are recovered directly-simply by appropriate arrangement of the tensor's coefficients. On a secondary level, we show new relations between fundamental matrix, epipoles, Euclidean structure and the trilinear tensor. On the practical side, the new results extend the existing envelope of methods of 3D recovery from 2D views-for example, new linear methods that cut through the epipolar geometry, and new methods for computing epipolar geometry using redundancy available across many views.