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
New Geometric Methods for Computer Vision: An Application toStructure and Motion Estimation
International Journal of Computer Vision
Determining the Epipolar Geometry and its Uncertainty: A Review
International Journal of Computer Vision
Continuous Time Matching Constraints for Image Streams
International Journal of Computer Vision
Ambiguity in Structure from Motion: Sphere versus Plane
International Journal of Computer Vision
Dual Computation of Projective Shape and Camera Positions from Multiple Images
International Journal of Computer Vision
Reduced Multilinear Constraints: Theory and Experiments
International Journal of Computer Vision
Minimal Decomposition of Model-Based Invariants
Journal of Mathematical Imaging and Vision
Trajectory Triangulation: 3D Reconstruction of Moving Points from a Monocular Image Sequence
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Two-Way Ambiguity in 2D Projective Reconstruction from Three Uncalibrated 1D Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision - Marr Prize Special Issue
Tracking While Zooming Using Affine Transfer and Multifocal Tensors
International Journal of Computer Vision
Novel View Synthesis by Cascading Trilinear Tensors
IEEE Transactions on Visualization and Computer Graphics
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
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
Tensor Embedding of the Fundamental Matrix
SMILE'98 Proceedings of the European Workshop on 3D Structure from Multiple Images of Large-Scale Environments
Geometry of Multiple Affine Views
SMILE'98 Proceedings of the European Workshop on 3D Structure from Multiple Images of Large-Scale Environments
Trifocal Tensors with Grassmann-Cayley Algebra
RobVis '01 Proceedings of the International Workshop on Robot Vision
Some Applications of Clifford Algebra to Geometries
ADG '98 Proceedings of the Second International Workshop on Automated Deduction in Geometry
Revisiting Single-View Shape Tensors: Theory and Applications
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Random Sampling and Voting Method for Three-Dimensional Reconstruction
RobVis '01 Proceedings of the International Workshop on Robot Vision
A New Linear Method for Euclidean Motion/Structure from Three Calibrated Affine Views
CVPR '98 Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
About the correspondences of points between N image
VSR '95 Proceedings of the IEEE Workshop on Representation of Visual Scenes
A canonical framework for sequences of images
VSR '95 Proceedings of the IEEE Workshop on Representation of Visual Scenes
The 3D Line Motion Matrix and Alignment of Line Reconstructions
International Journal of Computer Vision
Rank Conditions on the Multiple-View Matrix
International Journal of Computer Vision
Reconstructing camera projection matrices from multiple pairwise overlapping views
Computer Vision and Image Understanding
Recovering Multiple View Geometry from Mutual Projections of Multiple Cameras
International Journal of Computer Vision
Structure-from-motion using lines: representation, triangulation, and bundle adjustment
Computer Vision and Image Understanding
Multiple View Geometry under Projective Projection in Space-Time
IEICE - Transactions on Information and Systems
Structure-from-motion using lines: Representation, triangulation, and bundle adjustment
Computer Vision and Image Understanding
Reconstructing camera projection matrices from multiple pairwise overlapping views
Computer Vision and Image Understanding
Geometric Algebra: A Powerful Tool for Solving Geometric Problems in Visual Computing
SIBGRAPI-TUTORIALS '09 Proceedings of the 2009 Tutorials of the XXII Brazilian Symposium on Computer Graphics and Image Processing
Real-time Quadrifocal Visual Odometry
International Journal of Robotics Research
Lines as the fundamental unit of vision
Proceedings of the 11th international conference on Theoretical foundations of computer vision
Simplified vehicle calibration using multilinear constraints
SCIA'03 Proceedings of the 13th Scandinavian conference on Image analysis
Multiple view geometry for non-rigid motions viewed from translational cameras
ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part II
Single-view matching constraints
ISVC'07 Proceedings of the 3rd international conference on Advances in visual computing - Volume Part II
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
Camera Models and Fundamental Concepts Used in Geometric Computer Vision
Foundations and Trends® in Computer Graphics and Vision
Motion from 3D line correspondences: linear and non-linear solutions
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Line reconstruction from many perspective images by factorization
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Tensor algebra: a combinatorial approach to the projective geometry of figures
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Multiple view geometry in the space-time
ACCV'06 Proceedings of the 7th Asian conference on Computer Vision - Volume Part II
Simultaneous Camera Pose and Correspondence Estimation with Motion Coherence
International Journal of Computer Vision
Relative bundle adjustment based on trifocal constraints
ECCV'10 Proceedings of the 11th European conference on Trends and Topics in Computer Vision - Volume Part II
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We explore the geometric and algebraic relations that exist between correspondences of points and lines in an arbitrary number of images. We propose to use the formalism of the Grassmann-Cayley algebra as the simplest way to make both geometric and algebraic statements in a very synthetic and effective way (i.e. allowing actual computation if needed). We have a fairly complete picture of the situation in the case of points; there are only three types of algebraic relations which are satisfied by the coordinates of the images of a 3-D point: bilinear relations arising when we consider pairs of images among the N and which are the well-known epipolar constraints, trilinear relations arising when we consider triples of images among the N, and quadrilinear relations arising when we consider four-tuples of images among the N. In the case of lines, we show how the traditional perspective projection equation can be suitably generalized and that in the case of three images there exist two independent trilinear relations between the coordinates of the images of a 3-D line.