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
Lines and Points in Three Views and the Trifocal Tensor
International Journal of Computer Vision
Algebraic Functions For Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Threading Fundamental Matrices
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume I - Volume I
A New Characterization of the Trifocal 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
Tensor Embedding of the Fundamental Matrix
SMILE'98 Proceedings of the European Workshop on 3D Structure from Multiple Images of Large-Scale Environments
A linear method for reconstruction from lines and points
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
Balanced Recovery of 3D Structure and Camera Motion from Uncalibrated Image Sequences
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Revisiting Single-View Shape Tensors: Theory and Applications
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
The Key to Three-View Geometry
International Journal of Computer Vision
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In this paper we derive a minimal set of sufficient constraints in order for 27 numbers to constitute a trifocal tensor. It is shown that, in general, eight nonlinear algebraic constraints are enough.This result is in accordance with the theoretically expected number of eight independent constraints and novel since the to date known sets of sufficient constraints contain at least 12 conditions. Up to now, research and formulation of constraints for the trifocal tensor has concentrated mainly on the correlation slices and has produced sets of constraints that are neither minimal (≥ 12) nor independent. We show that by turning attention from correlation to homographic slices, simple geometric considerations yield the desired result. Having the minimal set of constraints is important for constrained estimation of the tensor, as well as for deepening the understanding of the multiple view relations that are valid in the projective framework.