Structure from motion using line correspondences
International Journal of Computer Vision
A theory of self-calibration of a moving camera
International Journal of Computer Vision
A theory of the motion fields of curves
International Journal of Computer Vision
Canonic representations for the geometries of multiple projective views
ECCV '94 Proceedings of the third European conference on Computer vision (vol. 1)
Conic Reconstruction and Correspondence From Two Views
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
The Quadric Reference Surface: Theory and Applications
International Journal of Computer Vision
In Defense of the Eight-Point Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
Characterizing the uncertainty of the fundamental matrix
Computer Vision and Image Understanding
Motion Estimation in Image Sequences Using the Deformation of Apparent Contours
IEEE Transactions on Pattern Analysis and Machine Intelligence
Comparing Images Using the Hausdorff Distance
IEEE Transactions on Pattern Analysis and Machine Intelligence
Algebraic Functions For Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Generalised Epipolar Constraints
ECCV '96 Proceedings of the 4th European Conference on Computer Vision-Volume II - Volume II
The Geometry and Matching of Curves in Multiple Views
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume I - Volume I
Computing Structure and Motion of General 3D Curves from Monocular Sequences of Perspective Images
ECCV '96 Proceedings of the 4th European Conference on Computer Vision-Volume II - Volume II
Trilinearity of three perspective views and its associated tensor
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Ellipsoid Reconstruction from Three Perspective Views
ICPR '96 Proceedings of the 1996 International Conference on Pattern Recognition (ICPR '96) Volume I - Volume 7270
Using Conic Correspondences in Two Images to Estimate the Epipolar Geometry
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Quadric Reconstruction from Dual-Space Geometry
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Relative Pose Estimation from Two Circles
Proceedings of the 30th DAGM symposium on Pattern Recognition
Projective reconstruction of general 3D planar curves from uncalibrated cameras
ISVC'10 Proceedings of the 6th international conference on Advances in visual computing - Volume Part II
Ellipse constraints for improved wide-baseline feature matching and reconstruction
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
Affine epipolar direction from two views of a planar contour
ACIVS'06 Proceedings of the 8th international conference on Advanced Concepts For Intelligent Vision Systems
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We describe in this paper closed-form solutions to the following problems in multi-view geometry of n'th order curves: (i) recovery of the fundamental matrix from 4 or more conic matches in two views, (ii) recovery of the homography matrix from a single n'th order (n ≥ 3) matching curve and, in turn, recovery of the fundamental matrix from two matching n'th order planar curves, and (iii) 3D reconstruction of a planar algebraic curve from two views. Although some of these problems, notably (i) and (iii), were introduced in the past [15,3], our derivations are analytic with resulting closed form solutions. We have also conducted synthetic experiments on (i) and real image experiments on (ii) and (iii) with subpixel performance levels, thus demonstrating the practical use of our results.