Numerical continuation methods: an introduction
Numerical continuation methods: an introduction
A theory of self-calibration of a moving camera
International Journal of Computer Vision
Three-dimensional computer vision: a geometric viewpoint
Three-dimensional computer vision: a geometric viewpoint
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
The Quadric Reference Surface: Theory and Applications
International Journal of Computer Vision
Motion Estimation in Image Sequences Using the Deformation of Apparent Contours
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiple view geometry in computer visiond
Multiple view geometry in computer visiond
The Geometry of Multiple Images: The Laws That Govern The Formation of Images of A Scene and Some of Their Applications
Comparing Images Using the Hausdorff Distance
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
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
A Singular Introduction to Commutative Algebra
A Singular Introduction to Commutative Algebra
Projective reconstruction of ellipses from multiple images
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
Feature correspondences from multiple views of coplanar ellipses
ISVC'06 Proceedings of the Second international conference on Advances in Visual Computing - Volume Part II
High-Order differential geometry of curves for multiview reconstruction and matching
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Linear pose estimate from corresponding conics
Pattern Recognition
Camera pose estimation using first-order curve differential geometry
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part IV
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We introduce a number of new results in the context of multi-view geometry from general algebraic curves. We start with the recovery of camera geometry from matching curves. We first show how one can compute, without any knowledge on the camera, the homography induced by a single planar curve. Then we continue with the derivation of the extended Kruppa's equations which are responsible for describing the epipolar constraint of two projections of a general algebraic curve. As part of the derivation of those constraints we address the issue of dimension analysis and as a result establish the minimal number of algebraic curves required for a solution of the epipolar geometry as a function of their degree and genus.We then establish new results on the reconstruction of general algebraic curves from multiple views. We address three different representations of curves: (i) the regular point representation in which we show that the reconstruction from two views of a curve of degree d admits two solutions, one of degree d and the other of degree d(d − 1). Moreover using this representation, we address the problem of homography recovery for planar curves, (ii) dual space representation (tangents) for which we derive a lower bound for the number of views necessary for reconstruction as a function of the curve degree and genus, and (iii) a new representation (to computer vision) based on the set of lines meeting the curve which does not require any curve fitting in image space, for which we also derive lower bounds for the number of views necessary for reconstruction as a function of curve degree alone.