Robust egomotion estimation from affine motion parallax
ECCV '94 Proceedings of the third European conference on Computer vision (vol. 1)
International Journal of Computer Vision
Euclidean Shape and Motion from Multiple Perspective Views by Affine Iterations
IEEE Transactions on Pattern Analysis and Machine Intelligence
What can be seen in three dimensions with an uncalibrated stereo rig
ECCV '92 Proceedings of the Second European Conference on Computer Vision
Reliable Extraction of the Camera Motion using Constraints on the Epipole
ECCV '96 Proceedings of the 4th European Conference on Computer Vision-Volume II - Volume II
The Rank 4 Constraint in Multiple (=3) View Geometry
ECCV '96 Proceedings of the 4th European Conference on Computer Vision-Volume II - Volume II
A Paraperspective Factorization Method for Shape and Motion Recovery
ECCV '94 Proceedings of the Third European Conference-Volume II on Computer Vision - Volume II
Recursive Structure and Motion from Image Sequences using Shape and Depth Spaces
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
Matching constraints and the joint image
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Efficient Suboptimal Solutions to the Optimal Triangulation
International Journal of Computer Vision
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The fundamental matrix defines a nonlinear 3D variety in the joint image space of multiple projective (or "uncalibrated perspective") images. We show that, in the case of two images, this variety is a 4D cone whose vertex is the joint epipole (namely the 4D point obtained by stacking the two epipoles in the two images). Affine (or "para-perspective") projection approximates this nonlinear variety with a linear subspace, both in two views and in multiple views. We also show that the tangent to the projective joint image at any point on that image is obtained by using local affine projection approximations around the corresponding 3D point. We use these observations to develop a new approach for recovering multiview geometry by integrating multiple local affine joint images into the global projective joint image. Given multiple projective images, the tangents to the projective joint image are computed using local affine approximations for multiple image patches. The affine parameters from different patches are combined to obtain the epipolar geometry of pairs of projective images. We describe two algorithms for this purpose, including one that directly recovers the image epipoles without recovering the fundamental matrix as an intermediate step.