Motion and Structure from Orthographic Projections
IEEE Transactions on Pattern Analysis and Machine Intelligence
Motion from point matches: multiple of solutions
International Journal of Computer Vision
Finding point correspondences and determining motion of rigid object from two weak perspective views
Computer Vision, Graphics, and Image Processing
International Journal of Computer Vision
A theory of self-calibration of a moving camera
International Journal of Computer Vision
Invariants of Six Points and Projective Reconstruction From Three Uncalibrated Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Uniqueness of Solutions to Three Perspective Views of Four Points
IEEE Transactions on Pattern Analysis and Machine Intelligence
3D motion recovery via affine epipolar geometry
International Journal of Computer Vision
Dual Computation of Projective Shape and Camera Positions from Multiple Images
International Journal of Computer Vision
Reconstruction from Calibrated Cameras—A New Proof of the Kruppa-Demazure Theorem
Journal of Mathematical Imaging and Vision
Algebraic Functions For Recognition
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
Four Points in Two or Three Calibrated Views: Theory and Practice
International Journal of Computer Vision
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Methods for reconstruction and camera estimation from miminal data are often used to boot-strap robust (RANSAC and LMS) and optimal (bundle adjustment) structure and motion estimates. Minimal methods are known for projective reconstruction from two or more uncalibrated images, and for "5 point" relative orientation and Euclidean reconstruction from two calibrated parameters, but we know of no efficient minimal method for three or more calibrated cameras except the uniqueness proof by Holt and Netravali. We reformulate the problem of Euclidean reconstruction from minimal data of four points in three or more calibrated images, and develop a random rational simulation method to show some new results on this problem. In addition to an alternative proof of the uniqueness of the solutions in general cases, we further show that unknown coplanar configurations are not singular, but the true solution is a double root. The solution from a known coplanar configuration is also generally unique. Some especially symmetric point-camera configurations lead to multiple solutions, but only symmetry of points or the cameras gives a unique solution.