Motion and Structure from Orthographic Projections
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image and Vision Computing - Special issue: frequency increase for 1991
Structure-from-motion under orthographic projection
ECCV 90 Proceedings of the first european conference on Computer vision
Finding point correspondences and determining motion of rigid object from two weak perspective views
Computer Vision, Graphics, and Image Processing
Space and Time Bounds on Indexing 3D Models from 2D Images
IEEE Transactions on Pattern Analysis and Machine Intelligence - Special issue on interpretation of 3-D scenes—part I
Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
Model-based invariants for 3-D vision
International Journal of Computer Vision
3D motion recovery via affine epipolar geometry
International Journal of Computer Vision
International Journal of Computer Vision
Rigidity Checking of 3D Point Correspondences Under Perspective Projection
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Paraperspective Factorization Method for Shape and Motion Recovery
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Geometric Interpretation of Weak-Perspective Motion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Generalization to Novel Views: Universal, Class-based, andModel-based Processing
International Journal of Computer Vision
Limitations of Non Model-Based Recognition Schemes
Limitations of Non Model-Based Recognition Schemes
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In an earlier work by B. M. Bennett et al. (J. Opt. Soc. Amer. A 6, 1989, 1052-1069), an algebraic condition for four point pairs in two images to be projections from a rigid object was proposed. The condition was derived under the assumption that the images are projected orthographically from exactly the same viewing distance. This paper presents how the condition can be generalized for a more general viewing geometry: the two images are projected from different viewing distances and even under independent paraperspective projections. It turns out the generalized rigidity condition becomes a determination of the ratio of the cameras' viewing distances. The ratio depends only on the spatial relationships between the two viewpoints and the observed object, not on the choice of correspondences over the object. It is thus an invariant and can be helpful toward solving the correspondence problem in multiview vision cues including those based on motion and stereo parallax. This paper also shows how the rigidity condition is related to the well-known epipolar condition. Empirical studies and real image experiments are shown to illustrate the validity of the results.