Relative Viewing Distance: A Correspondence Invariance under Paraperspective Projection

In an earlier work by B. M. Bennett et al. (J. Opt. Soc. Amer. A6, 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 camerasʹ 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.