Affine 3-D Reconstruction from Two Projective Images of Independently Translating Planes
Lior Wolf and Amnon Shashua
School of Computer Science and Engineering,
The Hebrew University,
Jerusalem 91904, Israel
Consider two views of a multi-body scene consisting of $k$ planar
bodies moving in pure translation one relative to the other. We show
that the fundamental matrices, one per body, live in a 3-dimensional
subspace, which when represented as a step-3 extensor is the common
transversal on the collection of extensors defined by the homography
matrices $H_1,...,H_k$ of the moving planes.
We show that as much as five bodies are necessary for recovering the
common transversal from the homography matrices, from which we show
how to recover the fundamental matrices and the affine calibration
between the two cameras.