Affine 3-D reconstruction from two projective images of independently translating planes

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 H₁,...,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.