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.