Multi-view subspace constraints on homographies

The motion of a planar surface between two camera views induces a homography. The homography depends on the camera intrinsic and extrinsic parameters, as well as on the 3D plane parameters. While camera parameters vary across different views, the plane geometry remains the same. Based on this fact, the paper derives linear subspace constraints on the relative motion of multiple (⩾2) planes across multiple views. The paper has three main contributions. It shows that the collection of all relative homographies of a pair of planes (homologies) across multiple views, spans a 4-dimensional linear subspace. It shows how this constraint can be extended to the case of multiple planes across multiple views. It suggests two potential application areas which can benefit from these constraints: the accuracy of homography estimation can be improved by enforcing the multi-view subspace constraints; and violations of these multi-view constraints can be used as a cue for moving object detection. All the results derived in this paper are true for uncalibrated cameras