Issue No. 02 - February (2002 vol. 24)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/34.982901
<p><b>Abstract</b>—The image motion of a planar surface between two camera views is captured by a homography (a <tmath>2D</tmath> projective transformation). The homography depends on the intrinsic and extrinsic camera parameters, as well as on the <tmath>3D</tmath> plane parameters. While camera parameters vary across different views, the plane geometry remains the same. Based on this fact, we derive <it>linear</it> subspace constraints on the relative homographies of multiple (<tmath>\geq 2</tmath>) planes across multiple views. The paper has three main contributions: 1) We show that the collection of all relative homographies (homologies) of a <it>pair of planes</it> across <it>multiple views</it>, spans a 4-dimensional linear subspace. 2) We show how this constraint can be extended to the case of <it>multiple planes</it> across <it>multiple views</it>. 3) We show that, for some restricted cases of camera motion, linear subspace constraints apply also to the set of homographies of a <it>single plane</it> across multiple views. All the results derived in this paper are true for uncalibrated cameras. The possible utility of these multiview constraints for improving homography estimation and for detecting nonrigid motions are also discussed.</p>
Homographies, homologies, motion estimation, multiview analysis.
M. Irani and L. Zelnik-Manor, "Multiview Constraints on Homographies," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 24, no. , pp. 214-223, 2002.