AbstractÐThe image motion of a planar surface between two camera views is captured bya homography(a 2D projective transformation). The homographydepends on the intrinsic and extrinsic camera parameters, as well as on the 3D plane parameters. While camera parameters varyacross different views, the plane geometryremains the same. Based on this fact, we derive linear subspace constraints on the relative homographies of multiple ( 2) planes across multiple views. The paper has three main contributions: 1) We show that the collection of all relative homographies (homologies) of a pair of planes across multiple views, spans a 4-dimensional linear subspace. 2) We show how this constraint can be extended to the case of multiple planes across multiple views. 3) We show that, for some restricted cases of camera motion, linear subspace constraints applyalso to the set of homographies of a single plane across multiple views. All the results derived in this paper are true for uncalibrated cameras. The possible utilityof these multiview constraints for improving homographyestimation and for detecting nonrigid motions are also discussed. Index TermsÐHomographies, homologies, motion estimation, multiview analysis.
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