Multiview constraints on homographies
Zeinik-Manor, L.; Irani, M.
Pattern Analysis and Machine Intelligence, IEEE Transactions on
Volume 24, Issue 2, Feb 2002 Page(s):214 - 223
Digital Object Identifier 10.1109/34.982901
Summary:The image motion of a planar surface between two camera views is
captured by a homography (a 2D projective transformation). The
homography depends on the intrinsic and extrinsic camera 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, 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 apply also to the set of homographies of a single
plane across multiple views. All the results derived are true for
uncalibrated cameras. The possible utility of these multiview
constraints for improving homography estimation and for detecting
nonrigid motions are also discussed
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