Showing papers by "Shai Avidan published in 1996"

The Rank 4 Constraint in Multiple (>=3) View Geometry

Abstract: It has been established that certain trilinear froms of three perspective views give rise to a tensor of 27 intrinsic coefficients [8]. Further investigations have shown the existence of quadlinear forms across four views with the negative result that further views would not add any new constraints [3, 12, 5]. We show in this paper first general results on any number of views. Rather than seeking new constraints (which we know now is not possible) we seek connections across trilinear tensors of triplets of views. Two main results are shown: (i) trilinear tensors across m>3 views are embedded in a low dimensional linear subspace, (ii) given two views, all the induced homography matrices are embedded in a four-dimensional linear subspace. The two results, separately and combined, offer new possibilities of handling the consistency across multiple views in a linear manner (via factorization), some of which are further detailed in this paper.

Robust recovery of camera rotation from three frames

Abstract: Computing camera rotation from image sequences can be used for image stabilization, and when the camera rotation is known the computation of translation and scene structure are much simplified as well. A robust approach for recovering camera rotation is presented, which does not assume any specific scene structure (e.g. no planar surface is required), and which avoids prior computation of the epipole. Given two images taken from two different viewing positions, the rotation matrix between the images can be computed from any three homography matrices. The homographies are computed using the trilinear tensor which describes the relations between the projections of a 3D point into three images. The entire computation is linear for small angles, and is therefore fast and stable. Iterating the linear computation can then be used to recover larger rotations as well.