D. Sinclair, H. Christensen, and C. Rothwell, "Using the Relation Between a Plane Projectivity and the Fundamental Matrx," SCIA, pp. 181-188, 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....apply also to the homographies of a single plane across multiple views (Section 6) Different video related applications can benefit from such multiview constraints. For example, many algorithms based on planar homographies (e.g. 18] 21] 11] 28] 17] or on planar homologies (e.g. [23], 4] rely on accurate precomputation of these homographies (or homologies) However, the image region corresponding to a planar surface may be small. In such cases, the homography estimation tends to be highly inaccurate [25] i.e. when applied to small image regions) Adding the multiview ....

....the homography of 7r, yields a relative homography : H f = A) A. 6) This relative homography captures the induced relative image motion between the two planes and is a plane homology [20] Some properties and invariants of planar homologies have been discussed in [8] and used in [17] 4] [23]. Here, we present a different set of constraints on homologies. Using (5) and the Sherman Morisson formula 2 [19] it can be shown that, for rigidly moving planes 7r. and 7rp, the matrix H.f has the form H . I 7frh 1 h h2 ha ] h4 1 d h 5 h e , h7 h8 1 d h9 1. The superscripts ....

D. Sinclair, H. Christensen, and C. Rothwell, "Using the Relation Between a Plane Projectivity and the Fundamental Matrx," SCIA, pp. 181-188, 1996.

....we have one stereo view of two (or more) planes, and we can therefore compute the epipolar geometry, using for example, Pritchett s method [15] see 2. 5) The fundamental matrix can be computed from any left right plane induced homography Hlr and the epipole e, as F [Hlirie ] X HI r [17]. Projective camera matrices can be computed from F and scene structure generated by backprojection. Unsurprisingly, experiments show that the structure generated by this method is of reasonable quality as long as the rotations are as large as possible. Naturally we can also backproject the ....

D. Sinclair, H. Christensen, and C. Rothwell. Using the relation between a plane projectivity and the fundamental matrix. In Proc. Scandinavian Image Analysis Conf., 1995.

....two T matrices to give calibration and head geometry [5] Calculating the epipolar geometry in step 3 can be done by explicit use of the combined feature data. However, methods exist for calculating structure for piecewise planar scenes (as in the combined view) using the planar homographies I I [7, 8]. This is more accurate since planarity is then being enforced. Once we have image relationships between all images in a set of four (left and right, before and after a motion) we no longer need real image data. We can choose any set of points in one image and find their matches in the others ....

D. Sinclair, H. Christensen, and C. Rothwell. Using the relation between a plane projectivity and the fundamental matrix. In Proc. Scandinavian Image Analysis Conf , 1995.

.... ) 2 M 100 01 M 000 00 M 000 01 M 100 00 M 020 10 2M 010 10 M 100 00 M 000 01 M 010 00 9 = 2 (M 000 00 ) 4 M 200 00 M 000 00 (M 100 00 ) 2 M 020 00 M 000 00 (M 010 00 ) 2 2 inv[11] D 2GB 12 (similar) inv[12] = D 2BR 12 (similar) inv[13] D 3RG 12 = 8 : M 000 00 ) 2 M 010 10 M 200 01 M 000 00 M 010 10 M 000 01 M 200 00 2M 000 00 M 100 01 M 100 00 M 010 10 2M 000 01 (M 100 00 ) 2 M 010 10 M 000 00 M 000 10 M 010 00 M ....

....1 and H 2 , belonging to planes 1 and 2 respectively. Combining them as H 1 1 H 2 yields a planar homology, whose eigenanalysis reveals one fixed point (the epipole) and one line of fixed points (the common line of the planes 1 and 2 ) This line of fixed points is used by Sinclair et al. [12] to test whether two rigid planar motions are compatible. They project this common line to the other image using H 1 , and once again using H 2 . If the two planes are indeed in rigid motion, the two resulting lines in the second image should coincide, which can easily be checked. The geometric ....

D. Sinclair, H. Christensen, C. Rothwell. Using the Relation between a Plane Projectivity and the Fundamental Matrix, Proc. SCIA, pp. 181-188, 1995.

....a planar feature in a sequence of images, the analysis of the sequence can be reduced to the case of a purely translating camera. The planar curve is regarded as a curve on the plane at infinity. Thus it has no apparent image motion. This simplification has been used in (Heyden and Astrom 1995, Sinclair, Christiansenn and Rothwell 1995). It is known as projective reduction, which is a generalisation of the plane plus parallax method. This is illustrated in Figure 15. Only the direction of motion Deltac needs to be estimated. The sphere of possible directions can then be tessellated and the error function g can be calculated ....

Sinclair, D., Christiansenn, H. and Rothwell, C.: 1995, Using the relation between a plane projectivity and the fundamental matrix, Proc. 9th Scandinavian Conference on Image Analysis, pp. 181--188.

.... A planar homology H has two equal eigenvalues. The corresponding eigenvectors define the line of fixed points. The eigenvector corresponding to the non degenerate eigenvalue is the epipole in this case. The action of the homology is shown in figure 5. The fundamental matrix is computed as (see [19]) F = H i e] Theta H i for i = A or B (1) 4.2 Using planes to compute the trifocal tensor Similarly, the trifocal tensor can be estimated from two planes which induce homographies over three views. Denote these homographies by H A 12 , H B 12 , between the first and second views, and H A ....

D. Sinclair, H. Christensen, and C. Rothwell. Using the relation between a plane projectivity and the fundamental matrix. SCIA, 1995.

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