J. Fang and T. Huang. Solving three-dimensional small-rotation motion equations. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pages 253--258, Washington, D.C., June 1983. Computer Society of the IEEE, IEEE Computer Society Press.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....# # # # 1 0 0 0 0 0 0 0 0 0 0 0 0 i i i i i i i i i i Z Y X Z f Z f Z f Z f Z f f y (3.1) 36 The ego motion of the camera is decomposed into a rotation about an axis passing through the origin, and a translation. Any three dimensional motion can be represented as such [20]. This is denoted as ( i i T , where indicates a composite operator. Given a point in three dimensional space, i i Z Y X , and a camera motion, i z y x z y x T T T , the new location of the point, 1 1 1 i i i Z Y X , is given by (3.2) This ....

Fang, J.-Q., and Huang, T.S., Solving Three Dimensional Small-Rotation Motion Equation, IEEE Conference on Computer Vision and Pattern Recognition, pp. 253258, 1983.

....the homographies of a single plane can be derived when rotation is also introduced, but is restricted to small angles. This, however, increases the dimensionality from 4 to 7 (but is still smaller than 9) The small camera rotation assumption implies that the rotation matrix R of (3) has the form [5] Fig. 1. A quantitative comparison of homology estimation with and without enforcing the multiview subspace constraint of (11) a) Shows the image (of floor tiles) from which the 19 frame sequence was synthetically generated with ground truth known homologies. The tracked feature points are ....

J.Q. Fang and T.S. Huang, "Solving Three-Dimensional SmallRotation Motion Equations," Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 253-258, 1983.

....essential task is the same to determine the motion parameters relating corresponding points on surfaces in adjacent views. This problem has a long history in the computer vision literature. Approaches have included the determination of point correspondences and analysis of point configurations [5, 19, 27, 46, 45, 8, 48, 42, 6, 30, 44, 7, 12, 11, 13, 25], the analysis of flow fields [33, 29, 47, 2, 35, 36, 43] and photometric methods [32, 31, 23, 1] The method chosen is a function of both the data and how they are M m x x N x T S X N x Figure 4: Local surface representation the augmented Darboux frame acquired. In our application ....

J. Fang and T. Huang. Solving three-dimensional small-rotation motion equations. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pages 253--258, Washington, D.C., June 1983. Computer Society of the IEEE, IEEE Computer Society Press.

....determination un der a wide variety of scene structures (especially in an outdoor environment) has remained elusive. Naturally, this has led to investigations into the reason for such failures. Algorithm specific errors have been explored by Tsai and Huang [9] Barron [10] and Fang and Huang [7]. General methodologies for computing the precision of 3 D Parameters in the case of translational motion have been explored by Snyder [11] Large shifts in the Focus of Expansion have been shown to occur in the case of approximate translational motion when small ro tations have been ignored ....

....point in terms of the motion parameters, camera focal length and image displacement at that point. Hence, to find the effect of small rotational errors on environmental depth we use equation (10) and take the partial deriva tive with respect to the rotation around the Y axis, 2 to get 4 [7,16]. Usually most derivations proceed by assuming f to be 1. For convenience of experimental verification we have not made this assumption. 4There would have been higher order terms in the expression on the right hand side of equation (13) if we had consid ered higher order terms in the expansion ....

J. Q. Fang and T.S. Huang. Solving three dimen- sional small-rotation motion equations. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pages 253-258, June 1983.

....that has been conducted on this problem, robust depth determination under a wide variety of scene structures has remained elusive. Naturally, this has led to investigations into the reason for such failures. However, most investigations have been either algorithm specific or qualitative in nature [4 8]. The present paper is an attempt to remedy this situa tion. We begin by stating the small rotation image displacement equations in the next section. 2 Depth from Image Displacement Figure I shows a right handed coordinate system fixed with respect to the camera. Let us also assume the right ....

J. Q. Fang and T.S. Huang. Solving three dimensional small- rotation motion equations. Proceedings of the IEEE Computer Society Conference on Computer Vision and Patter tecognition pages 253 258 June 1983.

....essential task is the same to determine the motion parameters relating corresponding points on surfaces in adjacent views. This problem has a long history in the computer vision literature. Approaches have included the determination of point correspondences and analysis of point configurations [5, 19, 27, 46, 45, 8, 48, 42, 6, 30, 44, 7, 12, 11, 13, 25], the analysis of flow fields [33, 29, 47, 2, 35, 36, 43] and photometric methods [32, 31, 23, 1] The method chosen is a function of both the data and how they are 4 M m x x N x T x p S X N x Figure 4: Local surface representation the augmented Darboux frame acquired. In our ....

J. Fang and T. Huang. Solving three-dimensional small-rotation motion equations. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pages 253--258, Washington, D.C., June 1983. Computer Society of the IEEE, IEEE Computer Society Press.

....essential task is the same to determine the motion parameters relating corresponding points on surfaces in adjacent views. This problem has a long history in the computer vision literature. Approaches have included the determination of point correspondences and analysis of point configurations [5, 19, 27, 46, 45, 8, 48, 42, 6, 30, 44, 7, 12, 11, 13, 25], the analysis of flow fields [33, 29, 47, 2, 35, 36, 43] and photometric methods [32, 31, 23, 1] The method chosen is a function of both the data and how they are M m x x N x T x p S X N x Figure 4: Local surface representation the augmented Darboux frame acquired. In our application ....

J. Fang and T. Huang. Solving three-dimensional small-rotation motion equations. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pages 253--258, Washington, D.C., June 1983. Computer Society of the IEEE, IEEE Computer Society Press.

....of point or feature correspondences between two or more perspective views for determining structure 1 This research has been supported by the Defense Advanced Reseach Projects Agency under Army ETL contract DACA7689 C 0017 and the National Science Foundation CER grant number NSF CDA 8922572. [5, 6, 7, 8, 9, 10, 11, 12, 13]. These correspondence based approaches take advantage of the image displacements induced by egomotion. Most such methods match a large number of points or features in two temporally separated images and quantitatively measure the image displacements. A consistent set of motion parameters is ....

....determination under a wide variety of scene structures (especially in an outdoor environment) has remained elusive. Naturally, this has led to investigations into the reason for such failures. Algorithm specific errors have been explored by Tsai and Huang [14] Barron [15] and Fang and Huang [12]. General methodologies for computing the extent of precision of 3 D Parameters in the case of translational motion have been explored by Snyder [16] Large shifts in the Focus of Expansion have been shown to occur in the case of approximate translational motion when small rotations have been ....

J. Q. Fang and T.S. Huang. Solving three dimensional small-rotation motion equations. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pages 253--258, June 1983.

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J. Fang and T. Huang. Solving three-dimensional small-rotation motion equations. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pages 253--258, Washington, D.C., June 1983. Computer Society of the IEEE, IEEE Computer Society Press.

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