R. Y. Tsai and T. S. Huang, "Estimating Three-Dimensional Motion Parameters of a Rigid Planar Patch I," IEEE Trans. Accoust., Speech, and Sig. Proc., vol. ASSP(29), pp. 1147--1152, December 1981.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....identical anyway. The research elds concerned with these issues are among others object tracking [25] feature or token tracking [3] 13] 27] 38] and optical ow or motion estimation [12] 19] Applications range from surveillance [20] 30] 36] motion analysis, and structure from motion [31] [32] 35] 37] to (multi )target tracking [11] 21] 24] Here, we restrict ourselves to the case that for some reason the objects have indeed an identical appearance, which leaves us with the positional information as sole feature for identi cation. Therefore, the objects are simply referred ....

R.Y. Tsai and T.S. Huang. Estimating three dimensional motion parameters of a rigid planar patch, III: Finite point correspondences and the three view problem. IEEE Transactions on Acoustics, Speech, and Signal Processing, 32:213-220, 1984.

....plane at infinity invariant. For any given plane Pi of P , and any pair of cameras, there is a 3 Theta 3 matrix H Pi such that images of points of the plane are related by the projective linear relation: m = H Pi m. This matrix is invertible in the general case, and has the expression [12]: H Pi = A (R d tn )A (4) where n is the normal vector of the plane and d the distance to the origin. The limit as d 1 for this expression is H1 , the homography of the plane Pi 1 , the infinity homography. The matrix H1 is proportional to Q = A , and hence depends only on ....

R.Y. Tsai and T.S. Huang. Estimating Three-dimensional motion parameters of a rigid planar patch, II: singular value decomposition. IEEE Transactions on Acoustic, Speech and Signal Processing, 30, 1982.

....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 surfaces are assumed to be piecewise smooth, hence ....

R. Tsai and T. Huang. Estimating three-dimensional motion parameters of a rigid planar patch. IEEE Transactions on Acoustics, Speech, and Signal Processing, ASSP30: 525--534, Aug. 1982.

....the planar structure and relative camera locations may be recovered up to a two fold ambiguity, and that an additional camera resolves the ambiguity. The mathematical foundations of planar structure and motion recovery from image point correspondences were initially presented by Tsai and Huang in [13] and further developed by Weng, Ahuja, and Huang in [14] The latter work thoroughly develops the recovery of two possible solutions for the camera locations and plane parameters from two cameras and the recovery of a unique, closed form solution when three cameras are available. In our setting, ....

....2. Let ( n,d) be the parameters of # in the coordinate frame of camera 1, i.e. n X = d for all points X #. Following the convention in [3] express (R, t) the 3D rotation and translation of camera 1 with respect to camera 2, in the coordinate frame of camera 2. Tsai and Huang showed in [13] that the homography H may be decomposed as = M 2 (dR t n )M 1 1 . 2) Furthermore, they showed that given H, M 1 ,andM 2 , in general it is possible to recover two physically plausible solutions for (R, t, n,d) up to a scale factor. Finally, they showed in [12] that three cameras can ....

R.Y. Tsai and T.S. Huang. Estimating three-dimensional motion parameters of a rigid planar patch, ii: Singular value decomposition. IEEE Transaction on Acoustics, Speech, and Signal Processing, 30(4):525--534, August 1982. 21

....by supposing that the scene points visible in only one of the images lie on a planar surface. Consider a scene point P that is visible 0 at w 0 but is not visible in 1 . We compute an estimate w 1 that is the image of w 0 under the projective transformation induced by the planar surface [21]. Then (w 0 , w 1 ) can be treated as a correspondence, and the projection w s of P in s can be estimated as w s = 1 s)G(w 0 ) sH( w 1 ) However, in this case we should only use the color of the point in the image where it is visiblethat is, s (w s ) 0 (w 0 ) We take a similar ....

R.Y. Tsai and T.S. Huang. Estimating the Three-Dimensional Motion Parameters of a Rigid Planar Patch. IEEE Trans. ASSP, vol. 25, no. 6, pp. 1147--1152, December 1981.

....Let P be at the intersection of the ray OP with .Then P P M T . Since n P = d , wehave: P P . Since the term in parentheses describes the homographydueto,wehave which is the generalization of the classical motion of planes in the calibrated case [9, 43]. For the point P wehave: z RMp ; p) d ; n P ) zd p P 0 0 0 p p P 0 Figure 2: Affine structure under parallel projection is dp=do . This can be seen from the similarity of trapezoids followed by the similarity of triangles: 0 ; p ; p ....

....Euclidean structure and projective structure. The homography A due to the plane was described as a product of the rigid camera motion parameters, the parameters of , and the internal camera parameters of both cameras. This result is a natural extension of the classical motion of planes found in [9, 43], and also in [22] The relative affine structure k was described as a product of the affine structure under parallel projection and a term that contains the location of the camera center of the reference view. Geometrically, k is the product of two ratios, the first being the ratio of the ....

R. Tsai and T.S. Huang. Estimating three-dimensional motion parameters of a rigid planar patch, II: singular value decomposition. IEEE Trans. on Acoustic, Speech andSignalProcessing, 30, 1982.

....and in part by System Development Foundation. 1. Introduction 1 1. Introduction The problem of determining rigid body motion and surface structure from image data has been the topic of many research papers in the area of machine vision [1 22] Many approaches based on, tracking feature points [5,11,19,20] or contours [9] using motion flow field [1,3,4,10,12,16,17,21,22] texture [2] or image intensity gradients [14,15] have been proposed in the literature. In the feature point matching schemes, information about a finite number of well seperated points is used to recover the motion (general ....

....in the literature. In the feature point matching schemes, information about a finite number of well seperated points is used to recover the motion (general 8 point 2 frame algorithms of Longuet Higgins [11] Tsai and Huang [20] Buxton et al. 5] and the algorithm of Tsai, Huang and Zhu [19] for planar surfaces) These methods require identifying and matching feature points in a sequence of images. The minimum number of points required depends on the number of image frames. With 2 frames, in most cases, a minimum of 5 points results in a unique solution from a set of nonlinear ....

Tsai, R.Y., Huang, T.S., Zhu, W.L., "Estimating Three-Dimensional Motion Parameters of a Rigid Planar Patch, 11: Singular Value Decomposition," IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. ASSP-30, No. 4, August 1982.

....(x; y; z) coordinates on the object and the camera position parameters. Numerical techniques for solving the nonlinear equations are discussed, as well as methods for choosing good initial conditions and handling noise in the data. Assuming that rotational increments are small, Tsai and Huang, in [7, 8], give an elegant analysis of the motion estimation problem that addresses both the computational and theoretical problems. In [7] it is shown that the eight pure parameters relating the spatial positions of the object match points in successive images are unique, given several constraints on ....

....of the object match points in successive images are unique, given several constraints on the spatial relationships of the match points. Using a singular value decomposition of the pure parameters matrix, the conditions under which the motion parameter estimates are unique are discussed in [8]. Fang and Huang [9] have implemented the approach, and present detailed experimental results. They report successful experiments in extracting features and establishing match point correspondence when the rotation and scale change between successive images is small. 3 In [10] a modification ....

R. Y. Tsai, T. S. Huang, and W. L. Zhu. Estimating three-dimensional motion parameters of a rigid planar patch, II: Singular value decomposition. IEEE Transactions on Acoustics, Speech, and Signal Processing, ASSP-30:525--534, August 1982. 33

....(x; y; z) coordinates on the object and the camera position parameters. Numerical techniques for solving the nonlinear equations are discussed, as well as methods for choosing good initial conditions and handling noise in the data. Assuming that rotational increments are small, Tsai and Huang, in [7, 8], give an elegant analysis of the motion estimation problem that addresses both the computational and theoretical problems. In [7] it is shown that the eight pure parameters relating the spatial positions of the object match points in successive images are unique, given several constraints on ....

....discussed, as well as methods for choosing good initial conditions and handling noise in the data. Assuming that rotational increments are small, Tsai and Huang, in [7, 8] give an elegant analysis of the motion estimation problem that addresses both the computational and theoretical problems. In [7], it is shown that the eight pure parameters relating the spatial positions of the object match points in successive images are unique, given several constraints on the spatial relationships of the match points. Using a singular value decomposition of the pure parameters matrix, the conditions ....

[Article contains additional citation context not shown here]

R. Y. Tsai and T. S. Huang. Estimating three-dimensional motion parameters of a rigid planar patch. IEEE Transactions on Acoustics, Speech, and Signal Processing, ASSP-29:1147--1152, December 1981.

....filters are independent of each other. Structure from motion is another application area that has greately benefited from the SVD. Longuet Higgins [20] and later Hartley [11] extract the translational and rotational components of rigid 3D motion using the SVD of the essential matrix. Tsai et al. [40] also use the SVD to recover the rigid motion of a 3D planar patch. Kanade and co workers [39, 31, 29] assume special image formation models and use the SVD to factorize image displacements to structure and motion components. Using an SVD based method, Sturm and Triggs [38] recover projective ....

R.Y. Tsai, T.S. Huang, and W. Zhu. Estimating three-dimensional motion parameters of a rigid planar patch, II: singular value decomposition. IEEE Transactions on Acoustic, Speech and Signal Processing, 30(4):525--534, 1982.

.... KTNMO VU I MQ KW . M C L I . MXC P . R (2) Since non rigid motions of facial features are not captured well by this model we can use this model to extract the 3D rigid body component of motion and to align the images. To estimate the parameters we use the approach suggested by Tsai and Huang [10] with modifications. Tsai and Huang s method is based on perspective displacement field model which is different from the kind of model we are using. This method is basically a least square fit over the image gradients and we use Singular Value Decomposition to calculate the above parameters. ....

R. Y. Tsai and T. S. Huang, "Estimating three- dimensional motion parameters of a rigid planar patch," IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. 29, No. 6, pp. 1147-1152, 1981.

....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 application surfaces are assumed to be piecewise smooth, ....

R. Tsai and T. Huang. Estimating three-dimensional motion parameters of a rigid planar patch. IEEE Transactions on Acoustics, Speech, and Signal Processing, ASSP30: 525--534, Aug. 1982.

No context found.

R. Y. Tsai and T. S. Huang, "Estimating Three-Dimensional Motion Parameters of a Rigid Planar Patch I," IEEE Trans. Accoust., Speech, and Sig. Proc., vol. ASSP(29), pp. 1147--1152, December 1981.

No context found.

R. Tsai and T. Huang. Estimating three-dimensional motion parameters of a rigid planar patch. IEEE Transactions on Acoustics, Speech, and Signal Processing, ASSP30: 525--534, Aug. 1982.

No context found.

R. Y. Tsai and T. S. Huang, "Estimating three-dimensional motion parameters of a rigid planar patch," IEEE Trans. Acoust., Speech Signal Process., vol. ASSP-29, no. 6, pp. 1147--1152, Dec. 1981.

No context found.

Tsai R and Huang T, "Estimating three-dimensional motion parameters of a rigid planar patch," IEEE Trans. Acoustics, Speech and Signal Processing, vol. 29, no. 6, pp. 1147--1152, 1981.

No context found.

Tsai, R., Huang, T.: Estimating Three Dimensional Motion Parameters of A Rigid Planar Patch IEEE Trans. Acoustics, Speech and Signal Processing, vol. 29, no. 6, (1981) 1147-1152

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R. Tsai and T. Huang. Estimating threedimensional motion parameters of a rigid planar patch. IEEE Trans. Acoustics, Speech and Signal Processing, 29(6):1147--1152, 1981.

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R. Y. Tsai, T. S. Huang, and W. L. Zhu. Estimating three-dimensional motion parameters of a rigid planar patch, II: Singular Value Decomposition. IEEE Trans. On Acoustics, Speech, Signal Processing, 30:525--534, August 1982.

No context found.

R. Y. Tsai and T. S. Huang, "Estimating Three-Dimensional Motion Parameters of a Rigid Planar Patch I," IEEE Trans. Accoust., Speech, and Sig. Proc., vol. ASSP(29), pp. 1147--1152, December 1981.

No context found.

R. Y. Tsai and T. S. Huang, "Estimating three-dimensional motion parameters of a rigid planar patch", IEEE Transactions on Acoustics, Speech and Signal Processing, ASSP-29(6), December 1981.

No context found.

R. Y. Tsai and T. S. Huang, "Estimating three-dimensional motion parameters of a rigid planar patch," [EEE Trans. on Acoustics, Speech and Signal Processing 29(6), pp. 1147-1152, 1981.

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R. Y. Tsai and T. S. Huang, "Estimating three-dimensional motion parameters of a rigid planar patch," IEEE- ASSP 29(6), pp. 1147-1152, 1981.

No context found.

R. Y. Tsai and T. S. Huang. Estimating three-dimensional motion parameters of a rigid planar patch. IEEE Transactions on Acoustics, Speech and Signal Processing, 29(6):1147--1152, December 1981.

No context found.

R. Y. Tsai and T. S. Huang. Estimating three-dimensional motion parameters of a rigid planar patch. IEEE Transactions on Acoustics, Speech and Signal Processing, 29(6):1147--1152, December 1981.

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