S. Barnett. Matrices: Methods and Applications. Oxford University Press, 1992. Home/Search Document Not in Database Summary Related Articles Check |
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Learning to Track the Visual Motion of Contours - Blake, Isard, Reynard (1995) (53 citations) (Correct)
....1= Delta = 50Hz. As mentioned earlier, it is impossible in principle to estimate B uniquely, but the covariance coefficient C = BB T can be determined, from which a standard form for B can be computed as: B = p C ; 17) applying the square root operation for a positive definite square matrix [6]. The learning process is outlined below. First, to avoid overfitting, the state space must be restricted, during learning, to a low dimensional subspace. This could be the six dimensional affine subspace of the state space or some other space spanning an appropriate combination of rigid and ....
S. Barnett. Matrices: Methods and Applications. Oxford University Press, 1990.
Iterative Solution Of Cyclically Reduced Systems Arising.. - Chen Greif James (4 citations) (Correct)
....Theorem 3.7. The eigenvalues of interior blocks S (0) j,j are given by j = a 2 2be 2fg 4 # bcde cos(#jh) 4cd cos 2 (#jh) 3.36) 2 p befg 4 p cdfg cos(#jh) j = 1, n. Proof. Any four given matrices A, B, C, D with the appropriate sizes satisfy [2] (A O B) C O D) AC) O (BD) 3.37) Applying this, using (3.33) and (3.35) we have U 2n X 2n = T n Z n ) O (I 2 Y 2 ) 3.38a) X 2n U 2n = Z n T n ) O (Y 2 I 2 ) 3.38b) Since I 2 Y 2 = Y 2 I 2 = Y 2 and T n Z n = Z n T n we conclude that X 2n U 2n = U 2n X 2n , 3.39) hence X ....
S. Barnett, Matrices - Methods and Applications, Clarendon Press, Oxford, 1990.
Statistical Models of Visual Shape and Motion - Blake, Bascle, Isard, MacCormick (1998) (9 citations) (Correct)
....of expression and pose can be expressed bilinearly to give shape parameters X j i = i Y j where i is the weight associated with the ith expression and Y j is the jth component of an affine transformation. Decomposition of such products can be achieved using Singular Value Decomposition (SVD) [Barnett, 1990], as has been done elsewhere for structure and motion [Tomasi and Kanade, 1991] and shape and shading [Freeman and Tenenbaum, 1997] The practical result is good isolation of pose from expression, as figure 4 shows. Figure 4. Pose invariant transmission of facial expression. Separation of ....
Barnett, S. (1990). Matrices: Methods and Applications. Oxford University Press.
Blind Space-Time Algorithms For Wireless Communication Systems - Talwar (1996) (1 citation) (Correct)
....as S k 1 = proj[ XS y k ) y X] 3.3.2) and a MMSE scheme such as multi target LS CMA [60] without soft orthogonalization as S k 1 = proj[S k X y X] 3.3.3) Chapter 3. Memoryless model: Algorithms 43 Since the pseudo inverse does not satisfy (XS y k ) y = S k X y in general ([61], pp. 248254) the two algorithms yield different signal estimates. Note the matrix A k = XS y k in (3.3.2) is poorly conditioned near the solution A, if the angular separation between array response vectors is small. In contrast, the data matrix X in (3.3.3) becomes poorly conditioned for high ....
S. Barnett. Matrices - Methods and Applications. Clarendon Press, Oxford, 1990.
Blind Separation of Synchronous Co-Channel Digital.. - Talwar, Viberg, Paulraj (1995) (32 citations) (Correct)
....how they differ. We can express ILSP algorithm succinctly as S k 1 = proj[ XS k ) X] 20) and a MMSE scheme such as multi target LS CMA [25] without soft orthogonalization as S k 1 = proj[S k X X] 21) Since the pseudo inverse does not satisfy (XS k ) S k X in general [26], the two algorithms yield different signal estimates. Note the matrix A k = XS k in (20) is poorly conditioned near the solution A, if the angular separation between array response vectors is small. In contrast, the data matrix X in (21) becomes poorly conditioned for high SNR s. The MMSE ....
S. Barnett. Matrices - Methods and Applications. Clarendon Press, Oxford, 1990.
D Position, Attitude and Shape Input Using Video Tracking of.. - Andrew Blake (Correct)
....the appendix. This leaves just one constant c to be chosen to fix C . Now the default tracker has been specified except for the values of certain constants. Typically the number of measurements per B spline span is set to N = 3, a value which allows our tracker to 1 The Kroneckerproduct [5] A Omega B of two matrices A;B is obtained by replacing each element a of A with the submatrix aB. The dimensions of this matrix are thus products of the corresponding dimensions of A; B. run at video field rate, on a SUN IPX workstation, with 20 or more control points. The system and measurement ....
Stephen Barnett. Matrices: Methods and Applications. Oxford University Press, 1990.
Clustering Using a Random Walk Based Distance Measure - Yen, Vanvyve, Wouters.. (2005) (2 citations) (Correct)
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S. Barnett. Matrices: Methods and Applications. Oxford University Press, 1992.
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S. Barnett. Matrices: Methods and Applications. Oxford University Press, 1992.
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S. Barnett. Matrices: Methods and Applications. Oxford University Press, 1992.
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S. Barnett. Matrices: Methods and Applications. Oxford University Press, 1992.
Block Orderings for Tensor-Product Grids in Two and Three - Dimensions Gene Golub (Correct)
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S. Barnett. Matrices - Methods and Applications. Clarendon Press, Oxford, 1990.
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S. Barnett, Matrices: Methods and Applications. Press, Oxford England, 1990.
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Barnett, S. [1990] Matrices: Methods and Applications (Clarendon Press, London).
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