T. Papadopoulo and M.I.A. Lourakis. Estimating the jacobian of the singular value decomposition: Theory and applications. Research Report 3961, INRIA Sophia-Antipolis, June 2000. Home/Search Document Details and Download
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PDEs Based Regularization of Multivalued Images and Applications - Tschumperlé (2002) (3 citations) (Correct)
....and leads to these two relations : # and (3.11) Equations (3.11) formally tell us how eigenvalues of a diffusion tensor G vary with respect to a particular coefficient g kl of G. Actually, this interesting property can be proved for any symmetric matrix. For instance, authors of [132] proposed a similar demonstration in a purely matrix form, leading to the same result. They used it to deal with general covariance matrices. Moreover in our case, the matrices are very simple : #G #G With all these elements, we can express (3.8) as : # # # # #I i x ## ....
T. Papadopoulo and M.I.A. Lourakis. Estimating the jacobian of the singular value decomposition: Theory and applications. Research Report 3961, INRIA SophiaAntipolis, June 2000.
Error Characterization of the Factorization Method - Sun (2001) (9 citations) (Correct)
....square distance instead of the least square distance. Note that, in the latter studies the same 2 D covariance information is used in a different scenario. Error analysis of SFM based on eigensystem is also addressed in [23] and Jacobian of singular value decomposition is estimated in [31], but not specific for the factorization method. C. System Configuration Figure 1 summarizes the system configuration and the approach we take. In the noise free case, 3 D shape is projected onto 2 D images given motion and affine camera parameters. The perfect projections (u i , v i ) are ....
T. Papadopoulo and M. Lourakis, Estimating the Jacobian of the singular value decomposition: Theory and applications, in European Conference on Computer Vision, Dublin, Ireland, 2000, pp. 554--570.
Camera Self-Calibration Using the Kruppa Equations and the.. - Lourakis, Deriche (2000) (1 citation) Self-citation (Lourakis) (Correct)
....F ij is the 9 Theta 9 covariance matrix of the fundamental matrix F ij 6 and SF ij SF ij is the value of the Jacobian of SF ij at F ij . This last step, i.e. the computation of the derivatives of the SVD components of a matrix with respect to that matrix, is explained in more detail in [38, 29]. As will soon be clear, the variances oe 2 kl (SF ij ; K i ; K j ) are used to automatically weight the residuals kl (SF ij ; K i ; K j ) according to their uncertainty. The elements of matrices K i are computed from the solution of a non linear least squares problem, namely K 1 : KM = ....
T. Papadopoulo and M.I.A. Lourakis. Estimating the jacobian of the singular value decomposition: Theory and applications. Research report, INRIA Sophia-Antipolis, 2000. In preparation.
Vector-Valued Image Regularization with PDE's: A Common.. - Tschumperle (2002) (3 citations) (Correct)
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T. Papadopoulo and M.I.A. Lourakis. Estimating the jacobian of the singular value decomposition: Theory and applications. Research Report 3961, INRIA Sophia-Antipolis, June 2000.
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