Ponce, J. and Genc, Y. 196. Epipolar geometry and linear subspace methods: A new approach to weak calibration. Proc. 1996 IEEE Conf. on Computer Vision and Pattern Recognition, San Francisco, CA, pp. 776--781.  Home/Search   Document Details and Download   Summary   Related Articles   Check

...., where, OQP is a 3 vector containing the coefficients of the line. If in the second image 6= is the corresponding point to then = must belong to O P , this can be written as = S NR , 3) Several methods exists for computing the fundamental matrix. The most recent ones [2] 6][14] provide excellent results that can be used in practice. 2.3 3D reconstruction in the projective space It is possible to recover the projective three dimensional structure of a scene using images taken with uncalibrated cameras and pixel correspondences between these images[3] 7] 11] Although ....

J. Ponce and Y. Genc. Epipolar geometry and linear subspace methods: A new approach to weak calibration. International Journal of Computer Vision, 28(3):223--243, 1998.

.... T ) v [ v] q j 0: 26) 8 Because of this redundancy, each equivalence class [ v] can only be recovered up to its symmetric component s = 1 2 ( v v ) 2 [ v] This redundancy is the exact reason why different forms of the differential epipolar constraint exist in the literature [26, 17, 24, 14, 1], and, accordingly, various approaches have been proposed to recover and v (see [20] It is also the reason why the differential case cannot be simply viewed as a first order approximation of the discrete case a first order approximation of the essential matrix R T p is v, but this is ....

J. Ponce and Y. Genc. Epipolar geometry and linear subspace methods: a new approach to weak calibration. International Journal of Computer Vision, 28(3):223--43, 1998.

....four matched points to form a projective basis. After the change of coordinates with respect to this projective basis, the new fundamental matrix has a simple form. Boufama and Mohr (1995) then parameterize the fundamental matrix in terms of a homography related to a plane and one epipole, while Ponce and Genc (1996) set up the linear constraints on the epipole using the linear subspace method (Heeger and Jepson 1992) When the projective basis is appropriately chosen, very good results (comparable with those obtained with the normalized 8 point algorithm) have been obtained. As both approaches minimize some ....

Ponce, J. and Genc, Y.: 1996, Epipolar geometry and linear subspace methods: A new approach to weak calibration, Proceedings of the International Conference on Computer Vision and Pattern Recognition, IEEE, San Francisco, CA, pp. 776781.

....this method produces good results. Factors which contribute to this are the fact the dimensionality of the problem has been reduced, and the fact that the change of projective coordinates achieve a data renormalization comparable to the one described in Sect. 3.2.5. 3.9. 2 Linear Subspace Method Ponce and Genc (1996), through a change of projective coordinates, set up a set of linear constraints on one epipole using the linear subspace method proposed by Heeger and Jepson (1992) A change of projective coordinates in each image as described in (41) and (42) is performed. Furthermore, we choose the ....

....( 0, equation (51) provides a linear constraint on f , i.e. T f = 0, while for any value such that ( 0, the same equation provides a linear constraint on e e 0 , i.e. T e e 0 = 0. Because of the particular structure of g i and q i , it is easy to show (Ponce and Genc 1996) that the vectors ( and ( are both orthogonal to the vector [1; 1; 1] T . Since the vectors ( are also orthogonal to e e 0 , they only span a one dimensional line, and their representative vector is denoted by 0 = a ; b ; c ] T . Likewise, the vectors ( ....

Ponce, J. and Genc, Y.: 1996, Epipolar geometry and linear subspace methods: A new approach to weak calibration, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, San Francisco, CA, pp. 776781.

....and paraperspective cases. Finally,we conclude in Chapter 7 by summarizing the results of this thesis and giving some future research directions. Part of the material in this thesis has been published in a number of papers: The weak calibration method in Chapter 3 was rst presented in [86] and [87]. The point based imagebased rendering algorithm in Chapter 5 was presented in [26] Finally, the bilinear estimation algorithm of Chapter 6 was presented in [27] 5 CHAPTER 2 WEAK CALIBRATION The geometric information contained in two images taken by uncalibrated perspective cameras is ....

J. Ponce and Y. Genc. Epipolar geometry and linear subspace methods: A new approach to weak calibration. Int. J. of Comp. Vision, 28(3):223-243, 1998.

....perspective and paraperspective cases. Finally,we conclude in Chapter 7 by summarizing the results of this thesis and giving some future research directions. Part of the material in this thesis has been published in a number of papers: The weak calibration method in Chapter 3 was rst presented in [86] and [87] The point based imagebased rendering algorithm in Chapter 5 was presented in [26] Finally, the bilinear estimation algorithm of Chapter 6 was presented in [27] 5 CHAPTER 2 WEAK CALIBRATION The geometric information contained in two images taken by uncalibrated perspective cameras is ....

J. Ponce and Y. Genc. Epipolar geometry and linear subspace methods: A new approach to weak calibration. In Proc. IEEE Conf. Comp. Vision Patt. Recog., pages 776-781, San Francisco, CA, June 1996.

....(u; v; 1) T is the position of an image point, t is the translational velocity and is the rotational velocity. Equation (1) can be rewritten as (p Theta p) Delta t = t T ( p Theta ] 2 ) 2) This can be seen as an expression of the epipolar constraint in the infinitesimal motion case [19]. Suppose that we observe the motion field p i at n image points p i (i = 1; n) We define a vector of n coefficients = 1 ; n) T and the vector ( P n i=1 i p i Theta p i . It follows from (2) that ( Delta t = t T ( n X i=1 i [p i Theta ] 2 ) Hence, ....

J. Ponce and Y. Genc. Epipolar geometry and linear subspace methods: A new approach to weak calibration. Technical Report Beckman Institute Tech. Report UIUC-BI-AI-RCV-95-09, Beckman Institute, University of Illinois, December 1995.

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Ponce, J. and Genc, Y. 196. Epipolar geometry and linear subspace methods: A new approach to weak calibration. Proc. 1996 IEEE Conf. on Computer Vision and Pattern Recognition, San Francisco, CA, pp. 776--781.

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