R. Hartley. An algorithm for self calibration from several views. In Proc. IEEE Conference on Computer Vision and Pattern Recognition, pages 908--912, June 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....displacement by using image information alone. Therefore, if images are taken by the same camera with xed internal parameters, correspondences between three images are sufcient to recover both the internal and external parameters which allow us to reconstruct 3 D structure up to a similarity [12, 10]. Although no calibration objects are necessary, a large number of parameters need to be estimated, resulting in a much harder mathematical problem. Other techniques exist: vanishing points for orthogonal directions [2, 11] and calibration from pure rotation [9, 16] To our knowledge, there does ....

Richard I. Hartley. An algorithm for self calibration from several views. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 908--912, Seattle, WA, June 1994. IEEE.

....of structure from motion, approaching it in two computational stages. In a first step, the correspondence of points in successive image frames is established; in a second step, this is used to recover the intrinsic parameters and the motion parameters, and subsequently the structure of the scene [2, 7, 8, 12, 13, 19, 22, 26]. Assuming the camera motion to be discrete, this problem is quite difficult. In [8, 19] the epipolar geometry between pairs of views is computed and projective geometry techniques are used to obtain a set of constraints leading to high degree polynomial equations. The method developed in [12] ....

....22, 26] Assuming the camera motion to be discrete, this problem is quite difficult. In [8, 19] the epipolar geometry between pairs of views is computed and projective geometry techniques are used to obtain a set of constraints leading to high degree polynomial equations. The method developed in [12] computes the parameters of interest in steps using non iterative and iterative estimation techniques. First a projective reconstruction is derived from which the Euclidean structure and the extrinsic and intrinsic camera parameters are computed by utilizing the constraint of positive depth. ....

R. I. Hartley. An algorithm for self calibration from several views. In Proc. IEEE Conference on Computer Vision and Pattern Recognition, pages 908--912, Seattle, WA, 1994.

.... H K 1 0 01 ## I 0 v (13) 5 where the right hand matrix in equation 13 is the transformation from the projective reconstruction to the quasi a#ne reconstruction, and the left hand matrix is the transformation from a quasi a#ne reconstruction to a Euclidean reconstruction [12]. Thus the camera calibration problem is transformed into estimating the eight unknowns of H (five unknowns in K and three unknowns in v) Hartley s specific algorithm to perform the above calibration proceeds in five steps. The first step in Hartley s approach is to estimate a projective ....

....problem is transformed into estimating the eight unknowns of H (five unknowns in K and three unknowns in v) Hartley s specific algorithm to perform the above calibration proceeds in five steps. The first step in Hartley s approach is to estimate a projective reconstruction of the scene [12]. The reconstruction is performed by using the Essential Matrix, E. When the camera calibration is known, it is possible to use E to determine the relative placements of cameras as well as the relative location of 3D points [13] However, it is shown in [13] that even when the cameras are ....

[Article contains additional citation context not shown here]

Richard I. Hartley. An algorithm for self calibration from several views. In Proceedings of the Conferences on Computer Vision and Pattern Recognition, pages 908--912, 1994.

.... for computing a projective scene representation from multiple images have been proposed (e.g. 5, 12, 15, 21, 27, 28, 35] As in the affine case, the projective reconstruction can be upgraded to a full metric model [7] by exploiting a priori knowledge of camera calibration parameters (e.g. [8, 9, 13, 20, 23, 24]) or scene geometry (e.g. 1] Now, although the internal parameters of a camera may certainly be unknown (e.g. when stock footage is used) or change from one image to the next (e.g. when several different cameras are used to film a video clip, or when a camera zooms, which will change both ....

R.I. Hartley. An algorithm for self calibration from several views. In Proc. IEEE Conf. Comp. Vision Patt. Recog., pages 908--912, Seattle, WA, June 1994.

.... from old ones [ Laveau and Faugeras, 1994, Seitz and Dyer, 1995b ] convex hull computation [ Robert and Faugeras, 1993 ] image rectification [ Hartley and Gupta, 1993, Seitz and Dyer, 1995a ] motion segmentation [ Nishimura et al. 1993 ] and self calibration [ Faugeras et al. 1992, Hartley, 1994 ] As mentioned by Faugeras [ 1993 ] the problem of estimating the epipoles and the epipolar transformations compatible with seven point correspondences was first posed by Chasles [ 1855 ] and solved by Hesse [ 1863 ] see the article by Sturm [ 1869 ] for an analysis of Hesse s method and ....

R.I. Hartley. An algorithm for self calibration from several views. In Proc. IEEE Conf. Comp. Vision Patt. Recog., pages 908--912, Seattle, WA, June 1994.

.... images from old ones [ Laveau and Faugeras, 1994, Seitz and Dyer, 1995b ] convex hull computation [ Robert and Faugeras, 1993 ] image rectification [ Hartley and Gupta, 1993, Seitz and Dyer, 1995a ] motion segmentation [ Nishimura et al. 1993 ] and self calibration [ Faugeras et al. 1992, Hartley, 1994 ] As mentioned by Faugeras [ 1993 ] the problem of estimating the epipoles and the epipolar transformations compatible with seven point correspondences was first posed by Chasles [ 1855 ] and solved by Hesse [ 1863 ] see the article by Sturm [ 1869 ] for an analysis of Hesse s method and the ....

R.I. Hartley. An algorithm for self calibration from several views. In Proc. IEEE Conf. Comp. Vision Patt. Recog., pages 908--912, Seattle, WA, June 1994.

.... Luong and Faugeras [68] discuss many other applications, including the construction of stereo projective invariants [31, 34, 35, 99] the synthesis of new images from old ones [57, 95] convex hull computation [91] image recti cation [38, 94] motion segmentation [80, 110] and self calibration [21, 36]. We propose in Chapter 3 a linear algorithm for weak calibration that generalizes Jepson s and Heeger s method to the nite motion case. This algorithm has been implemented and comparisons with other techniques are presented. 2 Second, we consider the problem of image based rendering from point ....

.... Luong and Faugeras [68] discuss many other applications, including the construction of stereo projective invariants [31, 34, 35, 99] the synthesis of new images from old ones [57, 95] convex hull computation [91] image recti cation [38, 94] motion segmentation [80, 110] and self calibration [21, 36]. We will assume throughout the presentation that a static scene is observed by a mobile perspective camera. In the in nitesimal case we assume that the motion eld is known. In the nite motion case we suppose that discrete point correspondences used as input to the weak calibration process have ....

R.I. Hartley. An algorithm for self calibration from several views. In Proc. IEEE Conf. Comp. Vision Patt. Recog., pages 908-912, Seattle, WA, June 1994.

.... and general (upper triangular) we have the uncalibrated image case, from which we can only recover a projective reconstruction of world [Fau93] If some information about V k is known (e.g. that it is temporally invariant, or that it has a reduced form) we can apply self calibration techniques [Har94,LF97]. The motion of a point between two images k and l can thus be written as u ik # V k R k (w il R 1 l V 1 l u il t l t k ) # H # kl u il w 1 il e kl , 3) with R kl = R k R 1 l . The matrix H # kl = V k R kl V 1 l is the homography (planar perspective transform) which maps points ....

R. I. Hartley. An algorithm for self calibration from several views. In CVPR'94, pages 908--912, 1994.

....displacement by using image information alone. Therefore, if images are taken by the same camera with fixed internal parameters, correspondences between three images are sufficient to recover both the internal and external parameters which allow us to reconstruct 3 D structure up to a similarity [16, 13]. While this approach is very flexible, it is not yet mature [1] Because there are many parameters to estimate, we cannot always obtain reliable results. Other techniques exist: vanishing points for orthogonal directions [3, 14] and calibration from pure rotation [11, 21] Our current research ....

R. I. Hartley. An algorithm for self calibration from several views. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 908--912, Seattle, WA, June 1994. IEEE.

....problem. 1 Introduction The computation of the intrinsic camera parameters is one of the most important issues in visual guided robotics. One important method of selfcalibration is based on the image of the absolute conic and it requires as input only information about the point correspondences [5, 4, 1]. In this paper we re establish the idea of the absolute conic in the context of Pascal s theorem and we get different equations than the Kruppa equations [4, 1] Although the equations are different they rely on the same principle of the invariance of the mapped absolute conic. The consequence is ....

.... selfcalibration is based on the image of the absolute conic and it requires as input only information about the point correspondences [5, 4, 1] In this paper we re establish the idea of the absolute conic in the context of Pascal s theorem and we get different equations than the Kruppa equations [4, 1]. Although the equations are different they rely on the same principle of the invariance of the mapped absolute conic. The consequence is that we can generate equations so that we require only a couple of images whereas the Kruppa equation method requires at least three images [4] As a prior ....

Hartley, R. I. 1994. An algorithm for self--calibration from several views. In Proc. Conference on Computer Vision and Pattern Recognition, Seatle, WA, pp. 908--912.

....A first class of approaches is to perform a projective reconstruction from two views [4, 9] However, the amount of deformation can be very large, which limits the usefulness of the reconstruction. A second class of approaches is to recover metric representations by performing self calibration [11, 8] (which requires a large number of views to obtain stable results) or by using scene knowledge [1, 6] This required line segments and geometric constraints which are not available in images of natural terrain. It is generally believed that the area based approaches to stereo are the most adequate ....

R. Hartley. An algorithm for self calibration from several views. In Proc. Conference on Computer Vision and Pattern Recognition, pages 908--912, Seattle, WA, 1994.

.... [62] ffl Segmentation of rigid independent motions [56, 72, 78] ffl Stereo analysis: rectification of images [27, 15] and stereo matching with uncalibrated cameras [61] feature based) 15] area based) 63, 11] taking orientation into account) ffl Self calibration of a moving camera [51, 16, 44, 25]. The Fundamental matrix represents indeed the minimal information (two views, no additional hypotheses) in a hierarchy of representations obtained by making further assumptions and adding views [76, 47] As a consequence, it is a theoretical and practical tool of primary importance. Its ....

R.I. Hartley. An algorithm for self calibration from several views. In Proc. Conference on Computer Vision and Pattern Recognition, pages 908--912, Seattle, WA, 1994.

....of structure from motion, approaching it in two computational stages. In a first step, the correspondence of points in successive image frames is established; in a second step, this is used to recover the intrinsic parameters and the motion parameters, and subsequently the structure of the scene [2, 7, 8, 12, 13, 19, 22, 26]. Assuming the camera motion to be discrete, this problem is quite difficult. In [8, 19] the epipolar geometry between pairs of views is computed and projective geometry techniques are used to obtain a set of constraints leading to high degree polynomial equations. The method developed in [12] ....

....22, 26] Assuming the camera motion to be discrete, this problem is quite difficult. In [8, 19] the epipolar geometry between pairs of views is computed and projective geometry techniques are used to obtain a set of constraints leading to high degree polynomial equations. The method developed in [12] computes the parameters of interest in steps using non iterative and iterative estimation techniques. First a projective reconstruction is derived from which the Euclidean structure and the extrinsic and intrinsic camera parameters are computed by utilizing the constraint of positive depth. ....

R. I. Hartley. An algorithm for self calibration from several views. In Proc. IEEE Conference on Computer Vision and Pattern Recognition, pages 908--912, Seattle, WA, 1994.

....and projective geometry. However, one can remark that the representations adopted in the literature are of very disparate nature, and that often they are not even minimal. The relationships between different levels of representation has not been investigated thoroughly (see the recent papers [22, 47] though) which is a consequence of the fact that as the mathematical language used was quite different, comparisons were difficult. Another important point which has not yet received much attention is the problem of dealing with multiple viewpoints to build a coherent representation in the case ....

....also holds if H1 is replaced by S. This means just that the knowledge of the F matrix does not allow one to recover completely H1 . The missing parameters can be obtained by applying again (10) H1 = S e 0 e 0T H1 =ke 0 k 2 z r T 1 (17) The vector r1 (also discovered by [22]) which appears in this relation is very important. Once the fundamental matrix is known, its knowledge is equivalent to the knowledge of the infinity homography matrix, or, in other words, the plane at infinity. It is thus a representation of the plane at infinity relative to the fundamental ....

R.I. Hartley. An algorithm for self calibration from several views. In Proc. Conference on Computer Vision and Pattern Recognition, pages 908--912, Seattle, WA, 1994.

....from motion than self calibration, where motion and calibration are estimated. However, for anything else than a robotic head, the method would not work, and thus we are still in need of an efficient general self calibration method. The closest one we are aware of is a recent work by Hartley [9]. However, we believe that our approach has still a number of advantages that we stress in the conclusion. The main goal of this paper is to present such a method and to illustrate its applicability by showing that usable 3D reconstruction can be obtained starting with as few data as three ....

R.I. Hartley. An algorithm for self calibration from several views. In Proc. Conference on Computer Vision and Pattern Recognition, pages 908--912, Seattle, WA, 1994.

....uncertainty are described again by bias and covariance matrices. Whereas calibration is an old and not the central issue of the paper, the necessity for analyzing the sensitivity with respect to calibration errors has been stressed only recently, for example directly in [ACDR94] or indirectly in [Har94]. The effect of calibration errors on the result of motion estimates (cf. KH94] and SfM ( FA96] SS97,Stu97] has been addressed in previous work. However, in all cases simplifications have been made, e.g. by restricting to only a few parameters, especially to errors in the principle point or ....

R. Hartley. An algorithm for self calibration from several views. In Proc. CVPR, pages 908--912, 1994.

....associated with a projection matrix and 3 unknowns associated with each point: a total of 11 Thetan 3 Theta k unknowns. In spite of this large number of variables, the minimization of such an error function can be easily carried out by such methods as Levenberg Marquardt [1] 10] 6] [5]. A good initial solution can be provided by using just two of the initial set of images (for example the first one and the last one) and by applying the epipolar constraint with its associated linear projective reconstruction [2] Such an initialization procedure is described in detail in [6] ....

R. I. Hartley. An algorithm for self calibration from several views. In Proceedings Computer Vision and Pattern Recognition Conference, pages 908--912, Seattle, Washington, June 1994. IEEE Computer Society Press.

....Mundy and Zisserman [18] which is a more general class of projections including orthographic, weak perspective and para perspective projection models. The concept of self calibration, introduced by Maybank and Faugeras in [16] for the perspective camera and by Hartley for the rotating camera in [10], is then applied for the affine camera. This paper introduces the 3 intrinsic parameters that the affine camera can have at most. The intrinsic parameters of the affine camera are closely related to the usual intrinsic parameters of the pin hole perspective camera, but different in general case. ....

....and numerically non stable calibration. To get Euclidean structure from uncalibrated affine cameras, the key idea is to use the self calibration idea originally proposed by Maybank and Faugeras in [16] for the perspective camera. More practical self calibration methods have been developed in [9, 10, 15], especially that for self calibrating a rotating camera. We will develop the self calibration method in the context of the affine camera model, introduced by Mundy and Zisserman [18] The affine camera generalises the orthographic, weak perspective and para perspective models. Parallelism is ....

[Article contains additional citation context not shown here]

R.I. Hartley. An algorithm for self calibration from several views. In Proceedings of the Conference on Computer Vision and Pattern Recognition, Seattle, Washington, USA, pages 908--912, 1994.

.... (image point or line correspondences) Therefore, if images are taken by the same camera with constant internal parameters, point correspondences between three images are sufficient to recover both the internal and external parameters which allow us to reconstruct 3 D structure up to a similarity [28, 29]. Self calibration can also be done for uncalibrated stereo rig, where the internal parameters and the relative orientation of the cameras and the motion of the stereo rig are all unknown [30 32] More knowledge about the camera internal parameters and camera motion will simplify the computation, ....

R. Hartley, "An algorithm for self calibration from several views," in Proc. IEEE Conference on Computer Vision and Pattern Recognition, (Seattle, WA), pp.908--912, 1994.

.... images from old ones [ Laveau and Faugeras, 1994, Seitz and Dyer, 1995b ] convex hull computation [ Robert and Faugeras, 1993 ] image rectification [ Hartley and Gupta, 1993, Seitz and Dyer, 1995a ] motion segmentation [ Nishimura et al. 1993 ] and self calibration [ Faugeras et al. 1992, Hartley, 1994 ] As mentioned by Faugeras [ 1993 ] the problem of estimating the epipoles and the epipolar transformations compatible with seven point correspondences was first posed by Chasles [ 1855 ] and solved by Hesse [ 1863 ] see the article by Sturm [ 1869 ] for an analysis of Hesse s method and ....

R.I. Hartley. An algorithm for self calibration from several views. In Proc. IEEE Conf. Comp. Vision Patt. Recog., pages 908--912, Seattle, WA, June 1994.

.... from old ones [ Laveau and Faugeras, 1994, Seitz and Dyer, 1995b ] convex hull computation [ Robert and Faugeras, 1993 ] image rectification [ Hartley and Gupta, 1993, Seitz and Dyer, 1995a ] motion segmentation [ Nishimura et al. 1993 ] and self calibration [ Faugeras et al. 1992, Hartley, 1994 ] As mentioned by Faugeras [ 1993 ] the problem of estimating the epipoles and the epipolar transformations compatible with seven point correspondences was first posed by Chasles [ 1855 ] and solved by Hesse [ 1863 ] see the article by Sturm [ 1869 ] for an analysis of Hesse s method and ....

R.I. Hartley. An algorithm for self calibration from several views. In Proc. IEEE Conf. Comp. Vision Patt. Recog., pages 908--912, Seattle, WA, June 1994.

....each time camera parameters were modified, there was a need to re calibrate. Image sequences coming from different (probably unknown) sources could not be used for recovery of scene structure. Recently there have been some attempts at self calibration using point and line features in the scene [8, 9, 10, 11]. Unfortunately most of these algorithms are reported to be quite sensitive to noise and need good feature correspondences. One of the first feature point reconstruction from an uncalibrated image sequence[12] was based on a parallel projection model rather than a full perspective camera model and ....

R. Hartley. An algorithm for self calibration from several views. In Proc. IEEE Conf. Comput. Vision Pattern Recog., pages 908--912, Seattle, Washington, USA, June 1994.

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R. Hartley. An algorithm for self calibration from several views. In Proc. IEEE Conference on Computer Vision and Pattern Recognition, pages 908--912, June 1994.

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R. Hartley. An algorithm for self calibration from several views. In Proc. IEEE Conference on Computer Vision and Pattern Recognition, pages 908--912, June 1994.

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