Y. Liu, T. Huang, O. Faugeras, "Determination of Camera Location from 2-D to 3-D Line and Point Correspondences", IEEE Transaction on Pattern Analysis and Machine Intelligence, Vol. 12, No. 1, January 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....are recovered during the creation of the image mosaic. Once the camera parameters are known, two opposite points plus an arbitrary point of a cuboid are enough to obtain the structure of the cuboid. Our method is closely related to the pose estimation problem of PnL (perspective n lines) [Liu et al. 1990] and PnA (perspective n angles) Kanatani, 1988; Wu et al. 1994] The novelty of our method lies in 1. The algorithm combines the approaches of PnL and PnA methods, which enables us to recover both the orientation and translation of a corner. 2. Our presentation is geometrically clearer than ....

....(8) is a plane with normal n passing the center of projection and the lines ox and # OX (Figure 1) The fact can be written as Rv = 0 (9) Rx 0 t) 0. 10) So each line correspondence provides two constraints. The pose can be solved if three or more line correspondences are available [Liu et al. 1990]. This problem is usually called the P3L(Perspective 3 Lines) problem. When the three lines intersect, i.e. forming a corner, the orientation of the camera can be determined from the angles between the three lines. This problem is called the P3A (Perspective 3 Angles) problem [Wu et al. 1994] ....

Yuncai Liu, Thomas S. Huang, and O. D. Faugeras, "Determination of Camera Location From 2D To 3D Line and Point Correspondences," IEEE Transactions on PAMI, 12(1):28--37, January 1990.

....the normal of the projection plane. These constraint equations (8 and 9) relate both rotation and translation pose parameters to the 3D model and 2D image coordinates. A separate constraint involving just rotation is obtained, if we subtract equation (9) for two points ff and if2 lying on a line [18]: ff, if2) 0 = 0 (10) The above equation is obtained by subtracting the left hand side of equation (9) for two 3D points lying on a line. Note, the direction vector d = 2) The constraint reflects the fact that the 3D line must lie in the projection plane formed by its corresponding ....

....performing better thon the previous olgorithm. Finolly, we show thor our olgorithm R ond Tmmd hosed on the Infinite Model Line constroint performs best of oll. Liu, Huong ond Fougeros present o solution to the comero locotion determinotion problem which works for both point ond line doto [18]. Their constroint is hosed on the Infinite Imoge Line cose ond on the observotion thor three dimensionol lines in the comero coordinote system must lie on the projection plone formed by the corresponding imoge line ond the opticol center. Using this foct, constroints for rotorion con be ....

[Article contains additional citation context not shown here]

Liu, Y., T. S. Huang and O. D. Faugeras, "Determination of camera location from 2D to 3D line and point correspondences," Proceedings IEEE Conference on Computer' Vision and Pattern Recognition, pp. 82-88,1988.

....decomposition. This approach calculates a true rigid body transformation of a rotation and a translation. Experimental results using real hardware showed depth and angular errors of about 0.3 . Liu et al. describe methods of pose determination using point correspondences and line correspondences [27]. Both nonlinear and linear solutions are given in which the rotation and translation are calculated separately. Three line or point correspondences are needed for the nonlinear iterative method while eight line or six point correspondences are needed for the linear technique. Simulation results ....

....are distant from the camera. An uncertainty measure is developed relating the variance in the solution to the noise in the input parameters. This measure assumes a perfect 3 D model with noise occurring only in the image data. The method used is based on the constraints given by Liu et al. [27] with a nonlinear optimization technique proposed by Horn [63] to solve the relative orientation problem. While algorithms for line correspondences are given, point algorithms have also been developed. Two basic methods are presented in which one first calculates rotation and then translation ....

Y. Liu, T. S. Huang, and O. D. Faugeras, "Determination of camera location from 2-d to 3-d line and point correspondences," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 12, no. 1, pp. 28--37, January 1990.

....feature points. Starting with the scaled orthographic projection, this method iteratively refines up to two different pose estimates, and provides an associated quality measure for each pose. Faugeras also developed a pose estimation methodology based on the 2D to 3D line or point correspondences [43]. Horaud [29] also proposed an analytic solution for the perspective 4 point problem. The solution proposed was found by replacing the four points with a pencil of three lines and by exploring the geometric constraints available with the perspective camera model. Solutions for coplanar BATISTA ....

Y. Liu, T. Huang, O. Faugeras, "Determination of Camera Location from 2D to 3D Line and Point Correspondences", in IEEE, 1988.

....perspective projection of a rectangle of unknown size in 3D space [Har89] and Michael Penna [Pen91a] generalized the Haralick approach to the 2D perspective projection of any quadrilateral. Faugeras also developed a pose estimation methodology based on the 2D to 3D line or point correspondences [Liu88]. Claus Madsen defined strategies for view point planning to determining the true angle of a junction consisting of a pair of edges on a polyhedral object, using the lengths of the projected junction or the angle between them [Mad94] More recently Abidi and Chandra [Abi95] proposed an approach ....

Y. Liu, T. Huang, O. Faugeras, "Determination of Camera Location from 2D to 3D Line and Point Correspondences", in IEEE, 1988.

....view of these issues, other researchers have investigated the use of higher level geometric features such as lines or curves as observed geometric entities to improve the robustness and accuracy of linear methods for estimating camera parameters. Over the years, various algorithms (Echigo, 1990; Liu et al. 1990; Chen and Tsai, 1990; Rothwell et al. 1992) have been introduced. In their analytic method, Liu et al. (Liu et al. 1990) and Chen (Chen and Tsai, 1990) discussed direct solutions for determining external camera parameters based on a set of 2D 3D line correspondences. The key to this algorithm ....

....curves as observed geometric entities to improve the robustness and accuracy of linear methods for estimating camera parameters. Over the years, various algorithms (Echigo, 1990; Liu et al. 1990; Chen and Tsai, 1990; Rothwell et al. 1992) have been introduced. In their analytic method, Liu et al. (Liu et al. 1990) and Chen (Chen and Tsai, 1990) discussed direct solutions for determining external camera parameters based on a set of 2D 3D line correspondences. The key to this algorithm lies in the linear constraint they used. This constraint uses the fact that a 3D line and its image line lie on the same ....

[Article contains additional citation context not shown here]

Liu, Y., Huang, T., and Faugeras, O. D. (1990). Determination of camera locations from 2d to 3d line and point correspondence. IEEE Trans. on Pattern Analysis and Machine Intelligence, 12(1):28--37.

....on the 2D perspective projection of a rectangle of unknown size in 3D space [7] and Michael Penna [5] generalized the Haralick approach to the 2D perspective projection of any quadrilateral. Faugeras also developed a pose estimation methodology based on the 2D to 3D line or point correspondences [14]. Claus Madsen defined strategies for view point planning to determining the true angle of a junction consisting of a pair of edges on a polyhedral object, using the lengths of the projected junction or the angle between them [1] The Iterative Multi Step Approach camera calibration uses for the ....

Y. Liu, T. Huang, O. Faugeras, "Determination of Camera Location from 2D to 3D Line and Point Correspondences", in IEEE, 1988.

....There are many applications where the scene can be assumed to be static, in particular object modelling [3] 47] It is also possible to relax the rigidity constraint if non1 Most SFM techniques use point features. Those based on line features have somewhat different input and output forms [28], 7] 71] 26] 4 rigid motion can be identified and segmented by other means [33] 5] 58] SFM also assumes that the correspondence problem is solved. Determining feature correspondences is non trivial because the exact camera motion between each image in the sequence is unknown. Features ....

....[51] and Shashua [50] described SFM techniques that differ in their camera model, linearity, number of features, and restrictions on camera motion and scene structure. Invariant properties of projected lines (as opposed to feature points) have also been explored; for example, Huang and Faugeras [28] gave a non linear solution for determining camera motion from lines projected to three images, Weng et al. 71] gave a linear solution to a similar problem, and Lagani re and Mitiche [26] combined lines and point features. Other SFM techniques have incorporated image velocity information, e.g. ....

[Article contains additional citation context not shown here]

Y. Liu, T.S. Huang and O.D. Faugeras, "Determination of camera location from 2-D to 3-D line and point correspondences," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 12, no. 1, 1990, pp. 28-37.

....to an algorithm. In addition to computing parameters for a camera model, algorithms based on 4tuple data must also implicitly solve for the unknown relative 3 D (X; Y; Z) spatial positions of each feature. To date 4 tuple methods have not incorporated lens distortion models [Faugeras et al. 1992] [Liu et al. 1990] [Luong and Faugeras, 1993] Maybank and Faugeras, 1992] Shashua, 1994] Several authors have studied methods of camera modeling based on the (X; Y; Z; U; V ) 5 tuple approach. Sutherland [Sutherland, 1974] describes a linear projection (non distorting) camera model which can be computed as the ....

....that the function PR nonlinear be defined. This is not yet dependent on any information about the camera. This could be a useful function to correct for errors in camera calibration approaches which assume projective distortion only, particularly those based on 4 tuple data [Faugeras et al. 1992] [Liu et al. 1990] [Luong and Faugeras, 1993] Maybank and Faugeras, 1992] Shashua, 1994] This function could also be used to map distorted images into undistorted ones for registration correction in augmented reality systems. Factoring the camera projection matrix CP 3 Theta4 By factoring the CP 3 Theta4 matrix ....

Liu, Y., Huang, T. S., and Faugeras, O. D. (1990). Determination of camera location from 2-d to 3-d line and point correspondences. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(1):28--37.

....testing of a number of more advanced numerical methods for this problem. In recent years, there has been a considerable increase in the number of publications on parameter solving for model based vision, with most of the work aimed at solving for viewpoint parameters of rigid objects. Liu et al. [18] and Kumar [15] have examined alternative iterative approaches to solving for the viewpoint parameters by separating the solution for rotations from those for translations. However, Kumar shows that this approach leads to much worse parameter estimates in the presence of noisy data. Therefore, he ....

Liu, Y., T.S. Huang and O.D. Faugeras, "Determination of camera location from 2-D to 3-D line and point correspondences," IEEE PAMI, 12, 1 (1990), 28--37.

....perspective projection of a rectangle of unknown size in 3D space [Har89] and Michael Penna [Pen91a] generalized the Haralick approach to the 2D perspective projection of any quadrilateral. Faugeras also developed a pose estimation methodology based on the 2D to 3D line or point correspondences [Liu88]. Claus Madsen defined strategies for view point planning to determining the true angle of a junction consisting of a pair of edges on a polyhedral object, using the lengths of the projected junction or the angle between them [Mad94] More recently Abidi and Chandra [Abi95] proposed an approach ....

Y. Liu, T. Huang, O. Faugeras, "Determination of Camera Location from 2D to 3D Line and Point Correspondences", in IEEE, 1988.

....equations can be applied to obtain initial estimates for these parameters. Other researchers have used the constraints described in equations (8) and (9) to recover the position of an observer with respect to a known constellation of straight line features from image data. Liu, Huang and Faugeras [24] presented an algorithm that solves for the camera orientation first and then the camera translation. Kumar and Hanson [25] proposed a related technique that solves for the rotational and translational parameters simultaneously. In this case, these constraints are being used to estimate both the ....

Yuncan Liu, Thomas S. Huang, and O. D. Faugeras, "Determination of camera location from 2D to 3D line and point correspondences ", in Proc. IEEE Conf. on Comp. Vision and Patt. Recog., 1988, pp. 82--88.

....into analytic solutions and least squares solutions which employ a variety of simplifications and or iterative methods. Analytic solutions for three and four points are given by [40 44] Unique solutions exist for four coplanar, but not collinear, points. Leastsquares solutions can be found in [45 51]. Six or more points always yield unique solutions. The camera calibration matrix can be computed from features on the target, then decomposed [49] to yield the target s pose. The least squares solution proceeds as follows. Using (15) we can define an objective function of the unknown pose ....

Y. Liu, T. S. Huang, and O. D. Faugeras, "Determination of camera location from 2-D to 3-D line and point correspondences," IEEE Trans. Pat. Anal. Machine Intell., no. 1, pp. 28--37, 1990.

....a moving robot is monitored in an environment by using a 3D model of the scene and a 2D view (image) of the scene from the current position of the robot. Though several techniques have been developed that determine the robot s position (or exterior orientation [11] camera location determination [15] [16] these techniques require either fairly accurate 3D scene models or noisy 3D models with a reliable estimate of the model noise. Since it is difficult either to automatically obtain accurate 3D models or to reliably estimate the error in noisy models, the 3D models have been constructed ....

Y. Liu, T.S.Huang and O.D. Faugeras, "Determination of Camera Location from 2D to 3D line and point correspondences," Proceedings IEEE Conference on Computer Vision and Pattern Recognition, pp 82-88, 1988.

No context found.

Y. Liu, T. Huang, O. Faugeras, "Determination of Camera Location from 2-D to 3-D Line and Point Correspondences", IEEE Transaction on Pattern Analysis and Machine Intelligence, Vol. 12, No. 1, January 1990.

No context found.

Y. Liu, T.S. Huang, and O.D. Faugeras, "Determination of Camera Location from 2-D to 3-D Line and Point Correspondences," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 12, pp. 28-37, 1990.

No context found.

Y. Liu, T. S. Huang, O. D. Faugeras, "Determination of Camera Location from 2-D to 3-D Line and Point Correspondences", IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 12, no. 1, pp. 28-37, 1990.

No context found.

Y. Liu, T. Huang, and O. D. Faugeras, "Determination of camera locations from 2d to 3d line and point correspondence," IEEE Trans. on Pattern Analysis and Machine Intelligence 12(1), pp. 28--37, 1990.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC