S. Ganapathy. Decomposition of Transformation Matrices for Robot Vision. In Proceedings of the IEEE International Conference on Robotics and Automation, pages 130--139, Atlanta (GA), USA, March 1984.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....7 5 Conclusion 10 1 Introduction Camera calibration is a necessary step in 3D computer vision in order to extract metric information from 2D images. Much work has been done, starting in the photogrammetry community (see [1, 3] to cite a few) and more recently in computer vision ([8, 7, 19, 6, 21, 20, 14, 5] to cite a few) According to the dimension of the calibration objects, we can classify those techniques roughly into three categories. 3D reference object based calibration. Camera calibration is performed by observing a calibration object whose geometry in 3 D space is known with very good ....

S. Ganapathy. Decomposition of transformation matrices for robot vision. Pattern Recognition Letters, 2:401--412, December 1984.

....an algorithm which computes the 3D coordinates of the vertices of a quadrangle relative to the camera frame given the corresponding image of the quadrangle. This method generates a direct solution of the exterior orientation problem, then uses the decomposition technique proposed by Ganapathy [17] to compute the final pose. Yuan [18] presented a general solution to the interior and exterior orientation problem showing that it can be formulated for an arbitrary number of features. He found a necessary condition for the existence of a solution and provided a proof of uniqueness for the case ....

....recover the position of the four target s points relative to the camera coordinate system. They are often referred to as the interior orientation parameters. In some applications, the exterior orientation parameters and or final pose are needed. The latter two have been extensively studied [11] [17], 21] Fig. 3 shows how the various components of the algorithm are interrelated. In a pinhole camera model (Fig. 1) the image coordinates of a point (x, y) are related to its camera coordinates (X , l x, Z ) by: x= X c f yc f f Z c Y= f Z . The transformation from the world coordinate ....

S. Ganapathy, "Decomposition of transformation matrices for robot vision," Proc. lnt'l Conf. on Robotics and Automation, vol. 1, pp. 130139, Rome, Italy, Nov. 1984.

....the DEM s major peaks and the second (Model Feature Point Database) con tains all major and minor peaks. 2. 2 Pose Computation Many analytical and iterativ e procedures ha ve been proposed to compute for camera pose from three or more point correspondences and an initial pose estimate ( 7] 9] [8], 11] etc) These procedures, how ever, cannot be used for our problem since no initial pose values are assumed. Weformulate pose computation, whichinvolv es the calculation of the position and orientation parameters that will best t or align three model feature points with three image ....

S. Ganapathy, \Decomposition of Transformation Matrices for Robot Vision," Pattern Recognition L etters, 2(6):401-412, 1984.

....methods. They frequently do not require an initial solution or can calculate one with relative ease. These methods still require a large number of points for good results. Examples of these methods include [ Faugeras and Toscani, 1987, Grosky and Tamburino, 1987, Tsai, 1987, Goshtasby, 1987, Ganapathy, 1984 ] None of the current solutions to the camera calibration problem are ideally suited to enhanced reality visualization. The linearization methods come closest to meeting the requirements of enhanced reality visualization, however there is room for improvement. Our Solution We have developed a ....

....is to enable the recovery of metric 3D information, such as the pose (position and orientation) of an object, from its two dimensional image. Clearly, to recover the pose of an object it is necessary to separate the intrinsic and extrinsic parameters. Separating the parameters is difficult [ Ganapathy, 1984 ] The problem is nonlinear and several of the parameters are closely coupled. In the presence of noise a single solution to the camera calibration problem does not exist, rather there exists a set of solutions. These solutions can differ significantly and yet give rise to nearly identical ....

Sundaram Ganapathy. Decomposition of transformation matrices for robot vision. In Conference on Robotics, pages 204--209. IEEE, March 1984. Atlanta, GA.

....can often be found quite easily. It is possible to calibrate stereo systems in this way. In the case where there is no lens distortion, we could find the transformation between the 3D world coordinates and image locations in the image planes of the two cameras using homogeneous matrices [18] [7]. Wemightnever bother to actually break down the transformation matrices into internal and external parameters. We could make accurate measurements of the location of one object relative to another object in the scene. If on the other hand we wish to find the location of the camera relativetothe ....

....Sutherland[19] shows how to obtain the matrix M in a least squares way using the known world coordinates and their corresponding image coordinates. The more difficult problem is obtaining the individual camera parameters from the matrix M. This involves solving nonlinear equations. Ganapathy[7] shows a non iterative method for their solution and a more geometrically intuitive method is described in [18] 43 Lenz and Tsai[21] 11] and Weng et al. 22] provide methods for determining the camera parameters in the presence of lens distortion. Lenz and Tsai[21] assume only one parameter of ....

Ganapathy,S., "Decomposition of transformation matrices for robot vision" Pattern Recognition Letters2, 401-412 (1984)

....imoge meosurements ond ore less toleront to noise. Pose determinotion techniques ore less susceptible to imoge noise but one needs to know the intrinsic comero porometers. In Section 5, the effect of errors in the intrinsic comero porometers on the pose determinotion problem is studied. Ganapathy [8] presents a linear closed form solution for point data. In addition to solving for the rotation and translation parameters, he also solves for the center of the image and scaling along the x and y directions in the image. Our implementation of his technique shows that it is extremely ....

Ganapathy, S., "Decomposition of transformation matrices for robot vision," Proceedings IEEE Conference on Robotics, pp. 130-139, 1984.

....and is more stable (not dependent on the relative orientation of the image plane and scene plane) The problem of multiple solutions persists and near coplanar points and noise produce unstable results. Ganapathy computes camera position and orientation using a non iterative analytical method [GANA84] His method also employs only 3 points (for external camera parameter estimation) and in general, there are multiple solutions. Although it can be extended to using n points, it requires iterative optimization. Uenohara et al. used a recursive method (Newton s method: multiple DSP chip ....

Sundaram Ganapathy, "Decomposition of Transformation Matrices for Robot Vision", Proceedings of Int. Conf. Ronotics and Automation, 1984, pp. 130-139

....= V L 1 i Q 1 Q L ref V 1 = V L 1 i L ref V 1 . 6) The left side of (6) describes the motion of the X ray camera between two image frames in world coordinates. This motion can be computed from the projection matrices. Traditionally this is done by decomposing the projection matrices [6, 5] into extrinsic and intrinsic parameters and then computing the motion from the extrinsic parameters. Di#erent authors [8, 12] have emphasized that the decomposition of projection matrices is an unstable process, and an approach for computing the motion between two image frames from projection ....

S. Ganapathy. Decomposition of transformation matrices for robot vision. In Proceedings International Conference on Robotics and Automation, pages 130--139, 1984.

....the the row of p. Examples Compute the image plane coordinates of a point at (10; 5; 30) with respect to the standard camera located at the origin. C = camcalp(pulnix) create camera calibration matrix C = 1.0e 05 0.7920 0 0.3513 0.0027 0 1.2050 0.2692 0.0021 0 0 0.0013 0. 0000 camera(C, [10 5 30]) ans = 479.9736 53.3093 See Also camera ccdresponse 14 ccdresponse Purpose CCD spectral response Synopsis r = CCDRESPONSE(lambda) Description Return a vector of relative response (0 to 1) for a CCD sensor for the specified wavelength lambda. lambda may be a vector. Examples Compare the ....

....not computed for pixels whose window crosses the border, hence the output image is reduced all around by half the window size. wrap the image is assumed to wrap around, left to right, top to bottom. Examples To compute the mean of an image over an annular window at each point. se = icircle([5 10]) out = iwindow(image, se, mean ) See Also iopen,iclose,icircle loadinr Purpose Load INRIMAGE format image Synopsis I = loadinr(fname) Description Returns a matrix containing a gray scale image read from an INRIMAGE format file with the specified name. If no extension is provided an ....

S. Ganapathy, "Decomposition of transformation matrices for robot vision," in Proc. IEEE Int. Conf. Robotics and Automation, pp. 130--139, 1984.

....in the value for an extrinsic parameter might be compensated for by an error in the value obtained for an intrinsic parameter. Several procedures have been presented with the purpose of extracting from the perspective transformation matrix the extrinsic and intrinsic camera parameters [42] 12] [17], 26] The Manual of Photogrammetry [46] claims that the strong coupling that exists between intrinsic parameters (principal point, focal length, etc. and extrinsic parameters (pose of the camera) can be expected to result in unacceptably large variances for these projective parameters when ....

K. Ganapathy, "Decomposition of Transformation Matrices for Robot Vision", IEEE, pp. 130-139, 1984.

....location (via sophisticated image analysis algorithms) of the features whose intrinsic geometry was assumed to be known a priori, and thereby reducing the problem to the equivalent algebraic framework of feature points whose precise perspective projection is provided by the images seen. See e.g. [1, 3 8]. The algebraic framework is very nice indeed and it provides the framework to do pose recovery computations that involve solving nonlinear (but polynomial) systems of equations via iterative, homotopy, or other suitable direct or least square methods. Also it enables one to analyze, via the use ....

S. Ganapathy. Decomposition of transformation matrices for robot vision. Pattern Recognition Letters, 2:401--412, 1984.

....in the computer vision community. The earliest camera calibration methods were formulated as the estimation of the 3 Theta 4 perspective transformation 1 matrix (e.g. see [7, pages 481 482] Some methods also proposed computing the camera parameters from the perspective transformation matrix [19]. The major disadvantage of these methods is that they do not model nonlinear lens distortion effects. Tsai [27, 34] proposed a method in which the camera calibration could proceed in two stages. The first stage computes the 3D position and orientation of the camera (extrinsic parameters) In the ....

..... Gammax n Gammay n Gammaz n 0 0 0 r nxn r n yn r n z n Gamma1 0 r n 0 0 0 Gammax n Gammay n Gammaz n c n xn c n yn c n z n 0 Gamma1 c n 3 7 7 7 7 7 5 : 15) The W is a standard change of variables found in the computer vision literature which linearizes the above equations [16, 19, 36]: W 1 = f u R 1 r 0 R 3 ; W 2 = f v R 2 c 0 R 3 ; W 3 = R 3 ; 16) w 4 = f u t 1 r 0 t 3 ; w 5 = f v t 2 c 0 t 3 ; w 6 = t 3 : where R 1 = r 11 ; r 12 ; r 13 ] T , R 2 = r 21 ; r 22 ; r 23 ] T , and R 3 = r 31 ; r 32 ; r 33 ] T for notational shorthand. In other words, the W ....

S. Ganapathy. Decomposition of transformation matrices for robot vision. In Proceedings of IEEE International Conference on Robotics and Automation, pages 130--139, Atlanta, Georgia, 1984.

....an error in the value for an extrinsic parameter might be compensated for by an error in the value obtained for an intrinsic parameter. Several procedures have been presented with the purpose of extracting from the perspective transformation matrix the extrinsic and intrinsic camera parameters [Str84, Bro86, Gan84, Fau86]. The manual of Photogrammetry [Phot] claims that the strong coupling that exists between intrinsic parameters (principal point, focal length, etc. and extrinsic parameters (pose of the camera) can be expected to result in unacceptably large variances for these projective parameters when ....

K. Ganapathy, "Decomposition of Transformation Matrices for Robot Vision", IEEE, pp. 130-139, 1984.

....estimation, flexible setup. 1 Motivations Camera calibration is a necessary step in 3D computer vision in order to extract metric information from 2D images. Much work has been done, starting in the photogrammetry community (see [2, 4] to cite a few) and more recently in computer vision ([9, 8, 23, 7, 26, 24, 17, 6] to cite a few) We can classify those techniques roughly into two categories: photogrammetric calibration and self calibration. Photogrammetric calibration. Camera calibration is performed by observing a calibration object whose geometry in 3 D space is known with very good precision. ....

S. Ganapathy. Decomposition of transformation matrices for robot vision. Pattern Recognition Letters, 2:401--412, Dec. 1984.

.... [27] and [3] The pose estimation algorithm presented in this Section decomposes of an image to mosaic homography matrix, in order to nd the rotation matrix and displacement vector relating the camera frame to a world frame (extrinsic parameters) In this sense, it relates to the work of Ganapathy[12], where the extrinsic parameters are recovered directly from a camera projection matrix. The use of image homographies induced by a plane in the scene has been explored by Faugeras and Lustman[8] for robot navigation tasks. They have shown how the homographies could be used to directly recover ....

S. Ganapathy. Decomposition of transformation matrices for robot vision. In Proc. 1st IEEE Conf. Robotics, pages 130-139. IEEE, 1984.

....The latter involves using homogeneous coordinates to linearly model the perspective projection. The rotation and translation can be mathematically extracted by using either prior knowledge of the focal length, digitization scale factors, and offsets, or analytically deriving all the parameters[Ganapathy 84] Strat 87] Strat determines the parameters geometrically which may provide some insight when the equations fail. On the other hand, Ganapathy s derivation is based on the mathematical equations and constraints of the transformation. In addition [Ganapathy 84] attempts to decompose the system ....

....deriving all the parameters[Ganapathy 84] Strat 87] Strat determines the parameters geometrically which may provide some insight when the equations fail. On the other hand, Ganapathy s derivation is based on the mathematical equations and constraints of the transformation. In addition [Ganapathy 84] attempts to decompose the system parameters robustly, in the case where there are errors in the transformation matrix, by constraining the system in a symmetric fashion. 3.7 Results The results of the calibration between the CT data and two specific radiographs are shown in Figures 3.2 3.3. ....

S. Ganapathy, "Decomposition of Transformation Matrices for Robot Vision," IEEE Int'l Conf. on Robotics and Automation, 1984, 130139.

....required. Some of these iterative solutions are discussed below. Since the object pose from a single view problem is nonlinear, choices for (i) the mathematical representation of the problem, ii) the error function to be minimized, and for (iii) the optimization method are crucial. Ganapathy [10] and others (see for example [8] mention a linear solution for point correspondences. Rotation is represented by a 3 Theta3 matrix. The linear method is extremely susceptible to noise mainly because the orthogonality constraints associated with the rotation matrix are not taken into account. Yuan ....

....onto the image plane. An image point m which has pixel coordinates u and v has the following coordinates in the camera frame just described: x = u Gamma u 0 ) ff u y = v Gamma v 0 ) ff v z = 1 4 where u 0 , v 0 , ff u , and ff v are the intrinsic parameters of the camera model [10] [6] 29] Let X, Y , and Z be the camera coordinates of a space point M which projects onto the image at m. We have: 8 : x = X Z y = Y Z (1) Moreover, the point m is constrained to lie on an image line and the equation of this line is: ax by c = 0 (2) By substituting eq. 1) in ....

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S. Ganapathy. Decomposition of transformation matrices for robot vision. Pattern Recognition Letters, 2(6):401--412, December 1984.

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S. Ganapathy. Decomposition of Transformation Matrices for Robot Vision. In Proceedings of the IEEE International Conference on Robotics and Automation, pages 130--139, Atlanta (GA), USA, March 1984.

No context found.

S. Ganapathy. Decomposition of transformation matrices for robot vision. Pattern Recognition Letters, 2(6):401--412, December 1984.

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S. Ganapathy. Decomposition of transformation matrices for robot vision. Pattern Recognition Letters, 2(6):401--412, December 1984.

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S. Ganapathy. Decomposition of transformation matrices for robot vision. Pattern Recognition Letters, 2(6):401412, December 1984.

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Ganapathy, S., Decomposition of transformation matrices for robot vision. In Proc. IEEE Int. Conf. Robotics and Automation, Atlanta, GA, Mar. 1984.

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S. Ganapathy, "Decomposition of Transformation Matrices for Robot Vision," Proc. IEEE Int'l Conf. Robotics and Automation, pp. 130-139, 1984.

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S. Ganapathy, "Decomposition of Transformation Matrices for Robot Vision", Proceedings of Int. Conf. On Robotics and Automation, pp. 130-139, 1984.

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S. Ganapathy. Decomposition of transformation matrices for robot vision. In Proc. IEEE Int.Conf. Robotics and Automation, pp. 130--139, 1984.

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