J. Weng, P. Cohen, and M. Herniou. Camera calibration with distortion models and accuracy evaluation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(10):965--980, October 1992.  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 ....

J. Weng, P. Cohen, and M. Herniou. Camera calibration with distortion models and accuracy evaluation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(10):965--980, October 1992.

....camera parameters. However, decisions about the type of camera calibration must take into account the fact that we use a wide angle lens to capture the activity over a wide area scene. Camera calibration techniques have been established across a range of requirements for accuracy and efficiency [49, 53]. However, the nature of a surveillance application based on a wide angle, static camera means that overcoming non linear distortion is significant whilst dynamic calibration is less important. An existing linear model [53] which does not take into account distortion, can serve as a starting ....

....established across a range of requirements for accuracy and efficiency [49, 53] However, the nature of a surveillance application based on a wide angle, static camera means that overcoming non linear distortion is significant whilst dynamic calibration is less important. An existing linear model [53], which does not take into account distortion, can serve as a starting platform for establishing a more accurate system based on the radial alignment model [49] Since these operations are computed off line, and it is only the resulting geometry that is used on line, the modelling can be quite ....

J. Weng, P. Cohen, and M. Herniou. "Camera calibration with distortion models and accuracy evaluation". IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(10), 1992. 33

....within a local window. Frequently a continuity constraint is used as well that results in rather smooth reconstruction. This additional constraint is unavoidable in homogeneous textured regions. If the orientation of the images is known it is also advisable to use the so called epipolar constraint[20]. Each corresponding point in one image has to lie on the projected line of sight of the other images. Therefore only one degree of freedom remains for each corresponding point. This leads to a significant improvement in accuracy as well in performance. A good collection and comparison of ....

J. Weng. Camera calibration with distortion models and accuracy evaluation. IEEE Trans. Patt. Anal. Machine Intell., 14:965--980, 1992.

....linear pinhole camera model. Most camera calibration methods estimate simultaneously the inverse radial distortion function and the parameters of the linear pinhole camera model. Therefore, classical camera calibration methods use calibration patterns or reference objects with known 3D structure [1, 2]. Thus, they can solve the calibration problem by establishing control points of which true coordinates are known, both in the 2D camera image and the 3D world. In practice, however, it is often necessary to perform computer vision tasks on images already recorded without any calibration object. ....

Juyang Weng, Paul Cohen, and Marc Herniou, "Camera calibration with distortion models and accuracy evaluation," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 14, no. 10, pp. 965--980, Oct. 1992.

....(D U) formulation in which the undistorted coordinates is expressed as a function of the distorted coordinates. 3) Although we consider only the radial distortion, the following discussion can be applied to another model involving higher order term or decentering distortion[12, 9] in Proc. ICPR2002, Vol. II, pp.584 587, Aug 2002. u =f (p d ) d =f (p u ) actual distortion 1000 2000 2000 Figure 1. Example of the distortion approximated by different formulations. The other is Undistorted to Distorted (U D) formulation, the distorted coordinates is expressed by ....

....to make a combined transformation with projection and distortion. Therefore, sometimes the U D model is used as an approximation of the former[6] The confusion is that the U D model is used as the exact formulation[4, 5, 16] and moreover the D U model is regarded as the approximation of the other[12, 17]. Such researches have not disclosed the reason of this usage, however, performed as well as the former method. Actually, almost vision applications require not the distortion parameters but just a corrected, distortion free image. Therefore, any formulation or even the nonparametric approach[18] ....

J.Weng, P.Cohen, M.Herniou, "Camera calibration with distortion models and accuracy evaluation," PAMI., 14(10), 965--980, 1992.

....may result in high calibration errors. The problem with these methods that compute the external and internal parameters at the same time arises from the fact that there is some kind of coupling between internal and external parameters that results in high errors on the camera internal parameters [28]. Another family of methods are those that use geometric invariants of the image features rather than their world coordinates, like parallel lines [6, 2] or the image of a sphere [19] The last kind of calibration techniques are those that do not need any kind of known calibration points. These ....

Weng J, Cohen P, Herniou M (1992) Camera calibration with distortion models and accuracy evaluation. IEEE Trans Pattern Anal Mach Intell 14(10): 965--980

....Methods that use known world points Most of the standard techniques for camera calibration for machine vision use a set of calibration points with known world coordinates. These are sometimes called control points. In laboratories, control points can be obtained using a calibration object [11] [22]. Outdoors, control points could be markings on the ground [17] or buildings whose positions can be verified from maps [18] If the aspect ratio is unknown then a three dimensional calibration object is required [11] i.e. the points cannot be coplanar) As a 3D object one can use a planar object ....

....result in unacceptably large variances for these particular projective parameters when recovered on a frame by frame basis . Despite this problem the calibration can still be used to accurately measure the position of an object in the workspace from it s image position in a stereo image pair. In [22], a simulation of camera calibration with noisy data resulted in an error greater or equal to 0:5 in both the focal length and the external parameters. This happened even with a simulation of a simple pinhole camera model with no lens distortion. Despite this error it was possible to use these ....

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Weng, J et al. "Camera Calibration with Distortion Models and Accuracy Evaluation" IEEE Trans. Pattern Anal. Machine Intell. 14,965-980 (1992) 47

....increase the reliability of the adjoining placement of dominoes. 4 Establishing Correspondences The following describes an algorithm for automatically finding rectilinear grids, imaged as described in Section 1. Grid like structures are often employed as calibration targets (see for instance [2, 9, 15, 21, 22]) A grid makes a good calibration target because it (a) uses features with maximum contrast (dots on a background) b) spans the imaged area evenly (so the resulting camera model is accurate for the entire image) and (c) presents a recognizable macro configuration (the grid structure) Our ....

J. Weng, P. Cohen and M. Herniou, "Camera Calibration with Distortion Models and Accuracy Evaluation", in IEEE Trans. on Pattern Analysis 84 Machine Intelligence, vol. 14 no. 10, Oct. 1992, pp. 965-980.

.... in figure 1, this notation means that images containing negative distortion, # 0, exhibit barrelling and such images are corrected by applying positive distortion (and vice versa for pin cushion images) Note that this notation is equivalent to that of Tsai [11] Li and Lavest [6] Weng et al. [12] and others up to first order. Figure 1. Radial Lens Distortion (left to right) Pin Cushion (# 0 # 0 # 0) Undistorted (# = 0 # = 0 # = 0) and Barrelling (# 0 # 0 # 0) The centre of distortion is not in general in the centre of the image, but will move as the camera internal ....

J. Weng, P. Cohen, and M. Herniou. Camera calibration with distortion models and accuracy evaluation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(10):965--980, October 1992.

....reality system in surgical planning applications. Calibration has been an important aspect of research in augmented reality, as well as in other fields, including robotics and computer vision. Camera calibration, in particular, has been studied extensively in the computer vision community (e.g. [26, 34, 24]) Its use in computer graphics, however, has been limited. Deering [7] has explored the methods required to produce accurate high resolution head tracked stereo display in order to achieve sub centimeter virtual to physical registration. Azuma and Bishop [1] and Janin et al. 21] describe ....

J. Weng, P. Cohen, and M. Herniou. Camera calibration with distortion models and accuracy evaluation. IEEE Trans. on Pattern Analysis and Machine Intelligence, 14(10):965--980, 1992.

....and, as a second step, the rest of parameters are iteratively computed. These techniques permit a rapid calibration reducing considerably the number of iterations. Moreover, the convergence is nearly guarantee due to the linear guess obtained in the first step. Examples: Tsai [6] Weng [7] and Wei [2] This article is a detailed survey of some of the most used calibrating techniques. A great deal of e#ort has been done to present the survey using the same notation. Moreover, the techniques have been implemented and comparative results are shown and discussed. The article is ....

....d P Y I X O I R Y R X R R O C W K Image coordi nate system Step 1 Step 2 Step 3 Step 4 Figure 1: The geometric relation between a 3D point and its 2D projection. In the following four di#erent camera models (Faugeras Toscani [3] FaugerasToscani with distortion [4] Tsai [6] and Weng [7]) are explained in detail considering how they carry out this four steps. 2.1. Changing from the world to the camera coordinate system Changing the system of coordinates of the world to the system of coordinates of the camera is carried out in the same way in the 4 surveyed models. This ....

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J. Weng, P. Cohen, and M. Herniou, "Camera calibration with distortion models and accuracy evaluation," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 14, pp. 965--980, October 1992.

....Some of these are Structure from Motion problems where aprioriknowledge of the object is not available. These methods use point features, generally, and require a large number of features per image to solve for the many state variables. Batch nonlinear optimization methods are also discussed [73] where estimates are made by analyzing an entire sequence of images at once. For real time applications such as robotic control, visual servoing, etc. batch analysis is not a feasible option. Extended Kalman filtering is the most widely used method of recursive estimation. A recursive method of ....

....as input. An EKF is used for estimation. The camera model uses the image plane as the origin to aid in parameterizing the imaging geometry. A single parameter, the depth, provides the estimate of the state for each structure point in contrast to other approaches that use three parameters per point [75, 73]. This parameterization is claimed to be more stable for recursive estimation than previous methods. However, recovery of the 3 D x and y point coordinates is subject to the noise present in the image features and could result in significant errors. Quaternions are used to represent rotation ....

J. Weng, P. Cohen, and M. Herniou, "Camera calibration with distortion models and accuracy evaluation," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 14, no. 10, pp. 965--980, October 1992.

....from 1958, which studies about 80 different approaches from the photogrammetry literature. There are analytic solutions for sets of three [3] four [5] and six points [4] However, iterative approaches using a greater number of points achieve a higher precision in the presence of noise [6, 12, 15]. Weng et al. 15] minimize the distances between the observations and the projections of the 3D model points onto the image plane. Here, we use an objective function which normalizes this distance by the covariance matrix of the observed point. Often using line features, rather than points, ....

....studies about 80 different approaches from the photogrammetry literature. There are analytic solutions for sets of three [3] four [5] and six points [4] However, iterative approaches using a greater number of points achieve a higher precision in the presence of noise [6, 12, 15] Weng et al. [15] minimize the distances between the observations and the projections of the 3D model points onto the image plane. Here, we use an objective function which normalizes this distance by the covariance matrix of the observed point. Often using line features, rather than points, results in higher ....

J. Weng, P. Cohen, and M. Herniou. Camera calibration with distortion models and accuracy evaluation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(10):965--980, 1992.

....may result in high calibration errors. The problem with these methods that compute the external and internal parameters at the same time arises from the fact that there is some kind of coupling between internal and external parameters that result in high errors on the camera internal parameters [27]. 2 Fr ed eric Devernay, Olivier Faugeras Another family of methods is those that use geometric invariants of the image features rather than their world coordinates, like parallel lines [6,2] or the image of a sphere [19] The last kind of calibration techniques is those that do not need any kind ....

J. Weng, P. Cohen, and M. Herniou. Camera calibration with distortion models and accuracy evaluation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(10):965--980, October 1992.

....the algorithms introduced in subsequent sections. In order to be able to use these algorithms the intrinsic camera parameters must be known in advance. Assuming a pin hole camera model with radial distortion we calculate the intrinsic camera parameters with a method introduced in [Tsai, 1987] and [Weng et al. 1992] prior to system operation. Thus we determine the following intrinsic camera parameters: ffl Focal length f of the camera 33 34 CHAPTER 4. OPTICAL HEAD MOTION TRACKING ffl Camera aspect ratio, s u and s v ffl Location of principal point (c 0 ; r 0 ) ffl Radial distortion coefficient 4.2 The ....

Weng, J., Cohen, P., and Herniou, M. (1992). Camera calibration with distortion models and accuracy evaluation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(10):965--980.

....eleven parameters. Six extrinsic parameters define the position and orientation of the camera with respect to the world coordinate system. Five intrinsic parameters describe the optical properties of the camera, including a 1st order approximation of a coefficient to correct for radial distortion (Weng et al. 1992). Given at least seven non coplanar 3D points and their corresponding 2D image positions, then the camera model parameters can be determined (eleven correspondences are required for a fully optimised solution) Correspondence information is supplied by the system operator via a graphical user ....

Weng, J., Cohen, P. and Herniou, M., 1992. Camera calibration with distortion models and accuracy evaluation. In: IEEE Trans. PAMI, vol. 14, pp 965 --- 980.

....issue in computer vision as soon as accurate metric information have to be extracted from a set of 2D images. This is a research area that received much attention since the early 70 s first in the photogrammetry community (e.g. 1] then in the computer vision and robotics communities (e.g. [3, 9, 11, 10, 6], etc. Most of the approaches consider the calibration issue as a registration problem that consists in determining the relationship between 3D coordinates of points (or other features: lines, ellipses, and their 2D projections in the image plane. These 3D features are usually part of a ....

....and their versatility: the camera model can be very general. The main drawback is that they may be subject to local minima and, worse, divergence. Therefore they usually require a good guess of the solution to ensure a correct convergence. ffl two steps techniques. These approaches (e.g. [9, 11, 10]) consider a linear estimation of some parameters while the others are estimated iteratively. Constraints (such as the Tsai s radial alignment constraint) are considered to linearize the estimation of some parameters. These algorithms allow a faster convergence of the algorithm. Let us finally ....

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J Weng, P. Cohen, and M. Herniou. Camera calibration with distortion models and accuracy evaluation. IEEE trans. on Pattern Analysis and Machine intelligence, 14(10):965--980, October 1992. Irisa

....of the features measured in 2D is assumed. Various camera calibration methods were introduced in a literature. The classical approach [9] based on methods used in photogrammetry, gives precise results but it is computationally extensive. Several simplification were made (such as [11] and [13]) but the nonlinear search used there may lead into computational instability. There are also methods which combine both minimization and closed form solution [4, 5, 7, 15] All these methods are based on physical camera parameters. Implicit camera calibration methods [12] on the other hand, use ....

J. Weng, P. Cohen, and M. Herniou. Camera calibration with distortion models and accuracy evaluation. IEEE Trans. on Pattern Analysis and Machine Intelligence, 14(10):965--980, October 1992.

....geometrically and radiomertrically calibrated. Algorithms for geometric calibration (recovering the intrinsic and extrinsic camera parameters, and their accuracy) have been subject of extensive research in the computer vision community, see [HS93] Fau93] for a textbook introduction; DA89] and [WCH92] for a review of papers; and [GM96] for recent results. The work on radiometric calibration and noise models of CCD cameras is limited, HK94] Radiometric calibration procedures are studied in videometric applications [LF90] photogrammetry [Bey92] astronomy [SHL 95] Mcl89] video ....

Juyang Weng, Paul Cohen, and Marc Herniou. Camera calibration with distortion models and accuracy evaluation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(10):265--980, Oct 1992.

....with a linear method in the first stage, and the remaining parameters are solved in the second stage with a nonlinear optimization method based on the initial values provided by another linear method. Unlike most of the other methods of using noncoplanar calibration points, e. g, 7] 8] 19] [25], 26] and [30] the image center is not estimated in the Tsai method [22] Instead, the image center and one scale factor are solved in another process described in [16] We have noticed that the nonlinear methods which estimate all the camera parameters including the image center can usually ....

....be solved up to a scale factor. In general, there are two ways to approach this problem. One is to compose f , s u and s v into two effective focal length parameters, namely, the horizontal and vertical effective focal length which eliminates the extra degree of freedom (refer to the Weng method [25]) Another way is suitable for a solid state camera and is adopted in the well known Tsai method [22] This is because the horizontal and vertical pixel spacing of the solid state camera can be directly obtained from the camera supplier. However, the horizontal pixel spacing will be rescaled with ....

[Article contains additional citation context not shown here]

J. Weng, P. Cohen and M. Herniou, "Camera Calibration with Distortion Models and Accuracy Evaluation," IEEE Trans. Pattern Anal. Machine Intell., vol. 14, no. 10, Oct. 1992, pp. 965-980.

....projection model and assume that the internal camera parameters are known [6] For such work, accurately calibrating the internal camera parameters is critical but the external camera calibration is not important. 1. 2 Related work More extensive reviews of calibration methods appear in [9] 10][11]. Most techniques for camera calibration use a set of points with known world coordinates (control points) Control points can be from a calibration object [11] or a known outdoor scene [9] The calibration process can be stated as follows: given a set of control points (X i ; Y i ; Z i ) and ....

....but the external camera calibration is not important. 1. 2 Related work More extensive reviews of calibration methods appear in [9] 10] 11] Most techniques for camera calibration use a set of points with known world coordinates (control points) Control points can be from a calibration object [11] or a known outdoor scene [9] The calibration process can be stated as follows: given a set of control points (X i ; Y i ; Z i ) and their image (x i ; y i ) find the external and internal parameters which will best map the control points to their image. A problem arises due to the interaction ....

Weng, J et al. "Camera Calibration with Distortion Models and Accuracy Evaluation" IEEE Trans. Pattern Anal. Machine Intell. 14,965-980 (1992)

....consists of some compound lens groups and various mechanical assembly. The relationship between the lens settings and the ICPs is quite complicated [6] One way to determine this relationship is to treat each configuration of lens settings as a monofocal lens and to perform camera calibration [5] for each configuration. However, this method is extremely inefficient because a motorized zoom lens usually has many configurations. In the past, Tarabanis et al. 4] proposed techniques for zoom lens calibration by using a special optical bench. They constructed a sparse table storing the ....

....and the translation vector between the origins of the world and the camera coordinate systems, t x , 1 t y , and t z . Among these CPs, the vertical pixel width, s v , can be obtained from the specification of the CCD camera. The remaining eleven CPs can be estimated by using Weng et al. s method [5], provided that a set of known calibration points are observed in the image. In the following, the 3 D world coordinates of the calibration points and their corresponding image measurements will be referred to as the calibration data. Since the influence of the aperture setting is negligible, as ....

J. Weng, P. Cohen, and M. Herniou. Camera calibration with distortion models and accuracy evaluation. IEEETransactions on Pattern Analysis and Machine Intelligence, 14(10):965-- 980, 1992.

....have been suggested for recovering lens distortion parameters. Tsai [1987] used known points in 3D space to recover some of the distortion parameters. Goshtasby [1989] utilized Bezier patches to model the distortions and used a uniform grid placed in front of the camera as a calibration object. Weng [1992] also used calibration objects to extract all the distortion parameters. All these methods fall in the category of stellar calibration [Brown, 1971] In contrast, Brown [1971] proposed a non metric approach that does not rely on known scene points. Instead, he relies on the fact that ....

J. Weng, P. Cohen, and M. Herniou. Camera calibration with distortion models and accuracy evaluation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(10):965--980, Oct 1992.

....with a high degree of precision and reproducibility. The robot is described in more detail in section 3. Camera calibration is a standard routine in photogrammetry (see [8,11,21] among many others) and has been discussed intensively in the computer vision society in the past decades, see [1,6,12,14,16,19,20] for a few examples. The calibration describes the relation between a known fixed world coordinate system and an image coordinate system. The world coordinate system is three dimensional and defines the absolute positions of the objects in the scene. The image coordinate system is two dimensional ....

....have used high quality cameras, optics, and film, the typical situation in computer vision is a low resolution CCD chip and optics of a moderate quality. During the last decades a large number of papers and books describing methods for camera calibration have been published. A few of these are [1,5,12,14,16,19,20]. A complete review of the publications within the area of camera calibration lies outside the scope of this work. However, section 2 offers a short review of two typical methods used to calibrate a single stationary camera. This paper describes a method whereby the DIKU robot camera system is ....

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J Weng, P. Cohen, and M. Heriou, Camera calibration with Distortion Models and Accuracy Evaluation, IEEE Transactions on Pattern Analysis and Machine Intelligence vol. 14, no. 10, p. 965-980, 1992

....with d r = a 1 ( r 2 R 2 0 Gamma 1) a 2 ( r 4 R 4 0 Gamma 1) 8) r = p (x Gamma x 0 ) 2 (y Gamma y 0 ) 2 : 9) The constant R 0 is set to half of the image border length. This computation of the distortion exhibits better numerical stability than a conventional model [7, 17]. The intrinsic parameters f x ; f y ; x 0 ; y 0 ; a 1 ; a 2 are not accurately known and therefore for each camera the number of parameters is now 14 6=20. A similar equation holds for the right image coordinates. Spiess Li: Kinematic Calibration and Online Computation of Epipolar Geometry 4 ....

J. Weng, P. Cohen, M. Herniou: "Camera Calibration with Distortion Models and Accuracy Evaluation. " IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 14, No. 10, Oct. 1992.

....iterative methods it then finds both external parameters (position and orientation) and internal camera parameters. The internal camera parameters include the parameters of the pinhole camera model (principal point, principal distance) and the parameters of lens distortion. See also Weng et al. [13]. Projective constraints: Under perspective projection, straight lines in space project to straight lines in the image. With real lenses the lines appear instead to be slightly to moderately curved. By searching for lens distortion parameters which straighten the lines the Plumb Line method and ....

J. Weng et al. Camera Calibration with Distortion Models and Accuracy Evaluation. IEEE Trans. PAMI 14,965-980 (1992)

....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 second stage he estimates the camera intrinsic parameters, such as the focal length and distortion coefficients. Weng et al. [36] proposed a camera calibration method to estimate intrinsic and extrinsic camera parameters. Weng models tangential lens distortions, as well as radial lens distortions, and estimates the distortion parameters through a separate nonlinear optimization method. More recent approaches to camera ....

..... 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 ....

[Article contains additional citation context not shown here]

J. Weng, P. Cohen, and M. Herniou. Camera calibration with distortion models and accuracy evaluation. IEEE Trans. on Pattern Analysis and Machine Intelligence, PAMI-14(10):965--980, 1992.

....v nj v 0j and the desired accuracy #u can be up to 1000 for high speed (see e.g. section 4.1) There are mainly two e#ects that have to be considered. The first is a nonlinear mapping due to lens distortions. This mapping is constant so that it can be identified o#ine and compensated online [9]. The image point (U, V ) in the real (distorted) image can be calculated by the point (u, v) of an idealized image by third order polynoms U = w 10 w 11 u w 12 v w 13 u 2 w 14 uv w 15 v 2 w 16 u 3 w 17 u 2 v w 18 uv 2 w 19 v 3 (7) V = w 20 w 21 u w 22 v w 23 u ....

J. Weng, P. Cohen, and M. Herniou. Camera calibration with distortion models and accuracy analysis. IEEE Trans. on Pattern Analysis and Machine Intelligence, 14(10):965--980, Oct. 1992.

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J. Weng, P. Cohen, and M. Herniou. Camera calibration with distortion models and accuracy evaluation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(10):965--980, October 1992.

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J. Weng, P. Cohen, M. Herniou, Camera calibration with distortion models and accuracy evaluation, IEEE Transactions on Pattern Analysis and Machine Intelligence 14 (10) (1992) 965--980.

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J. Weng, Paul Cohen, and M. Herniou, "Camera calibration with distortion models and accuracy evaluation, " IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), vol. 14(10), Oct 1992.

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Weng, J., Cohen, P., and Herniou, M. Camera Calibration with Distortion Models and Accuracy Evaluation. IEEE Transc. On Pattern Anal. and Machine Intelligence, 14, 965-980, 1992.

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J. Weng, P. Cohen, and M. Herniou. Camera calibration with distortion models and accuracy evaluation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(10):965--980, Oct 1992.

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J. Weng, P. Cohen, and M. Herniou. Camera calibration with distortion models and accuracy evaluation. IEEE Trans. on Pattern Analysis and Machine Intelligence, 14(10):965--980, 1992.

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J. Weng, P. Cohen, and M. Herniou, #Camera calibration with distortion models and accuracy evaluation", IEEE Trans. on Pattern Analysis and Machine Intelligence, PAMI-14#10#, pp. 965#980 #1992#.

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