Stein G. P., "Internal camera calibration using rotation and geometric shapes", Master's thesis, Massachusetts Institute of Technology, 1993.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of distortion from the projection on the image plane, because we want to calibrate the distortion without knowing anything about internal camera parameters. Consequently, in our model, the center of distortion (c x ,c y ) will be different from the principal point (C x ,C y ) It has been shown [24] that this is mainly equivalent to adding decentering distortion terms to the distortion model of Eq. 6. A higher order effect of this is to apply an (very small) affine transformation to the image, but the affine transform of a pinhole camera is also a pinhole camera (i.e. this is a linear ....

....[3, 4, 25, 27] First, it makes very few assumptions on the observed world: there is no need for a calibration grid [3, 4, 27] All it needs is images of scenes containing 3D segments, like interior scenes or city scenes. Second, it is completely automatic, and camera motion need not to be known [24, 25]. It can even be applied to images acquired offline, which could come from a surveillance videotape or a portable camcorder. Results of distortion calibration and comparison with a gridbased calibration method [18] are shown for several lenses and cameras. If we decide to calibrate distortion, ....

Stein GP (1993) Internal camera calibration using rotation and geometric shapes. Master's thesis, Massachusetts Institute of Technology, June 1993. AITR-1426

....in our method works well if radial distortion is not too great. It also works well if the fiducials are near the location of the enhancement. As a preliminary step, we measured the radial distortion for our camera setup. Radial distortion was measured using the plumb line method [ Brown, 1971, Stein, 1993 ] for a 16mm and 25mm lens. The results are summarized in Table A.1. Plots of the distortion are also shown in Figures A 1 and A 2. In order to gain some insight into the effect of radial distortion on our method we will attempt to quantify the difference between the radial distortion model Lens ....

Gideon P. Stein. Internal camera calibration using rotation and geometric shapes. Master's thesis, MIT, February 1993. MIT/AI/TR 1426.

....of distortion from the projection on the image plane, because we want to calibrate is the distortion without knowing anything about internal camera parameters. Consequently, in our model, the center of distortion (c x , c y ) will be different from the principal point (C x , C y ) It was shown [23] that this is mainly equivalent to adding decentering distortion terms to the distortion model of equation 6. A higher order effect of this is to apply an (very small) affine transformation to the image, Straight Lines Have to Be Straight 3 but the affine transform of a pinhole camera is also a ....

....[3,4,24,26] First, it makes very few assumptions on the observed world: there is no need for a calibration grid [3,4,26] All it needs is images of scenes containing 3 D segments, like interior scenes or city scenes. Second, it is completely automatic, and camera motion needs not to be known [23,24]. It can even be applied to images acquired off line, which could come from a surveillance videotape or a portable camcorder. Results of distortion calibration and comparison with a grid based calibration method [18] are shown for several lenses and cameras. If we decide to calibrate distortion, ....

Gideon P. Stein. Internal camera calibration using rotation and geometric shapes. Master's thesis, Massachusetts Institute of Technology, June 1993. AITR-1426.

....to obtain the pose of the camera and some of the intrinsic parameters. Methods for computing the camera parameters by tracking features in the image, without using special patterns for calibration, have been developed by Faugeras [40] Hartley [30] Dron [20] McLauchlan [28] Brady [7] Stein [8] and Basu [2] The main difference between these methods, called active and the previous, called passive, is the first require the camera be able to perform accurate and controlled movements. The use of the degrees of freedom of the camera introduces additional information compared to the static ....

G. Stein, "Internal Camera Calibration using Rotation and Geometric Shapes", Msc. Thesis, MIT, 1993.

....lens system in the distal tip. This distortion strongly affects the solution from the algorithm when the foe is near the image boundary, and its parameters should be estimated as well. 5.2. 3 Camera Calibration using Rotation The method we use for estimating the camera parameters is detailed in [78] and involves performing calibration from image data only; no actual measurements of object distances or sizes in the real world need be done. If we rotate a camera about an axis Omega = Omega x ; Omega y ; Omega z ) by an angle Gamma , then the world point R will have rotated to a point ....

....from image data only; no actual measurements of object distances or sizes in the real world need be done. If we rotate a camera about an axis Omega = Omega x ; Omega y ; Omega z ) by an angle Gamma , then the world point R will have rotated to a point R 0 given by Rodriguez s formula [78]: R 0 = ThetaR = h cos I sin Q (1 Gamma cos ) Omega Gamma T i R (5:12) Q = 2 6 6 4 0 Gamma Omega z Omega y Omega z 0 Gamma Omega x Gamma Omega y Omega z 0 3 7 7 5 (5:13) By projection, we find that the image point r 0 corresponding to the new world point R ....

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Gideon P. Stein. Internal camera calibration using rotation and geometric shapes. Master's thesis, Massachusetts Institute of Technology, 1993.

....on the curve from [1] The results show that the overall change in our case is about 2 while in the case of data from [1] it is about 5 . We do not know why the distortion of our lens decreases with increasing distance while it increases for data in [1] Similar results are reported by Stein in [6] who also found that distortion decreases with growing distance. Overall conclusion could be that the radial distortion certainly changes with the change of distance between the lens and the object but we are not able at the moment judge whether it has to be modeled and when it is important to ....

Gideon P. Stein. Internal camera calibration using rotation and geometric shapes. Master's thesis, Massatchusetts Institute of Technology, February 1993.

....cames with the fact that eye movements simplify the calibration problem. Methods for computing the camera parameters by tracking features in the image, without using special patterns for calibration, have been develloped by Faugeras [25] Hartley [21] Dron [14] McLauchlan [20] Brady [3] Stein [4] and Basu [1] Faugeras observed that there is a close connection between the calibration of a single camera and the epipolar transformation obtained when the camera undergoes a displace1 ment. The epipolar transformation imposes two algebraic constraints on the camera calibration. Lisa Dron uses ....

G. Stein, "Internal Camera Calibration using Rotation and Geometric Shapes", Msc. Thesis, MIT, 1993.

....cames with the fact that eye movements simplify the calibration problem. Methods for computing the camera parameters by tracking features in the image, without using special patterns for calibration, have been developed by Faugeras [19] Hartley [16] Dron [11] McLauchlan [14] Brady [5] Stein [6] and Basu [2] We based our approach on the use of feature correspondences from a set of images where the camera has undergone pure rotation. The closer the features are located to the camera the more important it is that the camera does not undergo any translation during the rotation. A method ....

G. Stein, "Internal Camera Calibration using Rotation and Geometric Shapes", Msc. Thesis, MIT, 1993.

....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 ....

....of orientation [principal point and focal length] and exterior elements can be expected to result in unacceptably large variances for these particular projective parameters when recovered on a frame byframe basis . The main problem is the error in focal length. For more about this issue see [9][10]. Geometric objects whose images have some characteristic that is invariant to the actual position of the object in space, can be used to calibrate some of the internal camera parameters. Results based on the plumb line method [2] which uses the images of straight lines for calibrating lens ....

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Stein, G.P., "Internal Camera Calibration using Rotation and Geometric Shapes" AITR-1426, Master's Thesis, Massachussets Institute of Technology, Artificial Intelligence Laboratory (1993).

....reconstruction. 1. Introduction Radial lens distortion can be a significant factor in medium to wide angle lenses. These are typically the lenses used when performing image based 3D reconstruction of large objects or in a confined space. The errors can be 10 100 pixels at the edges of the image [12]. This paper describes a new method for lens distortion calibration using point correspondences in multiple views without the need to know either the 3D location of the points or the camera locations. In fact one can use the same point correspondence data which is to be used for subsequent vision ....

....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 its derivatives [1] 5] [12] [2] find the lens distortion without needing to find the external parameters or the other internal camera parameters. One or more images can be used. Unknown world coordinates: Stein [12] and Du and Brady [3] use corresponding points or edges in images where the camera has undergone pure ....

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G.P. Stein. Internal Camera Calibration using Rotation and Geometric Shapes. AITR-1426, Master's Thesis, Massachussets Institute of Technology, Artificial Intelligence Laboratory (1993).

....1 Introduction: Radial lens distortion can be a significant factor in medium to wide angle lenses. These are typically the lenses used when performing image based 3D reconstruction of large objects or in a confined space. The errors can be tens of pixels at the edges of the image [11]. This paper describes a new method for lens distortion calibration using point correspondences in multiple views. One does not need to know neither the 3D location of the points nor the camera locations. In fact one can use the same point correspondence data which is to be used by subsequent ....

....constraints: Under perspective projection, straight lines in space project to straight lines in the image. With real lenses the lines appear slightly to moderately curved. By searching for lens distortion parameters which straighten the lines the Plumb Line method and its derivatives [1] 5] [11] [2] find the lens distortion without needing to find the external parameters or the other internal camera parameters. One or more images can be used. Unknown world coordinates: Stein [11] and Du and Brady [3] use corresponding points or edges in images where the camera has undergone pure ....

[Article contains additional citation context not shown here]

Stein, G.P., "Internal Camera Calibration using Rotation and Geometric Shapes" AITR-1426, Master's Thesis, Massachussets Institute of Technology, Artificial Intelligence Laboratory (1993).

....A camera centered coordinate system is used, therefore the external calibration is not important. 1.2 Brief review of other methods and related work We provide here a brief review of the various approaches to camera calibration. More extensive reviews of calibration methods appear in [12] 18] [20]. Since the cameras used in machine vision are not designed to highly accurate specifications nor to be highly stable they might have to be calibrated frequently. Therefore, camera calibration must be kept simple and as quick as possible. 1.2.1 Methods that use known world points Most of the ....

....Results using the plumb line method [3] which uses the images of straight lines for calibrating lens distortion, a method for finding the aspect ratio using the image of a sphere [16] are given in section 7 for comparison to the rotation method. More details on these experiments can be found in [20]. 1.2.3 Methods that do not require known calibration points Since the traditional methods of camera calibration use known world coordinates they are not suitable for self calibration of mobile robots. It would be a great advantage to be able to calibrate a camera using only feature coordinates ....

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Stein, G.P., "Internal Camera Calibration using Rotation and Geometric Shapes" AITR-1426, Master's Thesis, Massachussets Institute of Technology, Artificial Intelligence Laboratory (1993).

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Stein G. P., "Internal camera calibration using rotation and geometric shapes", Master's thesis, Massachusetts Institute of Technology, 1993.

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G.P. Stein. Internal camera calibration using rotation and geometric shapes. In MIT AI-TR, 1993.

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Gideon P. Stein. Internal camera calibration using rotation and geometric shapes. Master's thesis, Massachusetts Institute of Technology, June 1993. AITR-1426.

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