Nonmetric calibration of camera lens distortion: Differential methods and robust estimation

Electr. Eng. Dept., Assiut Univ., Egypt
IEEE Transactions on Image Processing (Impact Factor: 3.63). 09/2005; 14(8):1215 - 1230. DOI: 10.1109/TIP.2005.846025
Source: IEEE Xplore

ABSTRACT This paper addresses the problem of calibrating camera lens distortion, which can be significant in medium to wide angle lenses. Our approach is based on the analysis of distorted images of straight lines. We derive new distortion measures that can be optimized using nonlinear search techniques to find the best distortion parameters that straighten these lines. Unlike the other existing approaches, we also provide fast, closed-form solutions to the distortion coefficients. We prove that including both the distortion center and the decentering coefficients in the nonlinear optimization step may lead to instability of the estimation algorithm. Our approach provides a way to get around this, and, at the same time, it reduces the search space of the calibration problem without sacrificing the accuracy and produces more stable and noise-robust results. In addition, while almost all existing nonmetric distortion calibration methods needs user involvement in one form or another, we present a robust approach to distortion calibration based on the least-median-of-squares estimator. Our approach is, thus, able to proceed in a fully automatic manner while being less sensitive to erroneous input data such as image curves that are mistakenly considered projections of three-dimensional linear segments. Experiments to evaluate the performance of this approach on synthetic and real data are reported.

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    • "이러한 교정이 필요한 이유는 대량 생산 으로 인해 렌즈의 특성이 렌즈마다 다양하기 때문이며, 초점이나 줌 설정에 따라 달라질 수 있기 때문이다 [8] "
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    ABSTRACT: We propose an interpolation method considering barrel distortion of fisheye lens using nearest pixels on a corrected image. The correction of barrel distortion comprises coordinate transformation and interpolation. This paper focuses on interpolation. The proposed interpolation method uses nearest four coordinates on a corrected image rather than on a distorted image unlike existing techniques. Experimental results show that both subjective and objective image qualities are improved.
    07/2013; 50(7). DOI:10.5573/ieek.2013.50.7.181
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    • "Equidistant fish-eye cameras are designed such that the distance between a projected point and the distortion centre of the image is proportional to the incident angle of the projected ray, scaled only by the focal length. A commonly used model of radial distortion is the odd-ordered polynomial model [1] [2] [3] [4] [5]. However, due to the particularly high levels of distortion present in fish-eye cameras, there have been several alternative models developed, including the Fish-Eye Transform [6], the Polynomial Fish-Eye Transform [6], the Field Of View model [7], the Division model [8] [9] and the Rational Function model [10] [11] [12]. "
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    ABSTRACT: Radial distortion in an image is a geometric distortion that causes a non-linear variation in resolution across the image, with a higher spatial resolution in the central areas of the image, and lower resolution in the peripheral areas of the image. This is particularly evident in fish-eye cameras, with very wide fields-of-view. Equidistant fish-eye cameras are designed such that the distance between a projected point and the distortion centre of the image is proportional to the incident angle of the projected ray, scaled only by the focal length. The perspective of the projection of a given scene in an equidistant fish-eye camera differs greatly from the projection of the same scene in a rectilinear pin-hole camera. For example, while the field-of-view is significantly larger for a fish-eye camera, the non-linear radial distortion of the scene results in straight lines mapping to curves of a particular shape in the equidistant fish-eye image.In this paper, we describe equidistant fish-eye perspective in terms of the projection of sets of parallel lines to the equidistant fish-eye plane, and derive an equation that describes the projection of a straight line. We also demonstrate how the shape of a projected straight line can be accurately described by arcs of circles on the distorted image plane. We also describe an application of the equidistant perspective properties, by showing that the distortion centre of an equidistant fish-eye camera can be estimated by the extraction of the vanishing points. Additionally, we examine the accuracy of this estimation procedure on a large set of synthetically created images and a smaller set of real images from fish-eye cameras.
    Image and Vision Computing 03/2010; 28(3-28):538-551. DOI:10.1016/j.imavis.2009.09.001 · 1.59 Impact Factor
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    • "Utilizing all the parameter values calculated in the first step, camera lens distortion coefficient is calculated in the second step based on a camera model that incorporates distortion, using linear least squares method. Then the whole procedure is repeated for a number of time, using the inversed formulation of distortion model [14], to improve all the parameters. In [12], Weng et al. used an iterative nonlinear optimization approach in the second step, that computes and improves all the parameters. "
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    ABSTRACT: A methodology for determining spacecraft attitude and autonomously calibrating star camera, both independent of each other, is presented in this paper. Unlike most of the attitude determination algorithms where attitude of the satellite depend on the camera calibrating parameters (like principal point offset, focal length etc.), the proposed method has the advantage of computing spacecraft attitude independently of camera calibrating parameters except lens distortion. In the proposed method both attitude estimation and star camera calibration is done together independent of each other by directly utilizing the star coordinate in image plane and corresponding star vector in inertial coordinate frame. Satellite attitude, camera principal point offset, focal length (in pixel), lens distortion coefficient are found by a simple two step method. In the first step, all parameters (except lens distortion) are estimated using a closed-form solution based on a distortion free camera model. In the second step lens distortion coefficient is estimated by linear least squares method using the solution of the first step to be used in the camera model that incorporates distortion. These steps are applied in an iterative manner to refine the estimated parameters. The whole procedure is faster enough for onboard implementation.
    American Control Conference, 2009. ACC '09.; 07/2009
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