Imposing Differential Constraints on Radial Distortion Correction
Many radial distortion functions have been presented to describe the mappings caused by radial lens distortions in common commercially available cameras. For a given real camera, no matter what function is selected, its innate mapping of radial distortion
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stract. Many radial distortion functions have been presented to describe the mappings caused by radial lens distortions in common commercially available cameras. For a given real camera, no matter what function is selected, its innate mapping of radial distortion is smooth, and the signs of its first and second order derivatives are fixed. However, such differential constraints have been never considered explicitly in existing methods of radial distortion correction for a very long time. The differential constraints we claimed in this paper are that for a given real camera, the signs of the first and second order derivatives of the radial distortion function should remain unchanged within the feasible domain of the independent variable, although over the whole domain, or outside of the feasible domain, the signs may change many times. Our method can be somewhat treated as a regularization of the distortion function within the viewing frustum. We relax the differential constraints by using a deliberate strategy, to yield the linear inequality constraints on the unknown coefficients of the radial distortion function. It seems that such additional linear inequalities are not difficult to deal with in recent existing methods of radial distortion correction. The main advantages of our method are not only to ensure the recovered radial distortion function satisfy differential constraints within the viewing frustum, but also to make the recovered radial distortion function working well in case of extrapolation, caused by the features used for distortion correction usually distributed only in the middle part, but rarely near the boundary of the distorted image. The experiments validate our approach.
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Introduction
The ideal pinhole model is often employed in algorithms of 3D recovery from 2D images in the field of computer vision. Unfortunately, for common commercially available cameras, they usually do not strictly satisfy the ideal pinhole model, i.e., some deviations may exist. Such deviations can be more complex, and are called as lens distortions in literature [1]. There are many methods to model lens distortions. The most famous model was proposed by Brown [1] which described the radial, decentring and prism distortions. In fact, among these distortions, c Springer International Publishing Switzerland 2015 D. Cremers et al. (Eds.): ACCV 2014, Part I, LNCS 9003, pp. 384–398, 2015. DOI: 10.1007/978-3-319-16865-4 25
Imposing Differential Constraints on Radial Distortion Correction
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radial distortion is the most significant in recent cameras [2–12]. Other types of distortions are often little, and can be omitted in the calibration procedure of distortion correction. Many kinds of radial distortion functions are presented to describe the radial distortion [2–12]. If we assume the center of radial distortion is known in advance, we can define the distance from the original distorted image point to the center of radial distortion as the distorted radius rd , and the distance corresponding to the undistorted image point as the un
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