This paper addresses the question of identifying the right camera direct or inverse distortion model, permitting a high subpixel precision to fit to real camera distortion. Five classic camera distortion models are reviewed and their precision is compared for direct or inverse distortion. By definition, the three radially symmetric models can only model a distortion radially symmetric around some distortion center. They can be extended to deal with non-radially symmetric distortions by adding tangential distortion components, but still may be too simple for very accurate modeling of real cameras. The polynomial and the rational models instead miss a physical or optical interpretation, but can cope equally with radially and non-radially symmetric distortions. Indeed, they do not require the evaluation of a distortion center. When requiring high precisions, we found that the distortion modeling must also be evaluated primarily as a numerical problem. Indeed, all models except the polynomial involve a non-linear minimization, which increases the numerical risk. The estimation of a polynomial distortion model leads instead to a linear problem, which is secure and much faster. We concluded by extensive numerical experiments that, although high degree polynomials were required to reach a high precision of 1/100 pixels, such polynomials were easily estimated and produced a precise distortion modeling without overfitting. Our conclusion is validated by three independent experimental setups: the models were compared first on the lens distortion database of the Lensfun library by their distortion simulation and inversion power; second by fitting real camera distortions estimated by a non parametric algorithm; and finally by the absolute correction measurement provided by the photographs of tightly stretched strings, warranting a high straightness.
In this paper, we are concerned with the existence and uniqueness of multi-bump bound states of the nonlinear Schrödinger equations with electromagnetic potential
Image stereo-rectification is the process by which two images of the same solid scene undergo homographic transforms, so that their corresponding epipolar lines coincide and become parallel to the x-axis of image. A pair of stereo-rectified images is helpful for dense stereo matching algorithms. It restricts the search domain for each match to a line parallel to the x-axis. Due to the redundant degrees of freedom, the solution to stereorectification is not unique and actually can lead to undesirable distortions or be stuck in a local minimum of the distortion function. In this paper a robust geometric stereorectification method by a three-step camera rotation is proposed and mathematically explained. Unlike other methods which reduce the distortion by explicitly minimizing an empirical measure, the intuitive geometric camera rotation angle is minimized at each step. For un-calibrated cameras, this method uses an efficient minimization algorithm by optimizing only one natural parameter, the focal length. This is in contrast with all former methods which optimize between 3 and 6 parameters. Comparative experiments show that the algorithm has an accuracy comparable to the state-of-art, but finds the right minimum in cases where other methods fail, namely when the epipolar lines are far from horizontal.
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