A Precision Analysis of Camera Distortion Models
A Precision Analysis of Camera Distortion Models
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DOI：
10.1109/tip.2017.2686001
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发表时间：
2017-06-01
影响因子：
10.6
通讯作者：
Morel, Jean-Michel
中科院分区：
文献类型：
--
作者：
Tang, Zhongwei;von Gioi, Rafael Grompone;Morel, Jean-Michel
本文提出了正确的摄像机正、逆畸变模型的识别问题，以保证高的亚像素精度来拟合真实的摄像机畸变。综述了五种经典的摄像机畸变模型，并比较了它们在正畸变和逆畸变情况下的精度。根据定义，三个径向对称模型只能对围绕某个畸变中心径向对称的畸变进行建模。它们可以通过添加切向失真分量来扩展以处理非径向对称失真，但是对于真实的相机的非常精确的建模来说仍然可能太简单。多项式和有理模型反而错过了物理或光学解释，但可以同等地科普径向和非径向对称失真。实际上，它们不需要对畸变中心进行评估。当需要高精度时，我们发现失真建模也必须主要作为数值问题进行评估。事实上，除了多项式之外的所有模型都涉及非线性最小化，这增加了数值风险。多项式失真模型的估计反而导致线性问题，这是安全的并且快得多。通过大量的数值实验，我们得出结论，虽然需要高次多项式来达到1/100像素的高精度，但这样的多项式很容易估计，并产生精确的失真建模而不会过拟合。我们的结论是验证了三个独立的实验设置：模型进行了比较，首先在透镜畸变数据库的Lensfun库的失真模拟和反转功率;其次通过拟合真实的相机失真估计的非参数化算法;最后通过绝对校正测量提供的照片紧紧拉伸字符串，recrutting一个高的直线度。
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.