摘要:
提出了一种基于空间平行线段的摄像机标定算法和理论. 1)当两条平行线段的比值已知时: a)该平行线段的$n$幅图像可提供关于摄像机内参数的2(n-1)个二次约束方程; b)如果图像极点同时也是已知的,则该平行线段的n幅图像可提供关于摄像机内参数的5n-6个约束方程,其中3(n-1)个为二次约束,n-2个为三次约束,n-1个为四次约束. 2)当两条平行线段的比值未知时,则该平行线段的n幅图像可提供关于摄像机内参数的2n-3个约束方程,其中n-2个为四次约束, n-1个为六次约束.在理论分析的基础上,本文给出了摄像机标定的具体算法.模拟实验和真实图像实验均证明了本文方法的可行性.另外,鉴于在很多真实场景中均存在平行线段,因此本文所得到的结果不仅具有理论意义而且也有一定的实用价值.
Abstract:
A theory and algorithms of camera calibration based on two parallel line segments are proposed. 1) If the length ratio of the two parallel segments is known, then from its projections across n images, a) 2(n−1) quadratic constraint equations on camera internal parameters can be obtained; b) (5n−6) constraint equations can be obtained if additionally the epipoles across n images are known, among which 3(n − 1) are quadratic, (n − 2) third degree, and (n − 1) fourth degree. 2) If the length ratio of the two parallel line segments is unknown, (2n − 3) constraint equations are derived from n images, among which (n − 2) are of fourth degree, and (n − 1) of sixth degree. Based on the above theoretical results, two practical algorithms of camera calibration are also proposed. Experimental results on synthetic and real images validate the proposed theory and algorithms. The results in this paper seem to be not only of theoretical significance, but also of wide applicability as parallel line segments are not rare in any man-made scene.
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