如何验证相机校准是否正确？ （或如何估计再投影的误差） [英] How to verify that the camera calibration is correct? (or how to estimate the error of reprojection)

问题描述

校准的质量是通过重投影错误（有另一个？）来测量的，这需要一个3d点的知识世界坐标。

The quality of calibration is measured by the reprojection error (is there an alternative?), which requires a knowledge world coordinates of some 3d point(s).

有没有一种简单的方法来产生这样的已知点？是否有一种方法以某种其他方式验证校准（例如，张的校准方法只需要校准对象是平面的，并且系统的几何形状不需要知道）

Is there a simple way to produce such known points? Is there a way to verify the calibration in some other way (for example, Zhang's calibration method only requires that the calibration object be planar and the geometry of the system need not to be known)

推荐答案

您可以独立于姿态来验证估计的非线性透镜畸变参数的精度。捕获跨越视场的直边缘（例如铅垂线或平坦表面上的激光条纹）的图像。在所述线图像上选择点，不失真它们的坐标，拟合线，计算误差。

You can verify the accuracy of the estimated nonlinear lens distortion parameters independently of pose. Capture images of straight edges (e.g. a plumb line, or a laser stripe on a flat surface) spanning the field of view. Pick points on said line images, undistort their coordinates, fit lines, compute error.

对于直线部分，您还可以以已知的相对姿态捕获多个平面钻机的图像，使用可重复/精确的钻机移动一个平面目标），或以彼此已知的角度安装多个平面目标（例如，彼此成90度的三个平面）。

For the linear part, you can also capture images of multiple planar rigs at a known relative pose, either moving one planar target with a repeatable/accurate rig (e.g. a turntable), or mounting multiple planar targets at known angles from each other (e.g. three planes at 90 deg from each other).

一如既往，妥协是在精度要求和预算之间的顺序。有足够的钱和附近一个友好的机器店，你可以让你的幻想运行与钻机几何。我曾经是一个十二面体关于葡萄柚的大小，加工出白色塑料到1/20毫米规格。使用它来校准机器人手臂末端执行器上的摄像机的姿势，将其移动到围绕固定点的球体上。十二面体在闭塞角方面具有非常好的性质。不用说，它都是专利。

As always, a compromise is in order between accuracy requirements and budget. With enough money and a friendly machine shop nearby you can let your fantasy run wild with rig geometry. I had once a dodecahedron about the size of a grapefruit, machined out of white plastic to 1/20 mm spec. Used it to calibrate the pose of a camera on the end effector of a robotic arm, moving it on a sphere around a fixed point. The dodecahedron has really nice properties in regard to occlusion angles. Needless to say, it's all patented.

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