1.相机标定资料

这个视频是建议有一定基础的去看，详细介绍了整个标定的过程。

https://www.bilibili.com/video/BV1R7411m7ZQ/?spm_id_from=333.337.search-card.all.click&vd_source=c205d4d10f730a57820343328741984a

这个文章基础一点，可以先看

https://blog.csdn.net/sunshine_zoe/article/details/73457686

https://zhuanlan.zhihu.com/p/642155792?utm_id=0

2.案例分析

这里用sick的visionary 相机的sdk做分析

2.0基本参数定义

cxcy 就是图像坐标系下的原点在像素坐标系下的坐标，其中fx和fy表示每一列和每一行分别代表1mm多少个像素，即1mm=fx pix
k1k2是径向畸变的参数
f2c 是标定的z的起始位置，后面在介绍

class CameraParameters:""" This class gathers the main camera parameters. """def __init__(self, width=176, height=144,cam2worldMatrix=None,fx=146.5, fy=146.5, cx=84.4, cy=71.2,k1=0.326442, k2=0.219623,f2rc=0.0):self.cam2worldMatrix = [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1]self.width = widthself.height = heightif cam2worldMatrix:self.cam2worldMatrix = cam2worldMatrixself.fx = fxself.fy = fyself.cx = cxself.cy = cyself.k1 = k1self.k2 = k2self.f2rc = f2rc

2.1 visionary-s 双目

         # transform into camera coordinates (zc, xc, yc)#像素坐标系转为图像坐标系xp = (myCamParams.cx - col) / myCamParams.fxyp = (myCamParams.cy - row) / myCamParams.fy# coordinate system local to the imager# 图像坐标系转为相机坐标系 f=1 ,所以 xc=(xp*zc)/f #yc=(yp*zc)/fzc = distData[row][col]xc = xp * zcyc = yp * zc# convert to world coordinate system#相机坐标系转世界坐标系 ，因为矩阵m_c2w是一个单位矩阵。所以xyz还是原来的值xw = (m_c2w[0, 3] + zc * m_c2w[0, 2]  + yc * m_c2w[0, 1] + xc * m_c2w[0, 0])yw = (m_c2w[1, 3] + zc * m_c2w[1, 2]  + yc * m_c2w[1, 1] + xc * m_c2w[1, 0])zw = (m_c2w[2, 3] + zc * m_c2w[2, 2]  + yc * m_c2w[2, 1] + xc * m_c2w[2, 0])

2.2 visionary-tmini tof

  #calculate radial distortion# 像素坐标系转图像坐标系xp = (myCamParams.cx - col) / myCamParams.fxyp = (myCamParams.cy - row) / myCamParams.fy# 畸变校正r2 = (xp * xp + yp * yp)r4 = r2 * r2k = 1 + myCamParams.k1 * r2 + myCamParams.k2 * r4xd = xp * k # 畸变校正yd = yp * kd = distData[row][col]  #实际的距离值，不是z而是 np.sqrt(x*x + y*y + z*z)s0 = np.sqrt(xd*xd + yd*yd + 1) #  计算当前的坐标点在z=1的时候的d#  d/s0 就是实际的z值# 图像坐标系转相机坐标系 也是f=1  所以直接乘以z值xc = xd * d / s0yc = yd * d / s0zc = d / s0 - myCamParams.f2rc# convert to world coordinate systemxw = (m_c2w[0, 3] + zc * m_c2w[0, 2]  + yc * m_c2w[0, 1] + xc * m_c2w[0, 0])yw = (m_c2w[1, 3] + zc * m_c2w[1, 2]  + yc * m_c2w[1, 1] + xc * m_c2w[1, 0])zw = (m_c2w[2, 3] + zc * m_c2w[2, 2]  + yc * m_c2w[2, 1] + xc * m_c2w[2, 0])

3. 2D相机的手眼标定

看了上面的案例 ，我们发现相机的sdk只做了2个矩阵的计算。也就是把像素坐标转为实际的相机坐标。真正要使用的话还缺少 相机转为机器人、法兰盘、工作坐标系。其实这些都是上面文章所说的相机转世界坐标系。也就是需要求R T 旋转加平移。所以理论上我们只需要3个标定点就可以。

https://www.xjx100.cn/news/433771.html?action=onClick

3.1欧拉角

https://www.guyuehome.com/43450#2__148

https://blog.csdn.net/weixin_43134049/article/details/122826538?spm=1001.2014.3001.5501

4. 3D点云的手眼标定