Derivation of Halcon camera calibration principle

One 、 Translation and rotation matrix derivation

translation ：

 

Two 、 Calibration process

Coordinate transformation foundation

Camera coordinate system  、  Image physical coordinate system 、 Image pixel coordinate system   and   World coordinate system （ Reference coordinate system ） .

 

One 、 Image coordinate system (x,y) To pixel coordinate system (u,v)

1. The two coordinate axes are perpendicular to each other

 

 

 

  Two 、 Camera coordinate system (Xc,Yc,Zc) To image coordinate system (x,y)

According to the principle of triangle similarity

 

  3、 ... and 、 World coordinate system (Xw,Yw,Zw) To camera coordinate system (Xc,Yc,Zc)

 3 Rotation and translation of dimension

 

The last step ： Matrix multiplication between four coordinates

 

  3、 ... and 、 distortion

The most detailed 、 The most complete explanation of camera calibration _a083614 The column -CSDN Blog _ Camera calibration method

Distortion can generally be divided into ： Radial distortion 、 Tangential distortion
ps: Distortion is an inherent characteristic of the camera itself , Same as camera internal parameters , After one calibration .

Radial distortion comes from the lens shape .
Tangential distortion comes from radial distortion （ Barrel distortion and pillow distortion ）：
The lens of the actual camera always produces significant distortion at the edge of the imager , This phenomenon comes from “ Cylinder shape ” or “ fisheye ” Influence .
Here's the picture , Light rays are more curved at the center of the principle lens than near the center . For a common lens , This phenomenon is even more serious . Barrel distortion is very powerful in cheap webcams , But it's not obvious in high-end cameras , Because these lens systems do a lot of work to eliminate radial distortion .