Three-dimensional reconstruction of computer vision (2) (camera calibration)

Calibration diagram

Calibration target

$$P^{{}^{\prime }}=M{P}_w=K\left[RT\right]P{}_w$$
Among them $K$ is the internal parameter,$[RT]\; isan$ external parameter. This formula requires the use of at least six pairs of internal and external points to solve the internal and external parameters (11 unknown parameters).

Among them $R_{3\times 3},T_{3\times 1}$.

Calibration solution

• Use a system of homogeneous linear equations
  where the number of equations is greater than the number of unknown parameters to find an approximate solution.

Radial distortion calibration

• Image magnification decreases with distance from the optical axis

Compared with the conventional solution, add the distortion factor:

$$\begin{gathered} l=1\pm \sum _{p=1}^3{K}_P{d}^{2p} \\ {d}^2=u^2+v^2 \end{gathered}$$

Using Newton's method and $L-M$ method to solve.