As we all know, camera calibration is a process of obtaining camera parameters by inputting a calibration plate with a calibration pattern. The actual optical imaging is a very complex process, projecting from the three-dimensional world to the two-dimensional image in the camera. In the process of camera calibration, the placement of calibration plates is often involved. How should we place the calibration board? Here's a brief introduction:
Method for placing the calibration plate:
Camera calibration is a process to obtain camera parameters by inputting a calibration plate with calibration. The actual optical imaging is a very complex process, projecting from the three-dimensional world to the two-dimensional image in the camera. Camera calibration is to use abstract mathematical model to represent this complex imaging process.
Ideally, the lens will also map a line in a three-dimensional space into a line (that is, projective transformation), but in fact, the lens cannot be so perfect. After the lens is mapped, the line will become bent, so the distortion parameters of the camera are required to describe this deformation effect.
The image plane and the calibration board form a homography relationship. Each homography relationship can be represented by a homography matrix, and each matrix forms two constraints. There are 8 degrees of freedom in the homography matrix, considering the homogeneity of the matrix. Therefore, at least 4 points can be used to calculate the homography matrix. The number of corners of a chessboard is generally 9X6=54 points. that's enough. The placement angle of each calibration plate corresponds to a homography matrix. Then each matrix can form two constraints corresponding to two equations according to the unit orthogonality of the rotation matrix. The internal parameter matrix contains five degrees of freedom (principal points u0, v0) Focus (fx, fy), and sketch. Therefore, at least 3 homography relations can be solved, so at least 3 placement angles can be used. In addition, considering the modeling of distortion parameters, there are generally four, so the LM method is used to complete the nonlinear optimization. In practical application, there are 20 angles. Different angles can ensure that the objective function is closer to the convex function, which is convenient for completing the iterative optimization of all parameters and making the results more accurate.
To sum up, it is the method to place the calibration board. The diversity of the position and orientation of the calibration plate when taking pictures will make the estimation of internal parameters more accurate. Accurate internal parameters can better correct the distortion of the whole image, but if the given calibration plate position is too single, such as in the upper left corner of the image, the optimized internal parameters may only better correct the distortion of the upper left corner of the image. It is recommended to find a lens with large distortion for experiment, which will be more vivid.
