Utilisateur:Peter.fasogbon89/Brouillon

https://en.wikipedia.org/wiki/Camera_resectioning

Algorithms

There are many different approaches to calculate the intrinsic and extrinsic parameters for a specific camera setup.

1. Direct Linear Transformation algorithm
2. Tsai Algorithm.
3. Zhang's "a flexible new technique for camera calibration".

DLT Algorithm

using Direct linear transformation (DLT) method. The paper .

Tsai's Algorithm

Tsai method for calibration is based on the pin-hole camera model. This model transforms points in world reference frame $[x_{w}\,y_{w}\,z_{w}\,1]^{T}$ to points in image reference frame $[(u,v)]^{T}$ . To simplify his calibration model compared to other models, Tsai supposes known some of the camera parameters like s_x and s_y (the pixel value), and if they are known with enough accuracy, it is also possible to introduce the central projection point (c_x, c_y) as input data. Another simplification of the method consists of considering only radial distortion of the image, simplifying the model because most of the calculations are performed over linear equations.

The transformation between world coordinates and image coordinates is carried out in four basic steps:

It is a 2-stage algorithm, calculating the pose (3D Orientation, and x-axis and y-axis translation) in first stage. In second stage it computes the focal length, distortion coefficients and the z-axis translation .

Unlike Zhang that involves the use planar object for calibration (planr object means one axis betweeen X, Y or Z) is equal to zero. Tsai usesa 3D calibration target.

$P={\begin{bmatrix}R&T\end{bmatrix}}{\begin{bmatrix}r1&r2&r3&tx\\r4&r5&r6&ty\\r7&r8&r9&tz\end{bmatrix}}$

R is created using the Euler angles of the rotation around the three axes (X,Y,Z).