Given a point \(^kP\) in the camera coordinate system \(\{k\}\), the camera intrinsic matrix projects that point to the sensor plane. The projected point is in the homogeneous coordinate system. During this projection we lose imformation as we are going from \(3d\) to \(2d\). Because of this reason, the camera intrinsic matrix is non-invertible.
The camera intrinsic matrix is also called the calibration matrix and is defined as
\[k = \begin{bmatrix} c && cs && x_H \\ 0 && c(1+m) && y_H \\ 0 && 0 && 1 \end{bmatrix}\]Here \(c\) is the distance of the image plane from the camera, \(s\) is the sheer, \(m\) is the scale difference between \(x\) and \(y\) of the sensor and \(x_H\) and \(y_H\) are the coordinates of the [Principle Point] . Generally in a digital camera, \(s=0\).
Todo
- Prove how we got the intrinsic matrix.