Camera Calibration

Calibration Matrix

This matrix only represents the Camera Intrinsics.

Most Common Notation

Kajanan told me that the most common form is

$K=\left[\begin{array}{ccc}{f}_x& s& c_x\\ 0& f_y& c_y\\ 0& 0& 1\end{array}\right]$

• $s$ is the shear factor
• $f_x$​ and $f_y$​ represent the focal length of the camera in terms of pixels for the $x$ and $y$ axes
• $c_x$​ and $c_y$​ are the coordinates of the Principal Point

Cyrill Notation

Through Cyrill Stachniss course, I see it through $c,s,m,x_H,y_H$ (see Camera Calibration)

so we end up with this calibration matrix $K={}^s{H}_c{}^{c}K=\left[\begin{array}{ccc}c& cs& x_H\\ 0& c(1+m)& y_H\\ 0& 0& 1\end{array}\right]$

• $c$ is the distance between the camera origin and the image plane
• scale difference $m$ between $x$ and $y$
• Sheer compensation $s$ (for digital cameras, we typically have $s\approx 0$)

So we essentially have this additional scale difference $m$ through the Cyrill Stachniss notation, but the scale difference is generally $0$, so we have $K={}^s{H}_c{}^{c}K=\left[\begin{array}{ccc}c& cs& x_H\\ 0& c& y_H\\ 0& 0& 1\end{array}\right]$

Notice cs instead of s

Here, $s$ is merely a skew factor multiplied by $c$, the distance between the image plane and camera sensor. Cyrill makes no mention of focal length, I mean that is what $c$ is at the end of the day.