# Calibration Matrix

This matrix only represents the Camera Intrinsics.

### Most Common Notation

Kajanan told me that the most common form is

K = \begin{equation} \begin{bmatrix} f_x & s&c_x \\ 0& f_y& c_y\\ 0&0 & 1 \end{bmatrix} \end{equation}

- $s$ 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= c00 csc(1+m)0 x_{H}y_{H}1 $

- $c$ 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 $s≈0$)

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= c00 csc0 x_{H}y_{H}1 $

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.