# SwisTrack/Components/CalibrationLinear

## Description

Calibration of the camera system with a second order linear system. The non-linear transformation from image pixels to world coordinates is approximated by a second-order, non-symmetric polynomial of the form

${\displaystyle x=a_{11}u+a_{12}v+a_{13}+a_{14}u^{2}+a_{15}v^{2}+a_{16}uv}$
${\displaystyle y=a_{21}u+a_{22}v+a_{23}+a_{24}u^{2}+a_{25}v^{2}+a_{26}uv}$

with u, v the image pixels, and x, y the coordinates in world space (meters). The twelve parameters of this-very simple model-are estimated in a least-square fashion from a sufficiently large number of coordinate pairs. Thus, the software has to be provided with a number of image points which positions in the real world are known -- for instance by using a pattern of known dimensions. Hereby, increasing the number of pairs used in the estimation process over the minimum of six moderates the effect of noisy measurements during calibration.

Also, one observes that the precision of the approximation and hence the precision of the prediction is higher in the neighborhood of the training points. By that, we are able to bias the region within the camera frame where we want to minimize the prediction area.

Particles.

Particles.

## Parameters

### Calib. Points

Path the XML file containing the calibration points. The file must have the following format:

```<?xml version="1.0"?>
<pointlist>
<points>
<point>
<xworld>0.3</xworld>
<yworld>0.9</yworld>
<ximage>9.8</ximage>
<yimage>10.3</yimage>
</point>
<point>
<xworld>34.1</xworld>
<yworld>7.9</yworld>
<ximage>44.3</ximage>
<yimage>25.9</yimage>
</point>
</points>
</pointlist>
```

More points can be added like the two in this example. A minimum of 6 non-collinear points is needed to compute the calibration.