appendix.md

\appendix

Additional information

This chapter contains information to help reproduce the results of \Gaze{} but are not important enough to appear in the main text.

Calibrating OpenCV

OpenCV offers a tool to store camera calibration settings which can be used for certain functions to improve their results. \Gaze{} benefits from such functions, among others it uses solvePnP which is used to estimate the head pose in @sec:head-pose-estimation. This section explains briefly how to use the calibration tool. Please note that there is also a tutorial available which provides some videos and a more thorough explanation of the mathematics.

The calibration tool can be found in OpenCV's samples, samples/cpp/calibration.cpp. To be able to use it, OpenCV needs to be compiled manually by providing the CMake flag -DBUILD_EXAMPLES=ON to build the cpp-example-calibration executable. To calibrate the camera, the calibration tool needs to take a couple of pictures of a benchmark image: a checkerboard pattern as in @fig:calibcheck is used in the following. Calibration works best if the image is on a hard surface, like cardboard. An example call to the calibration tool is denoted in @cl:cvcalibcall. The parameters -h=6 and -w=9 describe the layout of the checkerboard pattern. It means that the checkerboard is seven squares down and ten squares across since the parameters expect the numbers of corners between four squares. -n=10 is the number of images to be taken, -d=1000 is the delay between two images. A higher delay allows that during calibration the image can be moved to more divers poses without triggering another image, resulting in a higher variety of points which in turn leads to a more exact estimation of the camera parameters. At least three pictures should be taken, but more images provide better results. The output file to which the calibration values are written is stored in the file passed with -o. The last parameter, -s=0.0015 is the size of one checkerboard square in meters. This value should be measured on the printout of the checkerboard, as slight variations can occur depending on page orientation, zoom levels, margins, printer settings, and other factors. In the example, the printed version's squares' side lengths were \SI{1.5}{\milli\meter}. After a successful calibration, camera_calib.yml will be written into the directory. It can be used to configure \Gaze{}, as explained in @sec:camera-and-screen-parameters.

./cpp-example-calibration -h=6 -w=9 -n=10 -d=1000 -s=0.0015 -o=camera_calib.yml

Determining the focal length

To find the effective focal length of a camera the angle of view needs to be measured, and the sensor size has to be known. For \Gaze{}'s examples the sensor width is assumed to be \SI{0.0055}{\meter}. After measuring the angle of view, it can be used to solve [@Wikipedia:aov] \begin{align} \alpha &= 2 \arctan \frac{d}{2f} \ f &= \frac{d}{2 \tan \frac{\alpha}{2}}, \end{align} with $d$ being the sensor size, either \SI{0.0055}{\meter} for horizontal calculations, or \SI{0.0031}{\meter} for vertical one. These values are taken from @sec:camera-and-screen-parameters. $\alpha$ is the angle of view and $f$ is the focal length. To find $\alpha$ the camera is placed parallel to a wall, facing it. Then the distance $w$ between the left most and the right most points which are still visible on the camera image, and the distance between the camera and the wall $v$ are measured for the horizontal calculations. For applying this to the vertical case, the top and bottom most points need to be used. Using trigonometry the angle of view can be calculated by substituting the values into \begin{align} \alpha = \arctan \frac{w}{2v}. \end{align} For the examples in \Gaze{} the focal length used is \SI{0.01}{\meter}, which is the approximate mean of the measured values for the horizontal and vertical focal lengths ($f_h, f_v$), measured using a folding rule at a distance of \SI{1.04}{\meter} for a MacBook Pro: \begin{align} f_h &= \frac{\SI{0.0055}{\meter}}{ 2 \tan \left( \frac{1}{2} \arctan \left( \frac{ w_h }{ 2v } \right) \right) } = \frac{\SI{0.0055}{\meter}}{ 2 \tan \left( \frac{1}{2} \arctan \left( \frac{ \SI{1.13}{\meter} }{ 2 \cdot \SI{1.04}{\meter} } \right) \right) } \approx \SI{0.011}{\meter} \ f_v &= \frac{\SI{0.0031}{\meter}}{ 2 \tan \left( \frac{1}{2} \arctan \left( \frac{ w_v }{ 2v } \right) \right) } = \frac{\SI{0.0031}{\meter}}{ 2 \tan \left( \frac{1}{2} \arctan \left( \frac{ \SI{0.66}{\meter} } { 2 \cdot \SI{1.04}{\meter} } \right) \right) } \approx \SI{0.01}{\meter} \ f &= \frac{f_h + f_v}{2} = \frac{\SI{0.011}{\meter} + \SI{0.01}{\meter}}{2} = \SI{0.0105}{\meter} \approx \SI{0.01}{\meter}. \end{align}

Tables

@file:assets/gen_files/table-relative-errors-pexels.md

@file:assets/gen_files/table-relative-errors-BioID.md

\newpage

@file:assets/gen_files/table-comptimes-pexels.md

@file:assets/gen_files/table-comptimes-BioID.md

Figures

{ #fig:examplefaces }

{ #fig:pupildetectioncomparison height=120% }

{ #fig:solvepnpcomparison }

{ #fig:landmarkscomparison }

{ #fig:bioid_examples }

{ #fig:calibcheck }

{ #fig:undetected_faces }

Code Listings

```{ .cpp file=assets/gaze/src/gaze/gaze_tracker.cpp label=cl:initpipeline caption="The init_pipeline() method. To extend it properly, a new `else if` case has to be added." shortcaption="The `init_pipeline()` method." lines=71-100 pathdepth=3 }

# References
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