mypapers/socc-img-calibr/socc-img-calibr.tex

   1 \documentclass[a4paper,10pt, twocolumn]{article}
   2 \usepackage{graphicx}
   3 \usepackage{picinpar}
   4
   5 \title{Camera calibration for CIIPS Glory soccer programs 1998/1999}
   6 \author{Petter Reinholdtsen $<$pere@td.org.uit.no$>$}
   7 \date{2000-03-01}
   8
   9 \begin{document}
  10 \maketitle
  11
  12 \section{Purpose of this paper}
  13
  14 The image processing functions in the CIIPS Glory soccer programs for
  15 year 1998 and 1999 uses lookup tables to determine distances.  These
  16 lookup tables depends on the cameras physical position, the servo
  17 configuration on the hardware description table and the lens view
  18 angle.  The tables assume a tilting camera.
  19
  20 The original programs ran on Eyebot robots with Color Quickcam, and
  21 the current tables reflect the settings which was valid then.  The
  22 current robots have different HDT settings, some of them have
  23 different lenses and others use different cameras (EyeCam).
  24
  25 This document gives a short description on how to calibrate the
  26 tables.  The method was developed by Birgit Graf for her diploma
  27 Thesis.
  28
  29 \section{Camera focusing}
  30
  31 \begin{figure}[here]
  32   \centering
  33   \includegraphics[height=2.7cm,width=2.7cm]{lensfocus}
  34   \caption{Focus pattern}
  35   \label{fig:lensfocus}
  36 \end{figure}
  37
  38 Before the camera can be used, we need to make sure the lens is in
  39 focus.  Focusing is done by turning the lens in it's socket.  The
  40 QuickCam lenses can be turned right away, while the EyeCam lenses need
  41 to have a screw on the side unscrewed before they will move.
  42
  43 The simplest way to focus the cameras is to connect them to a PC to
  44 see the color images at full framerate.  By using a simple pie drawing
  45 with 2.5 degree black and white arcs, focusing is done by turning the
  46 lense until the blurry center is as small as possible\footnote{Thanks
  47   to Mark Gaynor for this method.}.  Figure \ref{fig:lensfocus}
  48 gives an example of this pattern.
  49
  50 \section{Lookup tables}
  51
  52 The soccer code uses two lookup tables to calculate different
  53 distances and pixel widths.  Each table has tree different settings,
  54 reflecting the tree camera angles used; middle=0, up=1 and down=2.
  55 The two tables are used for horizontal and vertical calculations.
  56
  57 \subsection{The horizontal {\tt yfact} table}
  58
  59 The horizontal table {\tt yfact[3][imagerows]} gives the
  60 multiplication factor for each row to convert pixels to meters.  It
  61 can be used to convert $m$ meters to $p$ pixels on a given row.  {\tt
  62 campos} is the numeric representation of current camera position.
  63
  64 \begin{equation}
  65 p = {m \over yfact[campos][row]}
  66 \end{equation}
  67
  68 This is used to predict the ball width in pixels when searching for
  69 the ball in the images.
  70
  71 It can also be used to convert pixels to meters.  This assumes that
  72 the camera is mounted in the center of the robot, and calculates
  73 pixels to the left or to the right of the robot axes.  The field pixel
  74 located at (xpos,ypos) will then be located $m_y$ meters to the left or
  75 right of the robot.
  76
  77 \begin{equation}
  78 m_y = {imagecolumns \over 2} - 1 - ypos \times yfact[campos][xpos]
  79 \end{equation}
  80
  81 The {\tt yfact} table is generated using a rectangular white or light
  82 sheet of paper, placed perpendicular to the view direction.  The robot
  83 is placed on the soccer field, and the paper is placed in the upper
  84 center of the image.  The camera servo must be set to the correct
  85 angle.  Check {\tt servos.c} for the correct values.
  86
  87 Make sure the paper is visible in the upper rows of the image, and
  88 that the edges are visible.  Take a snapshot.  Move the robot closer
  89 to the paper.  The paper will now cover rows further down in the
  90 image.  Take a new snapshot.  Continue with this procedure until all
  91 rows are covered.  You will need tree sets of snapshots, one for each
  92 camera servo setting.  To take snapshots I used the ImACam eyebot
  93 program.  This will produce PPM images and upload them to the PC.
  94
  95 Using these images, you then measure the pixel width of the piece of
  96 paper for each row in the image.  This width, $p$, is then used
  97 together with the paper width, $w$, to calculate the {\tt yfact}
  98 value, $f_y$.
  99
 100 \begin{equation}
 101 f_y = {w \over p}
 102 \end{equation}
 103
 104 To measure the pixel width, I used xv to display the image, '$>$' to
 105 enlarge the image and the middle mouse button to read the pixel width.
 106
 107 \subsection{The vertical {\tt x2m} table}
 108
 109 To find the distance to the robot along the view direction, the soccer
 110 programs uses the table {\tt x2m[3][imagerows]}.  It translates from
 111 pixel row to distance in meters from the camera.  To make this table,
 112 the distance to the edge of a sheet of paper is measured, together
 113 with the row number it appears in.  This needs to be done for each
 114 row, and for each camera servo setting.
 115
 116 To find the distance $m_x$ from the robot, a simple table lookup is
 117 performed:
 118 \begin{equation}
 119 m_x = x2m[campos][xpos]
 120 \end{equation}
 121
 122 \section{Interpolation}
 123
 124 When the measured values are collected, one can use various tools to
 125 find a formula which closely matches the measured values.  I used
 126 Mathematica, with the help of Thomas Hanselmann, to interpolate one
 127 reading into a polynomial.
 128
 129 From the dataset, I made a textfile {\tt dataXY.txt} with the
 130 coordinates (x,y) as s space separated list: ``x1 y1 x2 y2 ...''.
 131
 132 I then used the following Mathematica commands to make the formula.
 133 You might have to adjust the parameters to {\tt Fit} to generate a
 134 more accurate formula..  The datafile must have all values on one line
 135 to make Mathematica happy.
 136
 137 \begin{quote}
 138 \begin{verbatim}
 139 dataXY = ReadList["data.txt",
 140   {Number, Number},
 141   RecordLists -> True][[1]];
 142 func =  Fit[dataXY, {1, x, x^1.1}, x];
 143 ymax = Max[Transpose[dataXY][[2]]];
 144 pOriginal = ListPlot[dataXY,
 145   PlotJoined->True,
 146   PlotRange->{{0,61},{0,ymax}},
 147   PlotStyle->{Hue[0.1]}];
 148 pFit = Plot[func, {x,0,61},
 149   PlotRange->{{0,61},{0,ymax}},
 150   PlotStyle->{Hue[0.6]} ];
 151 Show[pFit,pOriginal]; func
 152 \end{verbatim}
 153 \end{quote}
 154
 155
 156 \section{The hard way}
 157
 158 The best way to do such camera calibration would be using a
 159 mathematical model for the camera, taking the known properties of the
 160 camera and the servo into account.  If we make sure the HDT contains
 161 enough information to calibrate the cameras, the programs should be
 162 more generic and adapt better to changing settings.  I hope to find
 163 time to investigate this further.
 164
 165 \newpage
 166
 167 \section*{Appendix A}
 168
 169 Complete Postscript file to make lens focus pattern.
 170
 171 \label{appendix:lensfocus}
 172 \input{lensfocus.tex}
 173
 174 \end{document}