mypapers/socc-img-calibr/index.html

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   8 <title> Camera calibration for CIIPS Glory soccer programs 1998/1999</title>
   9
  10 <H1 align="center">Camera calibration for CIIPS Glory soccer programs 1998/1999 </H1>
  11
  12 <H3 align=center>Petter Reinholdtsen  &lt; pere@td.org.uit.no &gt;  </H3>
  13
  14 <H3 align=center>2000-03-01 </H3>
  15
  16 <p>
  17          <H2><A NAME="tth_sEc1">
  18 1</A>&nbsp;&nbsp;Purpose of this paper</H2>
  19
  20 <p>
  21 The image processing functions in the CIIPS Glory soccer programs for
  22 year 1998 and 1999 uses lookup tables to determine distances.  These
  23 lookup tables depends on the cameras physical position, the servo
  24 configuration on the hardware description table and the lens view
  25 angle.  The tables assume a tilting camera.
  26
  27 <p>
  28 The original programs ran on Eyebot robots with Color Quickcam, and
  29 the current tables reflect the settings which was valid then.  The
  30 current robots have different HDT settings, some of them have
  31 different lenses and others use different cameras (EyeCam).
  32
  33 <p>
  34 This document gives a short description on how to calibrate the
  35 tables.  The method was developed by Birgit Graf for her diploma
  36 Thesis.
  37
  38 <p>
  39         <H2><A NAME="tth_sEc2">
  40 2</A>&nbsp;&nbsp;Camera focusing</H2>
  41
  42 <p>
  43
  44 <p><A NAME="tth_fIg1">
  45 </A>   <center>  <img src="lensfocus.png" alt="lensfocus.png"><br>   <center>Figure 1: Focus pattern</center>
  46   <A NAME="fig:lensfocus">
  47 </A>
  48 </center><p>
  49 <p>
  50 Before the camera can be used, we need to make sure the lens is in
  51 focus.  Focusing is done by turning the lens in it's socket.  The
  52 QuickCam lenses can be turned right away, while the EyeCam lenses need
  53 to have a screw on the side unscrewed before they will move.
  54
  55 <p>
  56 The simplest way to focus the cameras is to connect them to a PC to
  57 see the color images at full framerate.  By using a simple pie drawing
  58 with 2.5 degree black and white arcs, focusing is done by turning the
  59 lense until the blurry center is as small as possible<a href="#tthFtNtAAB" name="tthFrefAAB"><sup>1</sup></a>.  Figure <A href="#fig:lensfocus">1</A>
  60 gives an example of this pattern.
  61
  62 <p>
  63         <H2><A NAME="tth_sEc3">
  64 3</A>&nbsp;&nbsp;Lookup tables</H2>
  65
  66 <p>
  67 The soccer code uses two lookup tables to calculate different
  68 distances and pixel widths.  Each table has tree different settings,
  69 reflecting the tree camera angles used; middle=0, up=1 and down=2.
  70 The two tables are used for horizontal and vertical calculations.
  71
  72 <p>
  73       <H3><A NAME="tth_sEc3.1">
  74 3.1</A>&nbsp;&nbsp;The horizontal <tt>yfact</tt> table</H3>
  75
  76 <p>
  77 The horizontal table <tt>yfact[3][imagerows]</tt> gives the
  78 multiplication factor for each row to convert pixels to meters.  It
  79 can be used to convert m meters to p pixels on a given row.  <tt>
  80 campos</tt> is the numeric representation of current camera position.
  81
  82 <p>
  83
  84 <br clear="all"><table border="0" width="100%"><tr><td>
  85 <Table align="center"><tr><td nowrap align="center">
  86 p = </td><td nowrap align=center>
  87 m<hr NOSHADE>yfact[campos][row]<Br></td><td nowrap align=center>
  88 </td></Table>
  89 </td><td width="1%">(1)</td></table>
  90
  91
  92
  93 <p>
  94 This is used to predict the ball width in pixels when searching for
  95 the ball in the images.
  96
  97 <p>
  98 It can also be used to convert pixels to meters.  This assumes that
  99 the camera is mounted in the center of the robot, and calculates
 100 pixels to the left or to the right of the robot axes.  The field pixel
 101 located at (xpos,ypos) will then be located m<sub>y</sub> meters to the left or
 102 right of the robot.
 103
 104 <p>
 105
 106 <br clear="all"><table border="0" width="100%"><tr><td>
 107 <Table align="center"><tr><td nowrap align="center">
 108 m<sub>y</sub> = </td><td nowrap align=center>
 109 imagecolumns<hr NOSHADE>2<Br></td><td nowrap align=center>
 110 <font face=symbol>-</font
 111 > 1 <font face=symbol>-</font
 112 > ypos &times;yfact[campos][xpos]</td></Table>
 113 </td><td width="1%">(2)</td></table>
 114
 115
 116
 117 <p>
 118 The <tt>yfact</tt> table is generated using a rectangular white or light
 119 sheet of paper, placed perpendicular to the view direction.  The robot
 120 is placed on the soccer field, and the paper is placed in the upper
 121 center of the image.  The camera servo must be set to the correct
 122 angle.  Check <tt>servos.c</tt> for the correct values.
 123
 124 <p>
 125 Make sure the paper is visible in the upper rows of the image, and
 126 that the edges are visible.  Take a snapshot.  Move the robot closer
 127 to the paper.  The paper will now cover rows further down in the
 128 image.  Take a new snapshot.  Continue with this procedure until all
 129 rows are covered.  You will need tree sets of snapshots, one for each
 130 camera servo setting.  To take snapshots I used the ImACam eyebot
 131 program.  This will produce PPM images and upload them to the PC.
 132
 133 <p>
 134 Using these images, you then measure the pixel width of the piece of
 135 paper for each row in the image.  This width, p, is then used
 136 together with the paper width, w, to calculate the <tt>yfact</tt>
 137 value, f<sub>y</sub>.
 138
 139 <p>
 140
 141 <br clear="all"><table border="0" width="100%"><tr><td>
 142 <Table align="center"><tr><td nowrap align="center">
 143 f<sub>y</sub> = </td><td nowrap align=center>
 144 w<hr NOSHADE>p<Br></td><td nowrap align=center>
 145 </td></Table>
 146 </td><td width="1%">(3)</td></table>
 147
 148
 149
 150 <p>
 151 To measure the pixel width, I used xv to display the image, ' &gt; ' to
 152 enlarge the image and the middle mouse button to read the pixel width.
 153
 154 <p>
 155       <H3><A NAME="tth_sEc3.2">
 156 3.2</A>&nbsp;&nbsp;The vertical <tt>x2m</tt> table</H3>
 157
 158 <p>
 159 To find the distance to the robot along the view direction, the soccer
 160 programs uses the table <tt>x2m[3][imagerows]</tt>.  It translates from
 161 pixel row to distance in meters from the camera.  To make this table,
 162 the distance to the edge of a sheet of paper is measured, together
 163 with the row number it appears in.  This needs to be done for each
 164 row, and for each camera servo setting.
 165
 166 <p>
 167 To find the distance m<sub>x</sub> from the robot, a simple table lookup is
 168 performed:
 169
 170 <br clear="all"><table border="0" width="100%"><tr><td>
 171 <Table align="center"><tr><td nowrap align="center">
 172 m<sub>x</sub> = x2m[campos][xpos]</td></Table>
 173 </td><td width="1%">(4)</td></table>
 174
 175
 176
 177 <p>
 178         <H2><A NAME="tth_sEc4">
 179 4</A>&nbsp;&nbsp;Interpolation</H2>
 180
 181 <p>
 182 When the measured values are collected, one can use various tools to
 183 find a formula which closely matches the measured values.  I used
 184 Mathematica, with the help of Thomas Hanselmann, to interpolate one
 185 reading into a polynomial.
 186
 187 <p>
 188 From the dataset, I made a textfile <tt>dataXY.txt</tt> with the
 189 coordinates (x,y) as s space separated list: ``x1 y1 x2 y2 ...''.
 190
 191 <p>
 192 I then used the following Mathematica commands to make the formula.
 193 You might have to adjust the parameters to <tt>Fit</tt> to generate a
 194 more accurate formula..  The datafile must have all values on one line
 195 to make Mathematica happy.
 196
 197 <p>
 198
 199 <blockquote>
 200 <pre>
 201 dataXY = ReadList["data.txt",
 202   {Number, Number},
 203   RecordLists -&#62; True][[1]];
 204 func =  Fit[dataXY, {1, x, x^1.1}, x];
 205 ymax = Max[Transpose[dataXY][[2]]];
 206 pOriginal = ListPlot[dataXY,
 207   PlotJoined-&#62;True,
 208   PlotRange-&#62;{{0,61},{0,ymax}},
 209   PlotStyle-&#62;{Hue[0.1]}];
 210 pFit = Plot[func, {x,0,61},
 211   PlotRange-&#62;{{0,61},{0,ymax}},
 212   PlotStyle-&#62;{Hue[0.6]} ];
 213 Show[pFit,pOriginal]; func
 214 </pre>
 215 </blockquote>
 216
 217 <p>
 218         <H2><A NAME="tth_sEc5">
 219 5</A>&nbsp;&nbsp;The hard way</H2>
 220
 221 <p>
 222 The best way to do such camera calibration would be using a
 223 mathematical model for the camera, taking the known properties of the
 224 camera and the servo into account.  If we make sure the HDT contains
 225 enough information to calibrate the cameras, the programs should be
 226 more generic and adapt better to changing settings.  I hope to find
 227 time to investigate this further.
 228
 229 <p>
 230
 231 <H2>Appendix A</H2>
 232
 233 <p>
 234 Complete Postscript file to make lens focus pattern.
 235
 236 <p>
 237 <A NAME="appendix:lensfocus">
 238 </A>
 239 <pre>
 240 %!PS-Adobe-1.0
 241 %%Title: Camera lens focusing sheet
 242 %%Creator: Petter Reinholdtsen &lt;pere@td.org.uit.no&#62;
 243 %%CreationDate: 1999-12-04
 244 %%BoundingBox: 13 14 574 575
 245 %%Pages: 1
 246 % Place this in front of the camera, and change
 247 % focus until the black center spot is as small
 248 % as possible.  The camera should then be in
 249 % focus.
 250 /cm { 28 mul } def .00001 setlinewidth
 251 % Center of circle
 252 10.5 cm 10.5 cm translate
 253 % scale 1 to fill page
 254 10 cm 10 cm scale
 255 newpath 0 0 1 0 360 arc stroke
 256 72 { newpath 0 0 moveto
 257   0 0 1 0 2.5 arc closepath fill 5 rotate
 258 } repeat showpage
 259 </pre>
 260
 261 <p>
 262 <hr><H3>Footnotes:</H3>
 263
 264 <p><a name="tthFtNtAAB"></a><a href="#tthFrefAAB"><sup>1</sup></a>Thanks
 265   to Mark Gaynor for this method.
 266 <p><hr><small>File translated from
 267 T<sub><font size="-1">E</font></sub>X
 268 by <a href="http://hutchinson.belmont.ma.us/tth/">
 269 T<sub><font size="-1">T</font></sub>H</a>,
 270 version 2.67.<br>On 23 Apr 2000, 20:18.</small>
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