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Calibration |
This webpage aims to guide you through the process of calibrating a camera using the Tsai Calibration software, with a view to using TsaiCal C++ Class in a multiple camera application.
Okay, from an image, identify a set of (say 50) points whose corresponding points in the real world are known.
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| Image for calibration of soccer game in sports hall. | Graphic of sports hall floor markings from above |
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Now create a file 'cam_cd.dat' of x y z u v correspondences.
0 32000 0 66 53 2450 30470 0 88 56 2450 24400 0 68 74 2450 22840 0 61 80 2450 19810 0 46 94 2450 16780 0 26 113 2450 15220 0 13 124 3200 27430 0 91 63 3200 24860 0 81 72 3200 22380 0 70 82 3200 19810 0 58 94 3200 17240 0 43 109 3200 14760 0 24 129 7130 30470 0 145 55 7130 27430 0 141 64 7130 24860 0 137 73 7130 22380 0 133 81 7130 17240 0 119 112 7130 14760 0 112 127 7130 12190 0 99 155 7130 9620 0 83 192 7130 7600 0 64 235 7130 7140 0 59 247 11130 30470 0 194 55 11130 27430 0 195 63 11130 24860 0 197 73 11130 22380 0 199 81 11130 19810 0 200 93 11130 17240 0 203 111 11130 14760 0 206 127 11130 12190 0 211 154 11130 9620 0 217 193 11130 7600 0 224 236 11130 7140 0 226 248 15050 27430 0 248 62 15050 24860 0 254 70 15050 22380 0 262 81 15050 19810 0 271 93 15050 17240 0 283 108 15050 14760 0 297 127 15050 12190 0 316 153 15050 9620 0 343 190 15800 30470 0 252 55 15800 27430 0 258 62 15800 24400 0 267 72 15800 22840 0 273 78 15800 19810 0 285 92 15800 16780 0 300 111 15800 15220 0 311 122 15800 12190 0 336 153 18000 32000 0 276 52 |
Next, we need to take this 'calibration data' and calculate the camera parameters. Having downloaded the Tsai Calibration Code, and compiled this, we are ready.
For fully optimised camera calibration, we use the routine 'ccal_fo', which calibrates a camera given a set of many 7 > x > 500 correspondences of the form Xw Yw Zw u v with Zw = 0 if coplanar data used. All world obs in [mm], image u,v in pixels.
ccal_fo cam_cd.dat > cam_cp.dat ccal_fo cam_cd.dat >& cam.calinfo |
Now we have two files, 'cam_cp.dat' containing the 12 camera parameters, and 'cam.calinfo' containing details about the calibration. viz.
| cam_cp.dat | cam.calinfo |
|---|---|
5.7600000000e+02 5.7600000000e+02 2.3000000000e-02 2.3000000000e-02 2.3000000000e-02 2.3000000000e-02 1.7904325577e+02 1.0016861245e+02 1.0000000000e+00 8.7777901191e+00 2.7367337113e-03 -1.0080366213e+04 5.8119331472e+03 2.0953966937e+03 1.8850872153e+00 8.9522740451e-03 -6.9566269979e-03 0.0000000000e+00 0.0000000000e+00 |
Coplanar calibration (full optimization)
camera type: Photometrics Star I
data file: cambal1_cd.dat (51 points)
f = 8.777790 [mm]
kappa1 = 2.736734e-03 [1/mm^2]
Tx = -10080.366213, Ty = 5811.933147, Tz = 2095.396694 [mm]
Rx = 108.007541, Ry = 0.512928, Rz = -0.398585 [deg]
R
0.999936 0.006363 -0.009383
-0.006956 -0.309194 -0.950974
-0.008952 0.950978 -0.309130
sx = 1.000000
Cx = 179.043256, Cy = 100.168612 [pixels]
Tz / f = 238.715743
distorted image plane error:
mean = 0.880966, stddev = 0.622206, max = 3.292051 [pix], sse = 58.938184 [pix^2]
undistorted image plane error:
mean = 0.907604, stddev = 0.629328, max = 3.321848 [pix], sse = 61.813687 [pix^2]
object space error:
mean = 49.155172, stddev = 43.147031, max = 239.972542 [mm], sse = 216311.090053 [mm^2]
normalized calibration error: 2.223167
5.7600000000e+02
5.7600000000e+02
2.3000000000e-02
2.3000000000e-02
2.3000000000e-02
2.3000000000e-02
1.7904325577e+02
1.0016861245e+02
1.0000000000e+00
8.7777901191e+00
2.7367337113e-03
-1.0080366213e+04
5.8119331472e+03
2.0953966937e+03
1.8850872153e+00
8.9522740451e-03
-6.9566269979e-03
0.0000000000e+00
0.0000000000e+00
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This file (cam_cp.dat) can now be used by the methods in Tsai's Calibration C software, giving a calibrated camera which can be used to project points from image to world and world to image in a tracking application or the like. (see wc2ic.c for an example program).
Tsai's C code only allows one camera at a time, so I've converted the useful code to C++, allowing use of several cameras at once in a tracking application.
The class 'TsaiCal' contains methods to convert from world to image coordinates. The constructor needs Camera Parameters in the format obtained from Tsai's Calibration C software. This class allows the use of several calibrated cameras within a single application, although Tsai's Calibration C software will need to be used in advance to work out the Camera Parameters from calibration data of correspondences between points (either coplanar calibration or non-coplanar). See wc2ic.cpp for a C++ style wc2ic.c program. Files for the TsaiCal C++ Class can be downloaded below:
For details of Tsai method, information can be found on Reg Wilson's site. From Horn's MIT page, the following paper may also be useful: Tsai's camera calibration revisited.
Chris Needham - Leeds Vision Group, School of Computing. 07-Feb-2003.