Second calibration example - Calibration using Zhengyou Zhang's data
The previous example showed you how to run
calibration from raw images. It is worth noticing that our toolbox may
also be used in case where some calibration data have been previously
computed. As an illustration, let us use our calibration engine on Zhengyou Zhang's
calibration data that he made available on his calibration
page at Microsoft Research. Do not bother downloading the data
from there, we have it all ready for you right here just one mouse
click away: zhang_data.zip (621Kb
zipped). After download, retrieve all the files present in the
package in a directory called zhang_data (this should be
automatic). This directory contains the original calibration images
(five of them) used by Zhang (in tif format), together with the
planar calibration rig model and the extracted corner coordinate files
that Zhengyou Zhang distributes on his web page.
In addition, you will find a small matlab script file called
demo_script.m. Under Matlab, run that script file
demo_script.m. This script converts all Zhang's data into my
calibration format, reads in the images, runs through the main
calibration engine, shows the results (intrinsic + extrinsic), and
saves them under a file called Calib_Results.mat. This small
script demonstrates that our calibration toolbox may easily be used in
cases where some data have already been extracted (in this case, the
corner coordinates). Observe that setting the variable dont_ask
to one lets you use the main toolbox functions (optimization +
graphical display) in script mode without being prompted. This is also
quite useful for including calibration calls in your own matlab script
files. In this present example, compare our calibration results
(fc, cc, kc, Rc_1, Tc_1,
Rc_2, Tc_2, ... , Rc_5, Tc_5) with Zhang's.
Quite similar no? (observe that our distortion model includes two
additional terms accounting for tangential distortion. The other terms
are defined in the exact same way. For more information, visit the page describing the calibration
parameters.
Once the script is finished running, we may
want to try to include the skew coefficient alpha_c in the
optimization. For that purpose, set the binary variable
est_alpha to 1 (est_alpha = 1), and click on
Calibration. Observe that the final computed skew coefficient
alpha_c is very close to zero (i.e. pixels are
rectangular). For more information, visit the page describing the calibration parameters.
As a final ultimate comparison, you may want to run the
estimation is the exact same configuration as Zhang. For that, disable
the tangential distortion part of the model and limit the radial
distortion model up to the 4th degree (est_dist =
[1;1;0;0;0]), and activate the skew estimation (est_alpha =
1). After calibration, you should observe that our results are
exactly the same as Zhang's. To
compare skew estimation, look at the camera matrix KK. Zhang's
skew coefficient is defined as fc(1)*alpha_c, which is the
(1,2) entry of the camera matrix KK. For more information,
visit the page describing the calibration
parameters.
You may also try to re-extract the square corners on the calibration
images, by clicking on Recomp. corners. Select all the images,
the window size of your choice (for example wintx = 6,winty
= 6), and the automatic mode (required here). Then run calibration
again, and compare the results. As a general advice, we recommend NOT
to use such a pattern for calibration (disjoint squares generating
asymmetric corner features) . It is better to use symmetric corner
features such as the corners of a checkerboard pattern (the pattern
used in the first example). To retrieve
that pattern, visit that link.
Second calibration example - Calibration using Zhengyou Zhang's data