Master Thesis - Fachbereich Informatik

4.7. TEACH-IN 95
The pair of a pixel length l(i) and a real world reference L(i) can be used to compute
the ideal factor fpix2mm(i) thatconvertspixelsintomm for a measurement i as follows:
fpix2mm(i) = L(i)
(4.29)
l(i)
This procedure has to be repeated several times for different reference tubes. Finally,
the estimated calibration factor is computed analog to Equation 4.25 using a k-outlier
filter before averaging:
fpix2mm =
N−k �
j=0
f ′ pix2mm(j) (4.30)
where k is the number of outliers, N the number of iterations, and f ′ pix2mm indicates the
single calibration factors sorted by the squared distance to the mean in ascending order.
The median could be also used instead of averaging.
The root-mean-square error at iteration i betweentheknownrealworldlengthsand
thelengthscomputedbasedontheestimatedcalibrationfactorcanbeusedasmeasure
of quality.
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Err(i) = � i �
(L(j) − l(j)fpix2mm) 2 (4.31)
j=1
If the error is low, this can be used as indicator that the learned calibration factor is
a good approximation of the ideal magnification factor that relates a pixel length in the
image into a real world length in the measuring plane ΠM without any knowledge on the
distance between ΠM and the camera.
In practice, the learning of the calibration factor is an interactive process. One can
define a minimum and maximum number of iterations Nmin and Nmax respectively. Once
Nmin correspondences have been acquired, fpix2mm and Err(i) are computed for the first
time. The operator continues the procedure as long as the calibration at iteration i +1
does change more than a little epsilon compared to iteration i. This means the learning
can be stopped if |Err(i +1)− Err(i)|