ıts X, Yand Z
st 4 uses four
case
bl Ed Bd EM
w
|
m the check
ime check
Case
hl Bu E EN
Og nw»
4
m the check
correlation
n of trans-
shows an
iduals for
calculated
(43)
ial reliabi-
lity is to see how many of the observations have an
diagonal element value above 0.5 in oF, as shown i
figure 7.
p 1,07
4 case
08 - EB A}
| Ed B
€
067 D
04 7
027 7
00 - AA
6 13
Fig6 Average values of the residual correlations pij from the
parameter calculation using 6 or 13 control points.
100,0%
| case
80,0% ++ B A 7
7 C 7A
60,0% +— El D p
| A
7
40,0% Z
| S
20,0% 7
0,0% %
6 13
Fig7 Estimation of internal reliability. The staples indicates
the percent of parameters in case A, B, C, and D with a value above
0.5 in the diagonal of À using 6 or 13 control points. The values for
case À and B using 6 control points are zero.
5. DISCUSSION
The evaluation is intended to give an estimate of the
precision and an idea of the internal reliability, using
different number of control points and cameras. The
evaluation is theoretical in that it is based on an ideal
simulated camera and comparator measurements. The
distance between camera and control/check points
have been short.
The test results of precision is shown in tables 4, 5 and
figures 5, 6. The values of mean deviation in table 4, 5
does not give anything on the distribution of precision
in the check point grid. However, the values are
intended for a comparison of case A, B, C and D as
shown in figure 4 and 5.
Figure 4 and 5 confirms the intuitive idea that itera-
tive DLT should give a better precision compared to
linear DLT and that bundle adjustment should give a
better precision with 6 compared to 9 unknown
parameters. It is also shown that the difference in
precision decreases between DLT and bundle
adjustment when the number of control points is
increased. An interesting result is that the difference
41
between DLT, case A and B, and Bundle adjustment
with 9 unknown parameters, case C, is rather small
when 13 control points are used. The iterative DLT in
case B is even better than Bundle adjustment in case C.
In general, the mean deviation in the Z-component is
about 2.5 to 3 times higher compared with the X and Y
component. The relative difference of the Z-
component between case A, B, C and D is
approximately the same as for the X and Y compo-
nents.
Correlation of the comparator measurement residuals
resulting from the calculation of transform parameters
are shown as average values in figure 6. It indicates
that DLT needs many control points to have an accep-
table internal reliability. In case A and B, with only 6
control points, the residuals are fully correlated, i. e.
the residuals of the comparator measurements are
dependent on each other. A gross errors in one of the
comparator measurements is not possible to locate
when DLT is used. Bundle adjustment has lower cor-
relation compared to DLT when 6 control points are
used. When 13 control points are used the difference
between DLT and Bundle adjustment becomes small,
but still Bundle adjustment is better.
Figure 7 gives an idea of in how many of the compara-
tor measurements a gross error can be detected. Using
DLT and 6 control points, i. e. case A and B, a gross
error can not be detected in any of the comparator
measurements. For Bundle adjustment the situation
is better. With 13 control points the difference between
DLT and Bundle adjustment becomes smaller. A gross
error can be detected in 70 - 85% of the measurements
in case A, B, C, and D.
An indication of future work in evaluating the
methods is to make a more extensive study of internal
and also external reliability which are important
aspects of the methods.
6. CONCLUSIONS
Bundle adjustment gives a better precision and inter-
nal reliability compared to DLT when the control
points are few. When more control points are used the
difference decreases in both precision and internal
reliability.
In a case where a non-metric camera is used, i. e. the
internal orientation of the camera is unknown, and
many control points are available and well distributed
in object space, the iterative DLT is preferable when
precision is important. The linear DLT gives almost
the same precision as Bundle adjustment but may also
be preferable because no estimates of the parameters
are needed.
