arization using
id T5 — 5 [gr?]
vs a clear seg-
indent of small
993], following
llowing model:
4, V), and
on in contrast
'y images, only
mark, the tem-
mation for the
nage b can be
(4)
(5)
=
late t, #b and
ding area of b
the size of the
valued, with a
imation can be
NO dimensional
olynomial in a
ixel position is
der polynomial
| l(à,6)(0) (9)
von p(u, v)
û,0)(0) (10)
nes Pu
Vo laa ism ( po ) l(à,6)(0)
The accuracy of this estimation is given by the covariance
matrix
; ù l = Pot 2] à !
B mec e AER el ae" s (1
»( $ ) m Pht [ p lay] T (11)
where
m is the number of pixels of the template t,
put — IS the similarity of the image and the template
at (à, 0),
Hp isthe roughness of the texture of the signal
(ref. equ. (10)) and
Az the size of a pixel assumed to be identical
in row and column.
The sub-pixel and the accuracy estimation are only based on
the analysis of the correlation function, and can therefore be
used for the binary as well as for the grey level correlation.
4.5 Consistency check
The result of the individual localizations on each pyramid level
is checked using a consensus criterion to detect outliers and,
if necessary, to predict a more likely position for the outliers.
The outlier detection is similar to the RANSAC technique pro-
posed by [BOLLES R. C. / FISHLER M. A. 81]. With a min-
imal set of observations a similarity transformation between
pixel and plate system is estimated. This transformation is
used to check the remaining observations based on remaining
errors. In contrast to the RANSAC we do a complete search
for the 'best solution' because the number of observations
is small. The best solution is defined as the transformation
having the smallest remaining errors. This transformation is
used to detect outliers and eventually to predict a more likely
position for the fiducial mark in the image.
5 SELF-DIAGNOSIS
It is important for each automatic system to be able to make
a selfdecision on the acceptability of the result. Automation
needs predictable results.
The principle of Traffic Light Programs proposed by
FORSTNER 1994 classifies the result in three different states:
red: The system was not able to solve the problem, or the
found solution has been classified as incorrect. The
system gives reasons for the failing.
yellow: The correctness of the solution is doubtful, the sys-
tem gives a warning including a certainty of the correct-
ness and a diagnosis of possibly correct and incorrect
parts.
green: The found solution is verified as being correct.
For the control of the traffic light an objective quality control
measure is necessary. The next section introduces the control
measure we use to classify the result in these three stages.
5.1 Sensitivity Analysis
Gross errors can hide behind small residuals or excellent fitting
of data and model, therefore they do not necessarily produce
large variances in the estimated parameters. Consequently,
an additional sensitivity analysis for self diagnosis is used, to
classify the result.
The task has not been solved.!!!
The reasons might be :
The task may have been solved.
The certainty is:
Possibly correct parts:
Possibly incorrect parts:
The task has been solved.
The result is:
The quality of theresultis: —
A
Figure 7: The principle of Traffic Light Programs
The concept of sensitivity analysis developed by Baarda
[BAARDA W. 67 ,68] is based on the measures for the inter-
nal and external reliability. The elementary theory has been
expanded and specified for our purpose [cf. FORSTNER W.
83, 92 ].
Here the sensitivity analysis is used to investigate the
influence of the observed position of each fiducial or each
combination of two fiducials onto the estimated transfor-
mation parameters. A single fiducial is represented by two
coordinates, a combination of two fiducials is represented by
four coordinates. Therefore the sensitivity analysis is applied
to groups of observations. The sensitivity measures are as
follows:
The empirical sensitivity
é T Lu: (12)
(internal reliability according to Baarda) measures the max-
imum influence of the observation group i to the estimated
parameters. |f this group is omitted an arbitary function
f = a” - y with variance c; = a" Dyya of the estimated
parameters y does not change more than
Vif x ó; gf (13)
The theoretical sensitivity
Óio — do + pi (14)
(external reliability according to Baarda) gives the maximum
influence of undetected errors in observation group à onto the
estimated parameters. The influence of an undetected error
in the observation group 4 is bounded by
Voif sS doi “Of (15)
where
749
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
