an ellipse?
To give an idea of how such an measurement mark is
represented on frame grabber, the following grey scale
picture of a well defined ellipse shown:
152.132 97 52 36:37: 31 27 31:40 54 72.835 78. 106
142 122 87 42 25 21 13. 12 20 24 32 56 69 72 109
127.97 70 36 11 5. 5 5 11-13-19 42.60 71 :106
116. 81-50: 257 ar] 4,0. 0.2.6 15 35..52 .70..102
107.6939 16 4 0 .0 0 O0 3 10 24 47 69. 99
87 53 34 16 0 0 0 0 0 0 2 14 39 65 95
76.153 30 ‘10° 0 20 0. 0 0 0° 0 8 “31 61:88
76 58-31.2. 0-0 0.0. 0-/10- 0.7. 22 +50 - 88
85 56 21 0 0 0 0.0 0 0 0,33. 15 43 80
8 52 13 0 0 00 0 00 60 1 2°3 H
8 53 14 0 0 0 0 0 6 G G 0 6.27 6
81.53 18.0.0 0, .0..0 40 0.0.0 5. 26.62
90 644 233 0 0 0 0 0 60 0 0 0 16 31 60
100.71 22:2 0 0° 0 0 0 0 0 Q0 14 3 63
1232 31.3 0 0 0 0: 0-0 0 O0 8 3% 66
113 70 30 1900 0 0 0 0 0 0 0 |! 39 60
10361 33 15 2 0 0 0 0 0 0 0 15 36 63
92 58 31 14-4 0 0 0 Q0 —0 0 5 2 4 70
100381 46 17 6 0 0 0 0 O0 4 14 27 48 7$
F592 52 17 3 0 0 0 0 0 6 17 30 52 8
133 105.60 23 1d4 11:4 0 0 0 5 20 39 76 109
139.109 71 44 28 10 8 6 3 7 14 24 44 87 125
153 132 100 64. 40 16 15 16 13 19$ 22 35 60 95 135
173 165 133 84 60 33 25 23 19 22 33 50 79 105 143
In order to show the measurement on an ellipse in de-
tail and how the problems described above can be
solved, an example of an ellipse measurement proce-
dure is given.
Based on an approximate value, seven straight lines in
50° ankles are set and the highest gradients of the grey
scale on these lines are identified. The coordinates of
these gradients are taken as potential ellipse margins.
With these seven coordinates a ellipse with minimal
error is approximated. If the initial approximate value
was not focused in the ellipse it will in most cases be
impossible to find an ellipse with a sufficiently small
error rate through these points, meaning that the ap-
proximate value has to be improved. Should the ad-
justment succeed erroneously, the same procedure
must be repeated with a number of straight lines selec-
table by the user. In this case, the adjustment of an el-
lipse with a relatively high number of straight lines will
fail if the approximate value was not situated in the
signal to be measured. Also in this case the approxi-
mate value is improved afterwards.
If the approximate value was initially placed within the
measurement mark the test described above is success-
ful and the real measurement with an amount of
straight lines adjusted by the user can be started. The
value resulting from the seven-lines-test is taken as an
approximate value for the accurate measurement. The
advantage is, that the second initial value is placed in
the center of the ellipse and therefore the straight lines
starting at this point cross the margins of the ellipse at
a 90? ankle. For this reason they cross distinctive el-
lipse margins, which can be calculated with high accu-
racy. Based on the error rate of the ellipse adjustment
it is possible to distinguish between objects and inter-
ferences. Should this interference be a perfect ellipse,
it is impossible to avoid that this false ellipse is re-
cognised as a signal mark. A further hint to identify
such false ellipses is the size of this mark in the frame
grabber system. In general, calculated values are taken
as an approximate value for measuring the ellipse.
These values result from approximately known object
coordinates and the recording position. As this also
gives the distance between signal marks and recording
position it is possible to calculate the size of the signal
marks in the negatives. This calculated size is used for
the identification and control of the signal.
The approximate value (or the potential ellipse focus)
must be improved in the following cases:
e the error rate resulting from the adjusting ellipse of
the first test or the main measurement is too high
e the difference between calculated and measured
size is too high
This is achieved by means of search of gradients on a
helical path around the starting point.
For this search it is presumed that the starting value is
not situated within the ellipse. In case of black target
marks it is then searched for a transition from bright to
dark on the helical path. Having found such a transi-
tion of sufficient size the search is continued until a
transition from dark to bright is found. The center of
the connecting line is used as the following starting
point for the described ellipse measurement. To avoid
an ellipse adjustment on an already tested position, the
positions on which the adjustment had already failed,
are stored and compared to probable new positions.
Only if the positions differ significantly from the ex-
isting ones, a new ellipse adjustment is tried. This pro-
cedure avoids repeated failing adjustments, as for ex-
ample on bright to dark margins.
A one-dimensional folding on a seven scale field is
used to identify the transitions. The corresponding
vector is the following:
A u 9 1 2 3
The gained folding values correspond roughly to the
first derivation of the function defining the basic grey
value spectre. This first derivation is examined under
the aspect of finding a maximum or a minimum. The
exact position of the maximum is determined by calcu-
lating the center point above the folding values. This
maximum, represented by sub-pixel values, cor-
responds to the turning point of the grey scale func-
tion. This turning point is the requested transition from
dark to bright or vice versa.
The search of gradients by means of a folding has the
advantage of being tolerant against interferences as it
takes into consideration a relatively large spectre of
grey values. This tolerance is intensified by the addi-
tional calculation of the center point above the detec-
ted folding values.
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