process is varied randomly, repeated digitizations of the
teature on the right window with ditterent starting pixel
positions will generate a number of combinations of the left
and right windows for matching. A precision of matching can
therefore be derived from all combinations from the root mean
square (RMS) of the differences between the correct matching
position of the right window and that actually computed by the
matching process. These results will be presented in the next
section.
4 Precision of Matching
Results of tests on the precision of matching based on the least
squares method are shown in Figures 1 to 4, while a
comparison of precisions obtained by least squares and cross-
correlation is given in Table 1. In Figure 1 the precision is
shown for a circular feature of 100um diameter, digitized by a
pixel size of 12.5jum and the same scale for the two images,
expressed as a function of the quantization level. The spread
functions used for the tests are shown on the appropriate lines.
This figure indicates that the highest precision obtained for
circles is from 0.03 to 0.05 pixel, for quantization levels of
greater than 5 bits (32 grey levels) and that the precision
deteriorates as the quantization decreases below 5 bits.
Indeed, the matching becomes erratic and on occasions, it fails
to converge. The magnitude of image blur, demonstrated by
the size of the Gaussian spread function, has little effect on the
precision of matching, although there is a tendency for the
matching to improve slightly as the spread function increases.
This may be partly due to the increase in the size of the
window brought about by the larger image blur. In Figure 2
the influence of the feature size for 2 cases of image blur and
quantization is demonstrated for a pixel size of 12.5um. In
this case the precision increases as the feature increases in size,
reaching .02 pixel for a feature size of 200um. These values
agree with the precisions of template matching achieved by
Beyer (1992). The effect of scale variations between the 2
images is demonstrated in Figure 3. A scale change of 10%
between the 2 images has almost no effect, but for scale
changes greater than 10%, the effects are much more
significant. For a scale difference of 30% the precision
deteriorates to greater than 0.2 pixel, while further changes in
scale would not result in successful matches.
The effect of rotations between the 2 images for crosses is
shown in Figure 4, which indicates a similar deterioration in
the precisions of matching as occurred for the circles.
130-
p Legend
8 120 +
Q ]| —Ow SF = 0.0 um
10- P
= moi SF = 25.0 um
X 100 - ST
S — SF = 50.0 um e
2 90 “I 221 $
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=
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5 507
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Q 407
o
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tC
0. 20 T T T T T T T
8 7 6 5 4 3 2
QUANTIZATION LEVEL (Bits)
Figure 1 Precision of least squares matching for circular feature
100 um in diameter, in terms of quantization level for
3 spread function sizes (SF) for pixel size of 12.5
um.
e Legend
—2 SF - 0.0 um
..... SF = 25.0 um
PRECISION OF MATCHING - RMS (pixel x 1000)
&
15 T T T T
50 100 150 200
SIZE OF THE FEATURE (um)
Figure 2 Precision of least squares matching in terms of circular
feature size for 2 spread functions (SF)
and pixel size of 12.5 um.
1704
160 - Legend
150 + ==" SCALE = 0.8 ’
4,
140. i... SCALE = 0.9 /
1304 $6
— SCALE = 1.0 5
120 4 Z
1104
PRECISION OF MATCHING - RMS (pixel x 1000)
888
704
60 -
50 -
40 A
30 +
20 T T T T T
8 7 6 5 4
QUANTIZATION LEVEL (Bits)
Figure 3 Precision of least squares matching in terms. of
quantization level for circular feature 100 um in size,
for 3 cases of scale variations between the two images,
290 - and pixel size of 12.5 um.
S 270 4 Legend
= 2501 000 PS = 12.5 yum ;
$ 23041 — PS - 16.5 um F
& 210-
=
& 190-
© 1704
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< 130 +
m 1104
£5
o 704
(Qj 50-
tc
a 30 T T T T
0 10 20 30
ROTATION ANGLE (deg)
Figure 4 Precision of least squares matching in terms of crosses
with 3 cases of rotations between the two images, and
pixel size of 12.5 um.
821
