face generally contain substantial difference in grey level value
with the background so recognition and location of these tar-
gets in a digital image is done by setting a suitable threshold
of grey level for the image. Disproportional influence of low
intensity outer pixels on centre of mass calculation may be
removed by weighting pixel position with the corresponding
grey values of the pixels [Trinder, 1989]. This approach re-
duces the influence of incorrect thresholding but errors due
to noise and uneven illumination become more significant.
Attempts are also made by different researchers to recover
perspective image distortion of circular targets by ellipse fit-
ting, focal length normalisation and Gaussian shape fitting.
However, the selection of a suitable threshold to segment the
real target area in a digital image (Figure 6) remain a major
problem for threshold based approaches.
Digital image | ... Histogram of
grey level
Target point
150 T 100
Figure 6: Asymmetry of a target image during different levels
of thresholding.
Differential variation of contrast of the target points with that
of the object's surface makes it very difficult to detect the
correct boundary of a target point. There is a considerable
influence of change in contrast and texture of object surface
on the target image information (Figure 7). A textured object
surface makes it very difficult to isolate the correct target
area.
Object surface Change of contrast ,
a
Si
id X
pr EN
pee
es
Error in centroid location
Grey value distribution in digital image
Figure 7: A simple case of texture influence on centroid lo-
cation.
2.1 Template matching
In practice it is very difficult to obtain an object with uni-
form texture. Even the surface of a massive sandstone strata
does not have ideally uniform texture. Beyer's (1992) inves-
tigations for precise digital measurement found least squares
based template matching to be the best solution for sub-
pixel target location of a well targetted textured images.
A comparison of simulation results for centroid location by
542
different techniques [Trinder et al., 1995] show best perfor-
mance of a least squares based template matching for flat
targets. Gruen's (1985) "adaptive least squares correlation"
algorithm was modified at UCL [Otto & Chau, 1989] to a
"region-growing" algorithm which provided excellent perfor-
mance for automatic three dimensional measurement [Day &
Muller 1989 ] from low resolution aerial and satellite images.
The basic adaptive least squares correlation algorithm has
vast potential for accurate centroid location and was used
during this study.
2.2 Template selection
In least squares based template matching, the algorithm finds
the best match of grey values for a patch called a template
to a patch around the estimated point in the image allow-
ing affine transformation. Best match minimises the sum
of the squares of the grey-level differences between the two
patches. As discussed above, least squares template match-
ing performs well for centroid location of target points placed
over a textured object but the selection of a suitable template
is not completely straightforward. There are two possibilities
for template selection: simulated templates of different sym-
metrical nature and templates extracted from the image itself.
It is possibleto simulate templates of different texture charac-
teristics but the texture variation of the original target image
Is too complicated to simulate (Figure 8). Texture variation
Figure 8: Texture variation in different templates.
Is the most important factor for the accuracy of least squares
based template matching. For both active and passive tar-
gets (Figure 9) simulated templates provided poorer results
in comparison to those of the templates extracted from the
image. For symmetrical target points, such as those produced
by the diffraction grating based laser diode, the template ex-
tracted from the image itself provided the best results.
2.3 Optimum size of template
The adaptive least squares matching algorithm uses an itera-
tive "Iinearise and solve" strategy. It is only likely to converge
if the initial estimates are good, so the nature and size of the
template play an important role during matching. Particu-
larly for a template extracted from an image, the size of the
template is an important factor. It is difficult to provide a
figure for the dimension of the template for different measure-
ments but minimum number of iterations and low eigen value
criteria can easily provide the optimum size of template for a
particular measurement. Different measurements were made
by varying the dimension of the template to find the optimum
size of the template. The variation of number of iterations
and eigen values of the covariance matrix for different tem-
plate size is shown in Figure 10 and Figure 11 respectively.
From these measurements it was observed that a template of
around 1.3 times the size of the target image provides opti-
mum performance. A simple statistical analysis of repeata-
bility of image co-ordinate measurement of these targets in
different frames is shown in Table 1. The accuracy of this
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