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the right image using ellipse. The rectangle in 
ellipse method is displayed as a measure of the 
affine parameters. 
3.2 Case2 
Here a 25x25 (7625) pixels template was found to be the 
best. Both methods started from the same approximation and 
returned a correctly matched point after 8 iterations. Once 
again the square template is obviously wrong, misplacing the 
matched point towards the centre of the pavement, probably 
because of the shadow. As one can see in figure 4, the 
pavement in this particular spot is under a tree, causing left 
and right images to differ considerably, not to mention a 
"strange" line on the left image due to scanning (fig. 5). 
On the other hand the ellipse method provides a much better 
localisation, exactly on the edge of the pavement. During the 
iterations, the maximum and minimum of the pixels used 
were 634 and 624 respectively, instead of 625. These 
differences (1.4%) are considered minor and certainly not 
able to influence the final match. Once again, the ellipse 
returned a better value for o,, 15.25 against 21.12 of the 
square template, verifying initial considerations. 
  
Figure 5. Comparison between the square and ellipse 
template:Case2. Bad localization of the square, 
returns wrong point. The line in the left (template) 
image is the effect of bad scanning, which 
surprisingly doesn't affect the match. The final 
affine parameters are different. Observe the shape 
of the rectangle in both cases. 
3.3 Case 3 
This is described to show that in some cases the square 
template cannot return a match, while elliptical template 
returns the correct position. 
In this case the best template was found to be 29x29 pixels. 
The square method failed completely. It did not return a 
matched point. After failing using the 29x29 template, it used 
a larger template of 37x37 to include more information, and 
after that a 41x41 template, which is the largest template 
allowed by the user. After the failure of the 41x41 template, 
which can be seen in figure 5, the matching algorithm 
returned a complete failure, instead of a point (fig. 6). 
The ellipse method used the 29x29 or 841 pixels and found a 
correct match after 3 iterations. Actually in the second and 
third repetition 840 and 846 pixels were used instead of the 
expected, 841, but this is also considered a small deviation 
since it is 0.6%. 
In this particular case the ellipse method not only did find a 
correct match accurately, but it was faster than the square. 
In this case o, was 7.81, the lowest from all presented cases, 
although this case is obviously the weakest. This can be 
explained by the fact that the two images are similar and 
therefore the grey level differences are very small while the 
g and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
algorithm cannot find a strong solution, because the 
information around the pixel is the same for every point on 
the line. 
isa 
   
Figure 6. Comparison between the square and ellipse 
template:Case3. Complete failure of the square 
template, even with the largest 41x41 template. 
The shift along the line is clear. 
3.4 Case 4 
This case is described to show that the ellipse works just as 
well or even better as the square template in normal cases. 
The best template was found to be 15x15. Both methods 
return a correct match after 2 iterations (fig. 7). Elliptical 
template uses 223 pixels instead of 225, which represents a 
0.9% decrease of the total pixels used. This difference is 
incapable to affect the final match. 
There is a difference between the returned values of the 
matched point, 356.79, 898.55 (ellipse) and 356.58, 898.42 
(square). The difference of 0.19, 0.13 pixels, which is almost 
indistinguishable in figure 6, is justified if one considers that 
the expected accuracy of LSM is 0.1-0.2 of the pixel (Guelch 
E..1988). The same figure of 0.2 pixels for random points is 
also reported in Trinder, J.C. et al. The o,, which is a measure 
of precision of the final match, is in favor of the ellipse (7.32 
against 10.54 of the square), thus indicating that the elliptical 
template might return a more accurate position. 
  
a 
Figure 7. Comparison between the square and ellipse 
template:Case4. Both cases return a corrct match. 
4. CONCLUSIONS AND FURTHER RESEARCH. 
Until know ellipse has been tested against square template, 
a number of features, including points, 
In point features and in 
all cases 
manually over 
corners, uniform areas etc. 
homogeneous areas, the ellipse is almost a circle. In 
ellipse returns a better o, value, which is indicative of better 
precision. In certain cases, especially in linear features, it 
provides not only more accurate results, but also correct 
results even in some cases where square fails completely. The 
superiority of the elliptical template is shown numerically in 
table 1.