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Some sample plots of the similarity functions , and
are shown in figure 4. These show the functions over a
relatively large range of translations, and demonstrate two important
features: that the secondary (incorrect) peak is downweighted in
, reducing the chances large mismatches; and in the closeup
results, the improved continuity of the similarity functions (which is
smoother and has less discontinuities for ).
Figure 4:
Example similarity functions for (left), (middle) and
(right). The top row shows the functions over a large range
of translations, the second and third rows show a closeup of the
functions, with the actual calculated values represented by circles.
The true translation value is 10.2mm for all of these plots.

Table 1 shows the values of and for 3 different SNR values and
2000 trials in each case. The low values of for are a
result of the downweighting of the secondary maxima, significantly
reducing bad mismatches. Also, was the most accurate (having
the smallest value of ) which is likely to be due to the decrease in
discontinuities in .
Table 1:
Results of robustness and accuracy measures for a simple object (see figure 3b) and a range of SNR values, for each of the three cost functions.
mm.

SNR = 5 
SNR = 15 
SNR = 50 

MR = 0.194 
MA = 0.71 
MR = 0.065 
MA = 0.26 
MR = 0.000 
MA = 0.20 

MR = 1.000 
 
MR = 0.909 
MA = 0.35 
MR = 0.807 
MA = 0.97 

MR = 0.516 
MA = 0.86 
MR = 0.494 
MA = 0.48 
MR = 0.129 
MA = 0.54 

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