## 3 Results and Discussion of Computational Experiments
### Parametrization of the Demons Algorithm
Default values are: \(N=100\), \(\rho=3\,\mathrm{y}\,\sigma=1.0\). Now, according to the solutions obtained in each scenario, the set of points with \(S^{corr}\geq 0.9600\) form discrete sets of solutions that allow for analyzing the solutions, obtaining a balance between the criterion for minimizing the registration time, and maximizing the correlation coefficient. Therefore, if we denote \(T_{max}\) and \(S^{corr}_{max}\) as the maximum computing time and the maximum correlation coefficient, respectively, obtained  
Figure 6: Efficient frontier coefficients, correlation coefficient vs. computing time, using local search algorithm. in each scenario, using the data shown in Figure 6, then we can establish the following intervals: \(T_{min}\leq t\leq T_{max}\) and \(S^{corr}_{min}\leq S^{corr}\leq S^{corr}_{max}\), \(S^{corr}_{min}\) is 0.9600 or the lowest correlation coefficient greater than 0.9600 and \(T_{min}\) is the corresponding registration time. Table 2 records the proportional increases in computing time (time increase ratio) calculated as \(\frac{T_{max}-T_{min}}{T_{min}}\), the length of the correlation coefficient interval (CC interval length) calculated as \(S^{corr}_{max}-S^{corr}_{min}\), and center value in the correlation coefficient interval (center of the CC interval). These values indicate how much the computation time should be increased for a given increase in the correlation coefficient, using the demon algorithm. For example, in Scenario 2, to increase the correlation coefficient by 0.0061 units then the recommendation would be to use a set of parameters \(\rho\), \(N\), and \(\sigma\) that require 3.5455 times longer. Scenario 4 requires the least time increase, requiring 52% times longer for an increase of 0.0050 (0.52%) units in the correlation coefficient. On the other extreme, Scenario 8 presents a potential increase of 0.83 units in the correlation coefficient (0.86%) and requires 24.24 times more time. The scenario that presents the highest rate of increase in the correlation coefficient with computation time is Scenario 7, where an increase of 70% in computation time generates an increase of 0.69% in the correlation coefficient. The above data corroborates that, although it is possible to improve the quality of the propagated contours using the demon algorithm, correlation coefficients around are good enough in relation to the computational effort. Figure 7 shows the impact and correlation coefficients with a difference of 0.0085 for Scenario 6. Table 3 presents the parameter values for \(\rho\), \(N\), and \(\sigma\) found with the local search algorithm for each of the breast CT scenarios. Very stable results are obtained for parameters \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Scenario**} & **Time Increment** & **Correlation Coefficient** & **Correlation Coefficient** \\  & **Ratio** & **Interval Length** & **Center Value** \\ \hline
2 & 3.5455 & 0.0061 & 0.9658 \\
3 & 2.2114 & 0.0051 & 0.9635 \\
4 & 1.5268 & 0.0050 & 0.9646 \\
5 & 5.4101 & 0.0050 & 0.9667 \\
6 & 16.7341 & 0.0084 & 0.9657 \\
7 & 1.7081 & 0.0066 & 0.9657 \\
8 & 24.2389 & 0.0083 & 0.9648 \\
9 & 21.8860 & 0.0065 & 0.9645 \\
10 & 3.3256 & 0.0079 & 0.9626 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Time increment ratio, correlation coefficient interval length, and center value correlation coefficient interval for Scenarios 2 through 10. Figure 7: Contrast between contour propagation with different correlation coefficients. The green and magenta colors show areas where the images do not match. corresponding to the number of levels in the smoothing pyramid \(\rho\) and the number of iterations in the first level of the pyramid \(N\), which are \(\rho=1\) and \(N=100\). However, for the parameters corresponding to the smoothing level for the Gaussian distribution \(\sigma\), the values differ significantly, varying between 1.5 and 2.9.