# Spatially Adaptive Regularization in Image Segmentation
## 4 Results and Comparisons
The latter observation is confirmed by the experiments performed on tiger. Table 3 reports the corresponding model and algorithmic details, while the segmentations are shown in Figure 4 along with (visual) information on quantities used to define \(\lambda_{i,j}\) (see (8) and (10)). We see that the CTD and MM strategies produce satisfactory results, although they have been obtained by generalizing a non-textural model. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \(\lambda\) & \(\mu\) & it & it\({}_{\text{GS}}\) & \(\lambda_{min}\) & \(\lambda_{max}\) & it & it\({}_{\text{GS}}\) \\ \hline
**Image** & & **CEN** & & & & **CTD** & & \\ \hline brain & \(0.7\times 10^{3}\) & \(0.1\times 10^{4}\) & 5 & 19.2 & \(0.9\times 10^{3}\) & \(0.4\times 10^{5}\) & 5 & 14.8 \\ squirrel & \(0.118\times 10^{3}\) & \(0.1\times 10^{4}\) & 6 & 50 & \(0.118\times 10^{3}\) & \(0.1\times 10^{4}\) & 15 & 50 \\  & & & & \(0.2\times 10^{3}\) & \(0.1\times 10^{4}\) & 5 & 45 \\ \hline  & & **CEN** & & & & **MM** & & \\ \hline bacteria2 & \(0.1\times 10^{3}\) & \(0.1\times 10^{4}\) & 2 & 50 & \(0.1\times 10^{3}\) & \(0.1\times 10^{4}\) & 10 & 50 \\ ninetyeight & \(0.2\times 10^{2}\) & \(0.1\times 10^{3}\) & 4 & 38.5 & \(0.1\times 10^{2}\) & \(0.5\times 10^{2}\) & 3 & 50 \\ \hline  & & **CEN** & & & & **THR** & & \\ \hline bacteria & \(0.5\times 10^{4}\) & \(0.1\times 10^{5}\) & 6 & 27.5 & \(0.4\times 10^{4}\) & \(0.8\times 10^{4}\) & 7 & 30.7 \\ flowerbed & \(0.1\times 10^{2}\) & \(0.1\times 10^{4}\) & 2 & 27 & \(0.3\times 10^{2}\) & \(0.1\times 10^{3}\) & 2 & 16.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Segmentation of six test images by the CEN and spatially adaptive models: parameters and iterations. The value of \(\mu\) is the same for all the models, thus it is reported only once per image. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**CEN**} & \multicolumn{3}{c}{**CTD**} \\ \hline
**Image** & \(\lambda\) & \(\mu\) & it & it\({}_{\text{MS}}\) & \(\lambda_{min}\) & \(\lambda_{max}\) & it & it\({}_{\text{MS}}\) \\ \hline cameraman & \(0.8\times 10^{3}\) & \(0.1\times 10^{3}\) & 4 & 2.8 & \(0.5\times 10^{3}\) & \(0.1\times 10^{4}\) & 4 & 3 \\ cameraman15 & \(0.3\times 10^{3}\) & \(0.1\times 10^{3}\) & 5 & 4.2 & \(0.3\times 10^{3}\) & \(0.1\times 10^{4}\) & 5 & 4.2 \\ cameraman25 & \(0.17\times 10^{3}\) & \(0.1\times 10^{3}\) & 6 & 7 & \(0.17\times 10^{3}\) & \(0.8\times 10^{3}\) & 6 & 7 \\ \hline \multicolumn{7}{c}{**MM**} & \multicolumn{3}{c}{**THR**} \\ \hline
**Image** & \(\lambda_{min}\) & \(\lambda_{max}\) & it & it\({}_{\text{MS}}\) & \(\lambda_{min}\) & \(\lambda_{max}\) & it & it\({}_{\text{MS}}\) \\ \hline cameraman & \(0.5\times 10^{3}\) & \(0.1\times 10^{4}\) & 4 & 3 & \(0.5\times 10^{3}\) & \(0.1\times 10^{4}\) & 4 & 2.8 \\ cameraman15 & \(0.3\times 10^{3}\) & \(0.1\times 10^{4}\) & 4 & 4.2 & \(0.3\times 10^{3}\) & \(0.1\times 10^{4}\) & 5 & 3.6 \\ cameraman25 & \(0.17\times 10^{3}\) & \(0.5\times 10^{3}\) & 6 & 7 & \(0.17\times 10^{3}\) & \(0.8\times 10^{3}\) & 7 & 5.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Segmentations of cameraman and its noisy versions by using CEN and the spatially adaptive models: parameters and iterations. The value of \(\mu\) is the same for all of the models, thus it is reported only once per image. Figure 3: Segmentations of bacteria and flowerbed by using CEN and THR.