## 4 Results
### Ki67 labeling Index Estimation  
Hot-spot detection is a complex process since each WSI presents specific characteristics for the tumor, cells, and Ki67 hot-spot distribution. In some WSIs, tumor proliferation is observed homogeneously throughout the whole specimen, while some samples present tumor proliferation areas in specific regions, which sometimes have multiple proliferation values. Therefore, WSIs usually present few tumor proliferation areas that represent significant values of the proliferation index. This fact makes manual Ki67 LI evaluation difficult, which leads to observed differences between automatic and manual evaluation. The results of the automatic (Auto) and manual (Manual) Ki67 LI evaluations are shown in Table 3 for 15 samples The manual evaluation was performed by two pathologists using two evaluation strategies. One pathologist performed the evaluation based on 10 FOV, while the second one performed the evaluation based on 1 FOV. Both methods are accepted as standard pathological procedures. As we can observe, the results achieved by our approach (Auto) provided a Ki67 LI that correctly estimated the manual values. There are several samples that deserve special comments:  
* Five specimens presented higher results using our automatic diagnosis with 10 FOV compared to the manual evaluation. This is because the automatic system always detects hot-spot areas with the highest tumor proliferation, which can be difficult to perform by manual evaluation, thereby skipping some regions of interest. * In three cases, we observed significantly smaller results than the medical evaluation for our automatic diagnosis of 10 FOV. We determined that the automatic system counts all cancer cells, while manual counting estimates the number of cells. This can lead to an imprecise estimation of the Ki67 proliferation factor. To evaluate the variations between medical estimations and the automated Ki67 LI process, three statistical tests were performed: the Bland-Altman plot, one-sided \(t\)-test, and [PERSON]'s \(\rho\) correlation. The Bland-Altman test allows one to compare two quantitative measures by setting agreement limits. These statistical limits are determined using the mean and standard deviation of the two measures. This is a popular method applied in clinical measurement comparisons, where each of the methods provides some errors. The results are presented in Figure 10 as a comparison between the various doctors' results and between the automatic results and the doctors' results. From these final results, the following can be concluded: \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Case** & **Auto 10 FOV** & **Auto 1 FOV** & **Manual 10 FOV** & **Manual 1 FOV** \\ \hline
1 & 15.70\% & 13.87\% & 22\% & 15\% \\
2 & 18.07\% & 19.36\% & 10\% & 15\% \\
3 & 36.24\% & 18.35\% & 40\% & 30\% \\
4 & 4.67\% & 6.07\% & 8\% & 5\% \\
5 & 20.47\% & 24.38\% & 17\% & 20\% \\
6 & 29.77\% & 27.77\% & 30\% & 25\% \\
7 & 48.40\% & 52.59\% & 50\% & 50\% \\
8 & 30.36\% & 23.78\% & 20\% & 25\% \\
9 & 67.60\% & 61.1\% & 90\% & 90\% \\
10 & 10.42\% & 2.68\% & 15\% & 15\% \\
11 & 31.44\% & 35.32\% & 30\% & 38\% \\
12 & 3.74\% & 10.23\% & 5\% & 10\% \\
13 & 24.62\% & 34.85\% & 25\% & 20\% \\
14 & 30.85\% & 30.29\% & 15\% & 15\% \\
15 & 9.34\% & 3.36\% & 8\% & 5\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Ki67 evaluation results. Number of samples: N = 15. * There is a difference between medical evaluation based on 1 or 10 FOV with a discrepancy equal to 0.47. This indicates a slight overestimation of Ki67 LI by the expert evaluating 1 FOV (Figure 10E). * Automatic diagnosis for 10 FOV and manual evaluation using 1 FOV resulted in a small underestimation for our method, with a discrepancy value of \(-\)0.25 (Figure 10A). * For the comparison between the automatic hot-spot evaluation for 1 FOV and the medical evaluation using 1 FOV, we observed a discrepancy of 0.93 (Figure 10C).