## 4 Results and Discussion
### Evaluation of the Proposed Approach  
In the first set of experiments, we investigate the choice of the inter-histogram distances of Section 3.1.2 on both datasets. In this experiment, we use the CP class as the reference. The results have been obtained by selecting \(N_{T}=500\) reference images and a number \(N_{bin}=50\) of histogram bins. Moreover, the \(\eta\) variable in (2) has been set to \(\eta=2\) for the CT dataset and to \(\eta=1.4\) for CXRs, respectively. Table 4 summarizes the results, obtained by the proposed approach, in terms of the Accuracy, Precision, Recall, and F-measure metrics, introduced in Section 3.4 and defined in Table 3.  
The results of Table 4 support the effectiveness of the proposed approach. In fact, all of the considered metrics reach high values, and, interestingly enough, they reach the top result of 100% with some distance measurements. Table 4 also reports the mean \(d_{m}\), standard deviation \(\sigma_{d}\), and the related threshold \(TH\) obtained by Equation (2). The second column of this table shows that the actual value of \(\sigma_{d}\) depends on the selected inter-histogram distance. By a careful examination of the rows of Table 4, we can draw three main considerations:  
* although all the considered distances provide good results for the CT datasets, the cosine distance is able to reach 100%;
* in case of CXR dataset, all the considered distances obtain the accuracy of 100%; and
* for both the datasets, the cosine distance provides the lower values of the standard deviation \(\sigma_{d}\). The results provided in Table 4 support the use of the cosine distance that works to advantage, compared to the other distance measurements. In fact, cosine distance is able to capture the \"spatial\" information provided by histograms, since it effectively measures their similarity, regardless of the single bin values. Motivated by these considerations, in the following tests and comparisons, we use the cosine distance. \begin{table}
\begin{tabular}{l l} \hline \hline
**Performance Metrics** & **Formula** \\ \hline Precision & \(\mathit{TP}/(\mathit{TP}+\mathit{FP})\) \\ Recall & \(\mathit{TP}/(\mathit{TP}+\mathit{FN})\) \\ F-measure & \(2\mathit{TP}/(2\mathit{TP}+\mathit{FP}+\mathit{FN})\) \\ Accuracy & \((\mathit{TP}+\mathit{TN})/(\mathit{TP}+\mathit{FN}+\mathit{FP}+\mathit{TN})\) \\ TP rate & \(\mathit{TP}/(\mathit{TP}+\mathit{FN})\) \\ FP rate & \(\mathit{FP}/(\mathit{FP}+\mathit{TN})\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The used performance metrics. In order to give visual insights about the results in Table 4 and justify the top 100% accuracy, we point out that Figure 3 shows the numerically evaluated spectra of the obtained cosine, KL, and Bhattacharyya distances. Since the \(\chi^{2}\) distance behaves as in the latter two distances, it is not explicitly depicted in the paper. This figure clearly shows the effectiveness of the proposed approach. In fact, we can see that the NCP CT scans (the first 500 bars in the left panels of Figure 3) are much more distant with respect to the corresponding reference images (the last 500 bars). Similar conclusions apply to the CXRs (the first 100 bars and last 97 bars in the right panels of Figure 3, respectively). The difference between the classes is about one order of magnitude for the cosine distance, while it is reduced for the KL divergence and the Bhattacharyya distance. These last cases also show a larger variance of the obtained distances with respect to the cosine distance, as already highlighted by the second column of Table 4. However, Figure 3 also underlines that the differences between the considered distances in the case of CXRs are more limited with respect to the CT case. As a final consideration on these first results, both Table 4 and Figure 3 confirm that a lower value of the standard deviation \(\sigma_{d}\) makes the performance more robust with respect to the outliers eventually present in the tested dataset.