## 4 Experimental Results
### Evaluation on Synthetic Images  
To better investigate the reasons that brought the CNN to produce such results, we developed a data set of synthetic images, as reported in Section 3.1.2, by adding healthy WBC to the original healthy ALL-IDB1 test images (six samples) in all the candidate positions. It must be noted that in this case, the number of cells added is different for each image. This data set is used as an additional testing set for the CNN models fine-tuned with the original ALL-IDB1 training set images. The results of such test are reported in Figure 6 and, as it can be observed, the performance degrades for all the tested CNN architectures.  
In order to understand under what circumstances the networks start to misclassify, we performed an in-depth investigation by selecting a portion of the previous synthetic data set, where the maximum number of added cells is 20. This value was chosen based on the limit of the image with the lowest number of candidate positions. Then we split this synthetic data set into 20 sub-sets, each one containing the synthetic images presenting the same number of images but with an increasing number of added WBC. That is to say: _imgSynt1_ contains images with one additional WBC, _imgSynt2_ contains images with two additional WBC, until the last one, _imgSynt2_ which contains 20 additional WBC. This experiment aims to verify if progressively adding healthy WBC to the original test images can affect the CNNs' predictive ability.  
This trend is completely confirmed for the majority of the networks exploited. As reported in Figure 7, three networks start to misclassify quite early, breaking the 100% results obtained on the original test sets. Indeed, VGG-16 and VGG-19 reached 63.6% and 78.8% accuracy after five additions, as indicated by the magenta line. GoogLeNet followed the  
Figure 4: Visual Grad-CAM explanations for ResNet-50 exploited on the original test set images belonging to the healthy category. (**a**) Image n. 34 (**b**) Image n. 43 (**c**) Image n. 47 (**d**) Image n. 71 (**e**) Image n. 72 (**f**) Image n. 74.  
Figure 5: Visual Grad-CAM explanations for ResNet-50 exploited on the original test set images belonging to the ALL category. (**a**) Image n. 31 (**b**) Image n. 32 (**c**) Image n. 33 (**d**) Image n. 48 (**e**) Image n. 49.  
same scheme starting from eight additions, while MobileNet-v2 from ten and Inception-v3 from fourteen. Finally, ShuffleNet performance began to degrade from the seventeenth addition. In this scenario, the only networks not affected by degradation are the residual networks ResNet-50 and ResNet-101, showing strong robustness based on the obtained accuracy. In Figure 8, we reported the activations computed on the synthetic images in order to analyse the behaviour on the same images when varying the number of cells. For the sake of brevity, we reported the activation maps for the ResNet-50 only and for the _imgSynt10_, _imgSynt15_, and _imgSynt20_.  
Even in this case, the CNNs do not give relevance to the features of WBC, but the classification score is entirely based on features that are not generally useful to predict the presence of leukaemia from blood images. In particular, it can be noted that the activations change with the addition of more WBC, although the changes are not linked to the number but mostly the position of the new cells.  
Figure 6: Classification accuracy obtained by the different CNNs adopted in the synthetic data set.  
Figure 7: CNNs’ accuracy trend when increasing the number of WBC inside the image. In particular, the x-axis values start with _imgSynt1_ that represent the synthetic test set with one WBC added and terminate with _imgSynt20_, composed of twenty WBC added.