## 5 Conclusions and Hints for Future Research  
In this paper, we investigate whether a traditional histogram-based approach can be used for the detection of CT and CXR scans of infected lungs. Specifically, we propose a histogram-based approach to detecting the new coronavirus pneumonia from CT and CXR scans. Since the number of these images is not high, we evaluate a target histogram on a reference class (i.e., normal or common pneumonia). A suitable inter-histogram distance is then used to evaluate how far this target histogram is from the corresponding histogram evaluated for an unknown test scan: if this distance is above a threshold, the test image is classified as anomaly, i.e., affected by the COVID-19 disease; otherwise, it is classified the same as the target class. A number of numerical results, evaluated on two open-source benchmark datasets, demonstrates the effectiveness of the proposed approach, since it is able to obtain a top degree of the considered performance metrics (i.e., accuracy, precision, recall, and F-measure), equal to unit value, comparable to the corresponding state-of-the-art DNN approaches, but with a limited computational complexity. In a nutshell, the main lesson stemming from the reported performance comparisons is that, at least when the images, embraced by the considered datasets, are homogeneous enough (i.e., few outliers are present, so that the standard deviations \(\sigma_{d}\) of the corresponding inter-histogram (normalized) distances are limited up to 0.1), it is not really needed to resort to complex-to-implement DNNs, in order to attain reliable detection of the COVID-19 disease. The proposed histogram-based approach attains, indeed, very good detection performance, comparable with those of DNNs, but at an (extremely) reduced implementation complexity and training time (see Table 10). In future works, we aim at extending our methodology to different types of medical images, other than CT, and/or different diseases. We expect, in fact, that the automatic screening by means of pathological images can take a great advantage by the simplicity of our methodology, in both the resulting accuracy and prediction time. To this end, it could be interesting to investigate, as a second line of research, more performing inter-histogram distances, such as the Earth Mover's Distance (EMD) [115], which measures how much work it would take to transform one histogram shape into another. A third hint of future research can be addressed towards the use of Variational Autoencoders (VAEs) and Generative Adversarial Networks (GANs) for generating additional examples in the case of new variants of COVID-19, in order to be fast in the automatic discrimination of these scans without awaiting the construction of sufficiently copious dataset. Finally, a fourth line of future research can be focused on the implementation of the proposed methodology atop distributed Cloud/Fog Computing technological platforms [116; 117], in order to produce fast and reliable clinical responses by exploiting the low-delay (and, possibly, multi-antenna empowered [118; 119]) capability of the supporting broadband wireless access networks [120]. Conceptualization, M.S. and E.B. ; methodology, M.S., E.B. and L.P.; software, M.S. and S.S.A. ; validation, A.M., M.S., L.P. and S.S.A. ; formal analysis, E.B. and M.S. ; investigation, M.S., L.P. and E.B. ; data curation, A.M. and S.S.A. ; writing--original draft preparation, M.S. ; writing--review and editing, M.S., L.P. and A.M.; visualization, A.M.; supervision, E.B. ; funding acquisition, E.B. All authors have read and agreed to the published version of the manuscript.