## 1 Introduction
In addition, the number of free parameters that must be adapted during the training leads to a high computational cost and many of the proposed DNN architectures can be trained only on powerful computers equipped with many GPUs in several hours. Moreover, the identification of scans of patients infected by COVID-19 is a problem more similar to the anomaly detection rather than the traditional classification, due to the small number of data present in each dataset [23]. It would, therefore, be appealing to design an anomaly detection algorithm, which is light from the computational point of view, and is capable of identifying radiology scans related to COVID-19 with high accuracy. In this direction, some works have focused on the application of GAN-based approaches to detect anomalies in medical images [24; 25]. However, such approaches suffer a not negligible computational cost. Considering all the above challenging limitations in employing DL techniques for detecting scans of infected patients, we wonder whether DNNs are absolutely necessary to detect such scans, or simpler methodologies may instead perform in the same way as the DNNs, although they do not have, in general, advantages over DNNs. Motivated by this still unanswered question, in this paper, we investigate whether traditional image processing techniques [26] can be reliable enough to detect images related to patients infected by COVID-19. Towards this end, we propose a histogram-based approach that exploits a suitable inter-histogram distance [27; 28]: the histograms of some target images (belonging to a reference class, i.e., not images of infected lungs) are averagedto produce a target histogram. This histogram is then used as a reference in the inference phase: for each unknown test scan, the related test histogram is obtained, and a suitable measurement of the distance between the tested and target histograms is evaluated. If this distance is below a certain threshold, the test image is classified the same as the target class; otherwise, it is considered an anomaly and labeled as COVID-19. Overall, the main contributions of this paper may be so summarized:  
* We propose a histogram-based technique to automatically detect the COVID-19 disease from CXRs and CT images. The histogram evaluation is a simple and very fast operation. In addition, in order to construct a target histogram, very few images are needed, in contrast to DNNs that have to use a huge number of scans to be trained. * We investigate different inter-histogram distances to evaluate how an unknown scan is far from the target one. These distances are used to label the test images as normal (reference class) or anomaly (NCP), depending on whether they are less or greater than suitably set thresholds. Although all the proposed distances can be computed with the same computational cost, we expect that some of them work better in practice. * We evaluate numerical results on benchmark datasets available in the open literature on CXRs and CT scans and compare the proposed approach to other state-of-the-art DNN-based architectures. We observed that the proposed approach, although very simple to implement, is able to obtain excellent results. We expect that the main insight, deduced from the numerical results of the proposed approach, is that, at least when the images of the considered datasets are homogeneous enough (i.e., a few outliers are present), it is not really needed to resort to complex-to-implement DNNs, in order to attain an effective detection of the COVID-19 disease. The rest of the paper is organized as follows. Section 2 presents the recent literature on the topic. Section 3 describes the proposed approach in terms of both the used methodology and inter-histogram distances, as well as introduces the experimental setup. Section 4 presents the obtained numerical results and performance comparisons, as well as provides the discussion on the proposed idea. Finally, Section 5 concludes the paper and outlines some future research.