## 5 Discussion and Conclusions  
In this paper, we analyzed the impact on cross-sensor use of introducing variety in the type of training data, i.e., when the test data has been acquired with a different sensor than the training data; and on cross-method use, i.e., when the test data have been acquired with different techniques. This allowed us to provide some insights to PAD designers based on cost/efficiency trade-offs and the specific application context of the system. We have reported the main findings of our investigation in Table 12, from which we can derive the following guidelines:  
* For intra-method and intra-sensor experiments, training on the target sensor is preferable; however, training on multiple sensors does not significantly worsen the results;
* For cross-method experiments, training on different types of images allows obtaining better results for operational points relative to low APCERs. In general, using numerous data for ScreenSpoof tests at the EER is comparable to or better than the single best training;
* For the cross-sensor experiments, it is not possible to detect a benefit related to the use of training on multiple sensors. However, even single-sensor training does not result in effective PADs, showing that the interoperability problem is still open, and it is not possible to solve it without references from the target sensor. In particular, the need to use in training =the same sensing technology for data acquisition with respect to that expected during system operation was highlighted.  
To sum up, if the usage of the AFIS is entirely controlled, there is no expectation of sensor change over time and there is a low probability of falsification using unknown techniques. It is preferable to train with specific target data. If the aim is to make the system more robust to never-before-seen attacks, it is preferable to train it on different data sources. However, an analysis of the image characteristics is necessary to select the best training data.  
This work also highlights the need for an in-depth study of the characteristics of both live and fake fingerprint images to obtain a representation capable of including all intra-class variations due to different factors such as sensing technology, sensor size, materials, techniques for making a fake (for PAs), or skin conditions (for lives).  
**Author Contributions:** Conceptualization, G.L.M.; methodology, M.M., G.O., and R.C.; software, M.M., G.O., and R.C.; validation, M.M., G.O., and R.C.; formal analysis, M.M., G.O., and R.C.; investigation, M.M., G.O., and R.C.; resources, M.M., G.O., and R.C.; data curation, R.C.; writing--original draft preparation, M.M., G.O., and R.C.; writing--review and editing, M.M., G.O., R.C., and G.L.M.; supervision, G.L.M. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research received no external funding.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study.  
**Data Availability Statement:** Data supporting reported results can be found at [[https://livdet.diee.unica.it/](https://livdet.diee.unica.it/)]([https://livdet.diee.unica.it/](https://livdet.diee.unica.it/)) (accessed on 25 September 2022).  
**Conflicts of Interest:** The authors declare no conflict of interest.