## 3 Interoperability Scenarios for the Design of Fingerprint PAD  
In this paper, we investigated to what extent the interoperability problem afflicts modern PAD systems and whether some solutions such as training on multiple types of data are beneficial or counterproductive. In particular, we want to evaluate whether training on data from different sensors helps the system to generalize or if it allows to it recognize more types of data, but lowers the general performance. For this purpose, we identified the following project scenarios based on the concept of interoperability applied to fingerprint sensors and the PAI fabrication methods:  
* Intra-sensor and intra-method: this is the standard and optimal application scenario. The PAD is used to analyze and classify images acquired with the same sensor used in the training phase. The type of PAI used to attack the system is known by the system;  
Figure 2: Mean histogram of grayscale for all the five considered datasets. * Intra-sensor and cross-method: this is a standard, but unfavorable application scenario. The PAD is used to analyze and classify images acquired with the same sensor used in the training phase. The type of PAI used to attack the system are unknown to the system. Such a scenario is unpredictable by the designer as new replication methods can be discovered and used after the PAD has been designed and trained;
* Cross-sensor and intra-method: the designer/manufacturer decides, knowing the risks, to use a PAD trained on a sensor on a AFIS consisting of a different acquisition sensor. This choice is not optimal, but is made for economic reasons or in the absence of data to retrain/fine-tune a new PAD. The type of PAI used to attack the system is known by the system, but since the acquisition sensor is different, the resulting images could be very different;
* Cross-sensor and cross-method: as in the previous scenario, the designer uses a PAD trained on a sensor on an AFIS consisting of a different acquisition sensor. Moreover, the type of PAI used to attack the system is unknown to the system. The first two scenarios exemplify the standard functioning of a PAD and allow us to evaluate the system's robustness to never-seen-before attacks. On the other hand, cross-sensor scenarios assess the ability of PADs to generalize concerning the scanner change. These are typically non-optimal cases, useful to assess a situation in which a designer cannot easily collect the data with the new sensor or cannot replace the PAD. Experimental Protocol  
To replicate the application scenarios identified in the previous section, we carried out the following experiments:  
* Intra-sensor and intra-method: the training set is partially or totally composed of data belonging to the target sensor. The PAIs are created with the same method in the two sets;
* Intra-sensor and cross-method: the training set is partially or totally composed of data belonging to the target sensor. The spoofs of the training set were created with a different method than the test set ones;
* Cross-sensor and intra-method: the training set does not contain data on the target sensor. The PAIs are created with the same method in the two sets;
* Cross-sensor and cross-method: the training set does not contain information on the target sensor. The spoofs of the training set were created with a different method than the test set ones. For each application scenario, we divided the experimentation into two protocols based on the designer's choice to use a pre-trained model or to train a model from scratch:  
* _Pre-trained_: some competitors from the eighth edition of the Fingerprint Liveness Detection Competition have been selected (Table 1). Certain of them used additional data for training, although the use of only the LivDet 2021 training dataset was recommended.