## 2 Fingerprint Presentation Attack Detection and Interoperability
### The Interoperability and Generalization Problem  
The interoperability challenge is fundamentally connected to the hardware and software variations between fingerprint acquisition sensors. Optical, solid-state, and ultrasonic sensors are the three most common types of acquisition hardware. Each type of sensor produces a particular distortion in the image linked to a different physical phenomenon, which encodes the valleys and ridges. In addition to the kind of acquisition, scanners can be grouped by image characteristics such as DPI (dot per inch), scan area, geometric precision, etc. The interoperability problem across sensors was recognized in the first instance from the point of view of fingerprint verification. Numerous works over the years have proposed effective solutions to mitigate the drop in accuracy due to the scanner change [12; 13]. Recently, this problem has also been addressed in the field of presentation attack detection, proving to be particularly critical. As a matter of fact, many modern solutions still suffer poor generalization performance when tested on data not seen during the training phase, leading to spoof detection error rates up to three times higher [14]. One potential reason for this complexity in generalizing across sensors is that fingerprint images from different sensors possess different textural characteristics (Figure 1). This complexity is exacerbated by the employment of different acquisition procedures and materials between the training and system use phases, which provides an additional degree of freedom to the fingerprint's appearance. In recent years, numerous works have aimed at overcoming these limits. For instance, authors in [1; 10; 15] mitigated such differences by designing a style-transfer wrapper to add on top of any CNN architecture in order to reduce the performance gap due to cross-sensor evaluations. Their idea is to use a limited number of live fingerprints of the \"new\" sensor, hereinafter called the _target_ sensor, in order to project its style into live and spoof samples coming from the \"old\" sensor. This new synthetically generated  
Figure 1: Examples of acquisitions with different sensors: (**a**) Biometrika, (**b**) DigitalPersona, (**c**) Orcanthus, (**d**) GreenBit, (**e**) Dermalog. The characteristics of the images are strictly influenced by the acquisition technology. to train a liveness detector from scratch, improving the average cross-sensor spoof detection performance by approximately 13%. Another plausible justification for the problem of interoperability is that the different ways of representing the ridges and valleys of a fingerprint affects the frequencies of the grey-level histogram of the images. Figure 2 supports this idea, where we can observe the mean grayscale histogram for the five sensors investigated in this paper. Starting from this peculiarity, [PERSON] et al. [16] reached a significant level of interoperability by shifting sensor-specific feature distributions based on the least squares algorithm. The feature vectors were calculated by using textural algorithms. This solution is optimal since it does not require any additional PAD training. Nevertheless, both live and spoof samples are needed to relocate the feature space of the target sensor into that of the original sensor. All these works generally acknowledge the need for a subset of the target sensor's samples to solve the interoperability problem. This inevitably leads to issues from an economic point of view. In fact, effort and money are necessary to collect a spoof dataset; it is essential to find volunteers willing to donate their fingerprints, fabricate fakes of each finger with a substantial number of materials, and finally acquire them via the scanner. Furthermore, based on the employed materials, costs can grow considerably. The procedure shown in [15] is not affected by these obstacles. On the other hand, it substitutes the original FPAD with a new one tailored to the target sensor. In many applications, this procedure is not feasible.