## 5 Conclusions  
In this work, a biometric recognition system based on palm vein patterns extracted from conventional 3D grayscale ultrasonic images is proposed for the first time and experimentally evaluated. The proposed feature extraction method is basically based on the detection of low brightness areas in B-mode images. The selected centroids are then linked using a minimum distance criterion. Only one vascular pattern is extracted from each sample.  
Different image processing methods were experimented with, differing in the kind of filter and adaptive threshold used. Recognition capabilities were evaluated by performing verification and identification experiments on a preliminary homemade database. Results demonstrated good recognition performances in both modalities and for all experimented methods even if results should be confirmed by experiments on a wider database. In particular, the best results are obtained when an SRAD filter is used to reduce speckle noise; in this case, 3D features, which are a peculiarity of ultrasound over infrared techniques, always provide better results than 2D ones.  
A procedure for extracting all vascular patterns present in the collected region is currently under study, which allows us to utilize a much higher number of samples from the database [29] and, consequently, to provide more reliable results. Furthermore, alternatives to the whole feature extraction procedure, including anti-speckle filters, binarization methods, and machine learning methods for vein segmentation, are being evaluated.  
A major merit of the proposed vein pattern recognition system relies on the possibility to implement a costless multimodal system by operating a fusion between 3D palmprints and 3D vein pattern as the two features are extracted from the same collected volume. To this end, an approach similar to that presented in [49], which has demonstrated its capability of dramatically improving recognition performances of hand geometry and palmprints extracted from the same volume, is being tested.  
The system also exhibits the other advantages of ultrasound, such as its capability to not be sensitive to many kinds of surface contamination, humidity, environmental light, and temperature, and, overall, to detect the liveness of the sample.  
Finally, to overcome a significant drawback of the proposed system that may limit its acceptability, i.e., the user has to get his hand wet, the possibility to extract vascular patterns from volumes collected with an acquisition system that uses gel as a coupling medium is under investigation, as has been successfully done for palmprints [50; 51; 52]. This system allows a comfortable positioning of the hand and, as the hand is in contact with gel, it is acceptable to users in a post-pandemic world. The proposed recognition system is intended for high-security applications. In such a perspective, the cost and encumbrance can be widely contained. In fact, a single-stepped motor can be used instead of the pantograph, and probes based on the emerging and potentially cheap MEMS technology [53; 54], which is nowadays showing up in the market [55], could be employed.  
Conceptualization, A.I.; methodology, A.I. and A.V.; software, A.V.; validation, A.I. and A.V.; data curation, A.V.; writing--original draft preparation, A.V.; writing--review and editing, A.I.; supervision, A.I.; project administration, A.I.; funding acquisition, A.I. All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by the Italian Government through the PRIN 2020 Program (Project n. 20205 HFXE7).  
Not applicable.  
The authors declare no conflict of interest.