## 1 Introduction  
With the increasing importance of information security in every aspect of our lives, biometrics is becoming one of the most popular and promising authentication techniques because traditional methods, based on smart cards and passwords, carry the risks of being stolen, lost, or forgotten. Biometrics is the science of identifying or verifying a person's identity based on physiological or behavioral characteristics. There is a wide variety of biometric features that can be used in different applications, including face shape and geometry, fingerprint, iris, palmprint, gait, and voice. Palm veins are gaining more and more attention because of their uniqueness and distinctiveness (even identical twins have different palm vein patterns). Additionally, veins lie underneath the skin, and thus, it is unchangeable and difficult to counterfeit [1; 2; 3; 4].  
The most common technologies used to collect palm vein images are near-infrared (NIR) and far-infrared (FIR) radiation. NIR is considered better than FIR because it is more tolerant to environmental changes (temperature or humidity) [5; 6; 7]. On the other hand, NIR 'faces the problem of pattern corruption because of visible skin features being mistaken for veins' [8]. IR technology is easily acceptable by users because it is contactless but, on the other hand, it allows one to collect only 2D patterns.  
Ultrasound is a well-established technology in medical diagnostic imaging as it allows one to achieve accurate 3D images of human organs in a non-invasive way. This capability can be profitably exploited for biometric recognition as well. In addition, ultrasound systems have other peculiar merits, including the ability to detect the liveness of the sample, which make them practically unspoofable, insensitivity to ambient conditions, such as thermic, illumination or humidity variations, and insensitivity to several kinds of skin contamination (grease, ink).  
Several ultrasonic devices have been studied and developed for biometric purposes [9]. The majority of attention was devoted to fingerprints [10; 11; 12], but other characteristics like palmprints [13] and hand geometry [14; 15; 16] have also been investigated. Additionally, 3D vein patterns were extracted using power Doppler techniques [17; 18; 19] and photoacoustics [20; 21; 22; 23]. However, even if quite accurate patterns were achieved, the acquisition time proved to be too long for both technologies.  
Palm veins are exploited in multimodal systems together with other characteristics, especially palmprints [24; 25; 26; 27]. This modality, also called biometric fusion, allows to improve the performance of the biometric system in terms of recognition accuracy, universality and security.  
In this work, a recognition system based on a 3D vascular pattern extracted from conventional grayscale volumetric ultrasound images is proposed for the first time and experimentally evaluated. This approach has twofold merit: the acquisition time is contained in less than 5 s, and the collected volumetric image can be exploited to extract other independent biometric characteristics, such as palmprints [28; 29] and/or inner hand geometry [14], upgrading the recognition system to a multimodal one.  
Hereinafter, Section 2 presents the experimental set up used for collecting volumetric ultrasound images of a portion of the human hand, Section 3 describes the proposed method for extracting 3D vascular pattern, Section 4 reports the results of verification and identification experiments, and Section 5 contains the conclusions and a discussion on the perspective of future works.