(a) Fingerprint minutia points [21] (b) Minutia points extracted from branches of facial vasculature 

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... 15] Buddharaju et. al showed that the performance of the biometric identification system based on facial vasculature is very promising. This leaves the following two characteristics of facial vasculature to be addressed in order to be considered as a good biometric technology: 1. Uniqueness: is it possible for two persons to have same vascular structure on the face? 2. Repeatability: is facial vasculature invariant with time? In [21] Pankanti et. al studied intra-class and inter-class variations among fingerprints probabilistically using the minutia points extracted from fingerprint ridges. Recently Zhu et. al developed a stochastic model to capture variability among fingerprint minutia datasets [22]. Similar techniques can be applied to study the variability among facial vasculature of different individuals. Minutia points can be extracted from branching points of vessels similar to the way fingerprint minutia points are extracted at the bifurcations and endings of fingerprint ridges as shown in Figure 12. The pattern of the underlying blood vessels of the face(and the corresponding thermal imprints) is quite complex (see Figure 1). The question is if this complex pattern is characteristic to each individual and can serve as a useful biometric signature. In the area of medicine some very interesting work was conducted regard- ing the uniqueness of the facial vascular network. The primary motivation behind this line of research was the localization of anatomical features for reconstructive surgery purposes. For example Pinar and Govsa in [23] conducted extensive research on the anatomy of the Superficial Temporal Artery (STA) and its branches. They studied the STA anatomy in 27 subjects. Among other things they found that the bifurcation point of STA (see Figure 13) was above the zygomatic arch in only 20 out of the 27 samples. In 6 samples the bifurcation was exactly over the arch and in one sample there was no bifurcation at all. Further variability was observed in the STA branches. Specifically, in one sample double parietal branches were observed. In 21 samples zygomatico- orbital arteries ran towards the face, parallel to zygomatic arch and distributed in the orbicularis oculi muscle. One has to take into account that STA is only one major facial vessel among many. Assuming that such variability is typical to other facial vessels and branches, their combination is bound to produce a very characteristic pattern for each individual. In another study, medical researchers found implicit evidence of uniqueness of the cutaneous vasculature in the high variability of reflex drives [24]. In addition, one has to take into account that the proposed face recognition method does not depend only on the topology of the facial vascular network but also on the fat depositions and skin complexion. The reason is that im- agery is formed by the thermal imprints of the vessels and not the vessels directly. Even if the vessel topology was absolutely the same across individuals, still the thermal imprints would differ due to variable absorption from different fat padding (skinny faces versus puffy faces) [25] and variable heat conductance from different skin complexion (dark skin is less conductive). Besides the medical evidence that appears to be strong and the support- ing heat transfer principles, “uniqueness” of the facial vascular network is also reinforced by experimental investigation we presented in our previous efforts [14, 15]. Such experimental investigations constitute the main “proof of uniqueness” in other biometric modalities (e.g., fingerprint recognition [21]) and of course they gain more weight as the size of the databases increases. In the case of thermal facial vessel imprints, the size of the databases is still relatively small, yet statistically significant (several hundred samples). One particular example that makes a very strong case for “uniqueness” is the dis- covery of different thermal facial vessel imprints even in identical twins [13]. In the last few years one relevant biometric that has gained acceptance is the venous structure at the back of the hand. It is imaged typically with active near-infrared light and the image is formed due to back-scattering. The claim of “uniqueness” is based primarily on experimental evidence from database classification efforts. No substantial medical research was pursued on the uniqueness of the hand’s venous structure, as reconstructive hand surgery is not as prevalent as facial surgery. In addition, the venous network at the back of the hand is not nearly as complicated as the facial vessel network (see Figure 1). Yet, it is increasingly accepted as a legitimate biometric [26] and it is used in practice [27] based mainly on experimental evidence from database classification efforts. Hence, evidence from medical research and reasoning based on heat transfer principles suggest that the facial vessel network is characteristic to each individual. As shown in Figure 12, minutia points can be extracted from the branches of blood vessel contours in ways similar to those used for fingerprint minutia extraction. Numerous methods have been proposed for matching fingerprint minutiae, most of which try to simulate the way forensic experts compare fingerprints [28]. Similar techniques can be employed to match thermal minutia points of two subjects. We first reported the complete matching algorithm and experimental results on University of Houston database in [14, 15], where the interested reader may find more details. A major challenge associated with thermal face recognition is the recognition performance over time [29]. Facial thermograms may change depending on the physical condition of the subject. This renders difficult the task of acquiring similar features for the same person over time. Previous face recognition methods in thermal infrared that use direct temperature data reported degraded performance over time [10, 30]. However, our method attempts to solve this problem by extracting facial physiological information to build its feature space. This information is not only characteristic to each person but also remains relatively invariant to physical conditions. Although, the thermal facial maps of the same subject appear to shift, the vascular network is more resistant to change. In imaging terms, the contrast between the temperatures in the vascular pixels and the surrounding pixels is relatively invariant, albeit the absolute temperature values shift appreciably. This is a direct consequence of the thermoregulatory mechanism of the human body. Our morphological image processing simply capitalizes upon this phenomenon and extracts the invariant vascular contours out of the variable facial thermal maps. Due to the small number of subjects in the University of Houston database for whom we had images spread over several months, no statistically significant quantification of the low permanence problem was possible. For this reason, we obtained permission to apply the method on the database of the University of Notre Dame [31]. This database has a large collection of facial images acquired from both visible and long-wave infrared cameras. They held acquisitions weekly and most of the subjects in the database participated multiple times. In more detail, the database consists of 2294 images acquired from 63 subjects during 9 different sessions under specific lighting and expression conditions. The spatial resolution of the images is 312 × 239 pixels (about half of that featured in the UH database). They used three lights during data collection, one located in the center approximately 8ft in front of the subject, one located at 4ft to the right, and the other 4ft to the left of the subject. The subjects were asked to provide two expressions during acquisition - “neutral” and “smiling”. The database is divided into four different gallery and probe sets using FERET style naming convention [32]: 1. LF (central light turned off) + FA (neutral expression) 2. LF (central light turned off) + FB (smiling expression) 3. LM (all three lights on) + FA (neutral expression) 4. LM (all three lights on) + FB (smiling expression) The database also contains an exclusive training set (different from the gallery and probe sets) with samples collected from several subjects, from which a face space can be constructed for the PCA recognition algorithm. We did not use this training set since our algorithm is feature-based and hence does not require any explicit training. However, each of the gallery sets (say LF—FA) can be tested against the other three probe sets (say LF—FB, LM—FA, and LM—FB). This way we tested our algorithm on 12 different pairs of gallery and probe sets. In each of these experiments, the gallery set had one image per subject, and the probe set had several disjoint images per subject depending on how many different acquisition sessions did the subject attend. Figure 14 shows a sample of the gallery and probe images of a subject from the University of Notre Dame ...

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... a and b are points of sets A and B respectively, and d ( a, b ) is any metric between these points ; for simplicity, we’ll take d ( a, b ) as the Euclidean distance between a and b . The algorithm to find out the Hausdorff distance is: Figure 11 shows the Hausdorff distance calculated between our manual segmented data and the original data. The low Hausdorff distance values indicate that the two sets in our case are close to each other. In other words, the automatically segmented vessel curves are very close to the expertly drawn ones. If a human physiological or behavioral characteristic has to be considered as a biometric feature, it should satisfy certain desirable characteristics such as universality , uniqueness , repeatability , collectability , performance , accept- ability , and circumvention [1]. Every living and non-living object at a finite temperature emits radiations, which are captured by infrared cameras. The temperature data can be universally extracted by applying Planck’s equation on the radiations captured from the face, which on further analysis yields vascular structure. The main advantage of face recognition among other biometric technologies is that it is completely non-contact and allows for on-the-fly identification. Minimal or no cooperation is demanded from a person in order to extract his/her facial vasculature. Hence, this technology is easily collectable and is highly acceptable . Since the vascular network lies below the skin and is imaged through its function (blood flow), it is almost impossible to be forged making it very hard to circumvent . In [14, 15] Buddharaju et. al showed that the performance of the biometric identification system based on facial vasculature is very promising. This leaves the following two characteristics of facial vasculature to be addressed in order to be considered as a good biometric technology: 1. Uniqueness: is it possible for two persons to have same vascular structure on the face? 2. Repeatability: is facial vasculature invariant with time? In [21] Pankanti et. al studied intra-class and inter-class variations among fingerprints probabilistically using the minutia points extracted from fingerprint ridges. Recently Zhu et. al developed a stochastic model to capture variability among fingerprint minutia datasets [22]. Similar techniques can be applied to study the variability among facial vasculature of different individuals. Minutia points can be extracted from branching points of vessels similar to the way fingerprint minutia points are extracted at the bifurcations and endings of fingerprint ridges as shown in Figure 12. The pattern of the underlying blood vessels of the face(and the corresponding thermal imprints) is quite complex (see Figure 1). The question is if this complex pattern is characteristic to each individual and can serve as a useful biometric signature. In the area of medicine some very interesting work was conducted regard- ing the uniqueness of the facial vascular network. The primary motivation behind this line of research was the localization of anatomical features for reconstructive surgery purposes. For example Pinar and Govsa in [23] conducted extensive research on the anatomy of the Superficial Temporal Artery (STA) and its branches. They studied the STA anatomy in 27 subjects. Among other things they found that the bifurcation point of STA (see Figure 13) was above the zygomatic arch in only 20 out of the 27 samples. In 6 samples the bifurcation was exactly over the arch and in one sample there was no bifurcation at all. Further variability was observed in the STA branches. Specifically, in one sample double parietal branches were observed. In 21 samples zygomatico- orbital arteries ran towards the face, parallel to zygomatic arch and distributed in the orbicularis oculi muscle. One has to take into account that STA is only one major facial vessel among many. Assuming that such variability is typical to other facial vessels and branches, their combination is bound to produce a very characteristic pattern for each individual. In another study, medical researchers found implicit evidence of uniqueness of the cutaneous vasculature in the high variability of reflex drives [24]. In addition, one has to take into account that the proposed face recognition method does not depend only on the topology of the facial vascular network but also on the fat depositions and skin complexion. The reason is that im- agery is formed by the thermal imprints of the vessels and not the vessels directly. Even if the vessel topology was absolutely the same across individuals, still the thermal imprints would differ due to variable absorption from different fat padding (skinny faces versus puffy faces) [25] and variable heat conductance from different skin complexion (dark skin is less conductive). Besides the medical evidence that appears to be strong and the support- ing heat transfer principles, “uniqueness” of the facial vascular network is also reinforced by experimental investigation we presented in our previous efforts [14, 15]. Such experimental investigations constitute the main “proof of uniqueness” in other biometric modalities (e.g., fingerprint recognition [21]) and of course they gain more weight as the size of the databases increases. In the case of thermal facial vessel imprints, the size of the databases is still relatively small, yet statistically significant (several hundred samples). One particular example that makes a very strong case for “uniqueness” is the dis- covery of different thermal facial vessel imprints even in identical twins [13]. In the last few years one relevant biometric that has gained acceptance is the venous structure at the back of the hand. It is imaged typically with active near-infrared light and the image is formed due to back-scattering. The claim of “uniqueness” is based primarily on experimental evidence from database classification efforts. No substantial medical research was pursued on the uniqueness of the hand’s venous structure, as reconstructive hand surgery is not as prevalent as facial surgery. In addition, the venous network at the back of the hand is not nearly as complicated as the facial vessel network (see Figure 1). Yet, it is increasingly accepted as a legitimate biometric [26] and it is used in practice [27] based mainly on experimental evidence from database classification efforts. Hence, evidence from medical research and reasoning based on heat transfer principles suggest that the facial vessel network is characteristic to each individual. As shown in Figure 12, minutia points can be extracted from the branches of blood vessel contours in ways similar to those used for fingerprint minutia extraction. Numerous methods have been proposed for matching fingerprint minutiae, most of which try to simulate the way forensic experts compare fingerprints [28]. Similar techniques can be employed to match thermal minutia points of two subjects. We first reported the complete matching algorithm and experimental results on University of Houston database in [14, 15], where the interested reader may find more details. A major challenge associated with thermal face recognition is the recognition performance over time [29]. Facial thermograms may change depending on the physical condition of the subject. This renders difficult the task of acquiring similar features for the same person over time. Previous face recognition methods in thermal infrared that use direct temperature data reported degraded performance over time [10, 30]. However, our method attempts to ...