MALASSIOTIS et al.: PERSONAL AUTHENTICATION USING 3-D FINGER GEOMETRY 13 A different approach is adopted in  for hand shape basedauthentication. A grating pattern is projected on the back of theuser’s hand and an image of the distorted pattern is captured witha CCD camera. Then a quad-tree representation of a binarizedversion of the image is used for similarity measurements. Theauthors achieved a veriﬁcation rate of 99.04% using 100 images. A touch-free technique of extracting hand geometry bio-metric data is proposed in . It is based on the localization ofﬁnger creases on the front size of the palm and the computationof cross ratios among ﬁve point tuples that are invariant toprojective transformations. Zero FAR for an FRR of 2.8%is claimed on a small dataset containing hand images from15 people. A uniform background was assumed in order to Fig. 1. (a) Image captured by the color camera with color pattern projected.facilitate the detection of ﬁngers. (b) Computed range image. Brighter pixels correspond to points closer to the Recently  investigated the utility of 3-D ﬁnger shape as a camera and white pixels correspond to undetermined depth values.biometric identiﬁer. They use a 3-D scanner to acquire a rangeimage and a corresponding color image of the back of the hand an off-the-shelf CCTV color camera and a standard video pro-placed on a ﬂat, dark surface. After ﬁnger alignment, a shape jector. While a colored pattern is projected on the surface ofindex is computed for each pixel based on the principal curva- the object, the color camera captures an image of the objecttures of the surface points. Matching of ﬁnger shapes is then [see Fig. 1(a)]. By analyzing the deformation of this pattern andachieved by computing the correlation between corresponding using the triangulation principle, the 3-D coordinates of everyshape index images. They have tested their technique on a data- pixel are estimated [Fig. 1(b)]. Switching rapidly between thebase of 132 persons with ﬁve images for each person collected colored pattern and white light, a color image, which is approx-during two recording sessions with one week lapse. For images imately synchronized with the depth image, may be captured asacquired on the same week the recognition rate was 99.4% but well. Using the double acquisition mode a frame-rate of aboutdropped to 75% when probe and gallery images were acquired 15 frames/s is achieved. Although the current system prototypewith one week lapse. uses visible light, which is moderately annoying to the user, a The main difference of our approach in comparison with the version using invisible light is under development.above techniques is that less constraints are posed on the place- In our experiments the system was optimized for an access con-ment of the hand and the on environment. Working on a com- trol application scenario. For subjects located about one meterbination of color and 3-D information, we present robust al- from the camera, and an effective working space of 60 cm 50gorithms which are capable of withstanding in some degree, cm 50 cm, the average depth accuracy is about 0.5 mm. Thecluttered background, illumination variations, hand pose, ﬁnger spatial resolution of the range images is equal to the color camerabending and appearance of rings. There are certainly limitations resolution in one direction, while in the other direction it dependson the working conditions under which the system may operate on the width of the color stripes of the projected light pattern andreliably, e.g., working outdoors or under large pose and ﬁnger the bandwidth of the surface signal. For a low-bandwidth surfacebending conditions may be problematic. However, these con- such as the back of the hand the resolution is close to the resolu-straints are far less than those imposed by existing systems. tion of the color camera. The image size is 580 780. The average Another novelty of this paper, is the exploitation of the 3-D size of the hand on the image is 400 450.shape of ﬁngers along with their 2-D silhouette to extract a Due to the 3-D acquisition principle, apart from image noise,set of discriminative features. Although 3-D ﬁnger shape as the acquired range images contain areas where no depth valuesa possible biometric has been proposed in , the present are assigned (see Fig. 1). These are mainly areas that cannottechnique offers several advantages. The work in this paper be reached by the projected light (e.g., the sides of the ﬁngers)utilizes a real-time low-cost 3-D sensor for 3-D image acqui- and/or are highly refractive (e.g., painted ﬁnger nails and rings).sition instead of a high-end range scanner used in . Also, Using the above setup, a hand image database was compiledthe proposed system facilitates relatively unconstrained hand and used for conducting the experiments. A group of 73 vol-placement, while in  the hand is placed on a ﬂat surface unteers participated in the recording. The recording was super-with uniform background. Finally, the use of a limited number vised mainly because it was difﬁcult for the users to place theirof cross-sectional 3-D ﬁnger measurements is adopted in this hands inside the limited working volume of the sensor withoutpaper, while  uses “3-D shape images” to represent each any feedback. In the future we plan to provide such a feedbackﬁnger. Therefore, biometric templates are only a few bytes and automatically.thus may be efﬁciently stored in smart-cards. Each subject was asked to place his/her hand in front of his/her face with the back of the palm facing the sensor. We have found that this posture is the most convenient for the users, III. DATA ACQUISITION is interpreted unambiguously and provides the best resolution The proposed system relies on real-time quasisynchronous of the hand in the images. Also in this way hand geometrycolor and 3-D image acquisition based on the color structured- authentication may be applied as an additional biometric afterlight approach . The sensor is based on low cost devices, 3-D face authentication.
14 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 1, NO. 1, MARCH 2006 where are prior probabilities of the head/torso, hand and arm blobs respectively, and Maximum-likelihood estimation of the unknown parameters from the 3-D data is achieved by means of the Expectation-Maximization algorithm: where are the posterior probabilities of the state given the data and the model parameters. The convergence of the above iterative procedure relies on good initial param-Fig. 2. Representative images from the recorded hand database depicting hand eter values. In our case these may be obtained by exploitingpose and posture variations and worn rings. prior knowledge of the body geometry. Initial estimates of the head/torso 3-D blob parameters are obtained by means of We have subsequently acquired several pairs of color and depth an initial rough segmentation of the depth values into fore-images for each subject (10–15 image pairs per person) depicting ground/background objects. This is easily obtained by ﬁndingseveral variations of the “ideal” hand posture (see Fig. 2). The the threshold that optimally separates the two modes in theusers were initially asked to keep their ﬁngers straight and af- histogram of depth values . Background pixels are assumedterwards to relax their ﬁngers introducing some ﬁnger bending. to belong to the head/torso blob and their mean and covari-Then the users were asked to wear a ring on one of their ﬁngers. ance are readily obtained from the 3-D coordinates of theseFinally, they were asked to variate the orientation of the palm for points. The remaining points with depth values smaller thanabout 10–15 degrees with respect to the sensor. The recording are initially classiﬁed as hand/arm points. The parameters ofwas repeated after one week with the same conditions. the two foreground blobs (hand and forearm) are initialized by exploiting prior knowledge of their geometric structure. Let be the sample mean of foreground points and IV. HAND DETECTION be the eigenvectors of the scatter matrix The ﬁrst step is the segmentation of the hand from the body, , computed from these foreground data pointswhich is achieved using available depth information and ex- , ordered according to the magnitude of the correspondingploiting a priori knowledge of the human body geometric struc- eigenvalues. Initial estimates of the unknown parametersture and the authentication scenario. were obtained by The distance of the user’s hand from his/her face is not guaran-teed to be sufﬁciently large (usually between 5–20 cm). Thereforewe may not rely on simple thresholding to separate the hand from wherethe face. Detection and segmentation of the hand is based on amore elaborate scheme that relies on statistical modeling of thehand, arm and head plus torso points in 3-D space. Let be the 3-D coordinates of each pixel computed fromthe range image. The probability distribution of a 3-D point ismodeled as a mixture of three Gaussians: where is the orthogonal eigenvector matrix of and the corresponding eigenvalues. Also, are constants related to the relative size of the hand and forearm with respect to the arm (in the experiments, the values , and and were used). The physical interpretation of the above equations is illustrated in
MALASSIOTIS et al.: PERSONAL AUTHENTICATION USING 3-D FINGER GEOMETRY 15 Fig. 4. Hand detection and segmentation. (a) Original image and (b) segmented image. Fig. 5. Estimation of the center and radius of the palm. (a) Foreground pixel mask and (b) distance transform with estimated palm circle centered on the distance transform maximum.Fig. 3. Illustration of knowledge-based initialization of 3-D blob distributionparameters. Ellipses represent iso-probability contours of posteriordistributions. Since depth estimation along the boundaries of the ﬁngers is inaccurate, containing holes and gaps, we may not rely on theFig. 3. The centers of the blobs corresponding to the hand and silhouette of the object but we rather follow a more elaborateforearm are placed along the principal axis of the arm, while the procedure which is described bellow.blobs’ relative position and size is selected a priori with respect The projection of the center of the hand blob on the imageto the position and size of the full arm. Moreover, the orientation plane is used as an initial estimate of the palm center that is sub-of each blob (reﬂected by their covariance matrix) is aligned to sequently reﬁned as described in the following. The chamferthe orientation of the full arm. distance  algorithm is used to efﬁciently compute the dis- The algorithm converges after a few iterations to a local max- tance transform inside a bounding box centered on the projec-imum of the data likelihood function given the parameters. The tion of . Since the distance transform provides the smallestobtained parameters corresponding to the hand blob pro- distance of each point to the object boundary, and the structurevide an estimate of the center and 3-D pose of the hand. In par- of the palm is approximately circular, a maximum distance isticular, the eigenvector of matrix corresponding to the expected near the center of the palm . Therefore, is an esti-smallest eigenvalue is approximately perpendicular to the plane mate of the palm radius (see Fig. 5).deﬁned by the hand surface. Then, it is straightforward to de- Then, a rough estimate of the hand-forearm axis is obtainedﬁne a cutting plane that separates the hand by computing the eigenvector corresponding to the largestfrom the face, where is the distance of the cutting plane from eigenvalue of the covariance matrix of 2-D foreground pixelthe hand plane. The choice of the parameter is a compromise coordinates. The slant of this axis with respect to the verticalbetween allowable closeness of the hand to the face and ﬁnger image axis gives approximately the orientation angle of thebending. A measure of ﬁnger bending is the scattering of hand hand.points with respect to the estimated hand plane and is propor- Given these global hand features we may proceed withtional to the smallest eigenvalue of . The points that lie be- the detection of the ﬁngers. Homocentric circular arcs arehind the cutting plane are discarded, while the rest of the points drawn around with increasing radius ( to at(termed foreground points in the sequel of the paper) are used steps) excluding the lower part of the circle that correspondsin subsequent processing steps (see Fig. 4). to the wrist as shown in Fig. 6(b). By scanning the nonzero pixels on each of these arcs, a list of circular segments is obtained. Very small or very large seg- V. HAND LOCALIZATION ments, compared to the average ﬁnger width, are rejected. In this step, we use the foreground pixels mask, whose values The midpoints of the remaining segmentsare one for foreground pixels and zero otherwise, in order to are considered candidates for the ﬁnger skeletons. Our nextlocalize the center and radius of the palm as well as the ﬁngers. goal is to cluster together the skeleton points corresponding toIn the following we assume without loss of generality that the each ﬁnger. First the minimum-spanning tree that has the setright hand is used. of points as its vertices is computed. Then by discarding
16 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 1, NO. 1, MARCH 2006Fig. 6. Finger detection. (a) Original depth image, (b) circular arcs used todetect ﬁnger segments, (c) clustering of segment mid-points, and (d) 2-D linesﬁtted on skeleton points and boundaries.from the minimum spanning tree those edges that are longerthan some threshold, an initial clustering is obtained. Then,clusters containing only a few points (fewer than three in ourexperiments) are discarded, while pairs of clusters that satisfya proximity threshold are merged together. The proximity oftwo clusters is measured by the collinearity of the two sets of Fig. 7. The 2-D ﬁnger model. Finger end-points (white circles) are thepoints. Let be the error in ﬁtting a 2-D line on the set of end-points of the projections of left and right boundary segments on skeleton axis (dashed line). The width of the ﬁnger model on the top and bottom, d andpoints belonging to the ﬁrst cluster, for the second cluster d respectively, are given by d = (d + d )=2 + ; d = (d + d )=2 + ,and for the union of the cluster points. Then the merging where is a constant offset that depends mainly on the distance of the handcriterion is simply , where is a constant from the camera.(equal to 1 in our experiments). After the merging step, the fourlongest remaining clusters are retained. These will normally by the projector are visible by the camera, and not all pointscorrespond to the four ﬁngers, excluding the thumb [Fig. 6(c)]. visible from the camera are illuminated by the projector. This The correct ordering of the ﬁngers is established by sorting has the effect of missing depth information along ﬁnger bound-the clusters with respect to the slant of the line segment de- aries. Therefore, color images are used as well to localize ﬁngerﬁned by the furthest point of each cluster and the center of the boundaries more accurately. Unfortunately, we have to copepalm . Then, 2-D line segments are ﬁtted on the points of each with cluttered background and low contrast, since the hand iscluster, and approximate ﬁnger skeletons are obtained. Finally, in front of the face and they have the same color. Thus, priorby searching in a direction perpendicular to the ﬁnger skeleton, knowledge of human hand geometry and photometric proper-we locate ﬁnger boundary points, and ﬁt 2-D line segments cor- ties of the object surface are exploited.responding to the left and right ﬁnger boundaries [Fig. 6(d)]. First, a 2-D geometric model of each ﬁnger is created, using The advantage of the approach described above compared with ﬁnger skeleton and boundaries estimated from the foregroundthose based on the silhouette of the hand, is that it works success- pixel mask during the previous step (see Fig. 7). Then, we samplefully for noisy masks, which contain also disconnected bound- points from the model boundary, and for each point a set ofaries (e.g., due to rings worn in one or more ﬁngers, sensor errors local gradient maxima is collected along a lineor segmentation errors). In addition, it is computationally efﬁ- that passes from and is perpendicular to the model boundarycient since it operates only on a small subset of image pixels. We ( few pixels around ). The optimal set from these candidatebelieve that this algorithm is also useful when hand segmentation points corresponding to the ﬁnger boundary , is subsequentlyis obtained by other means such as skin color segmentation. estimated by minimizing a global cost function VI. FINGER BOUNDARY LOCALIZATION Depth acquisition is not always feasible in the vicinity ofﬁnger discontinuities. This is due to the occlusion problem thatis inherent in 3-D acquisition techniques employing the trian- where and ) is the distancegulation principle. In our case, not all hand points illuminated of the line segment deﬁned by points from the 2-D ﬁnger
MALASSIOTIS et al.: PERSONAL AUTHENTICATION USING 3-D FINGER GEOMETRY 17 VII. FEATURE EXTRACTION AND MATCHING We use the above signature functions to extract 3-D geometric features of the ﬁngers and we utilize these features for simi- larity measurement. Altogether, ninety six measurements quasi- invariant to hand position, orientation and ﬁnger bending are used. The thumb is excluded since its measurements are unre- liable. Twelve width and twelve curvature measurements are computed for each of the remaining four ﬁngers. The length of each ﬁnger is estimated by the largest computed distance from the corresponding ﬁnger-tip. During the training phase weFig. 8. Finger boundary segments (a) before and (b) after subpixel correction. also compute the average length of each ﬁnger . Finger width and curvature measurements are computed by sampling and respectively on , where takesmodel. The optimization of the cost function is efﬁciently equally spaced values from 0.2 to 0.8. All 96 measurements areachieved using dynamic programming. From this set of points subsequently concatenated on a feature vector . Similarity be-we may subsequently estimate the ﬁnger-tip of each ﬁnger tween two feature vectors is estimated by means of the(by projection of all points on the symmetry axis of the model) distance .and a sequence of linear segments , The resulting similarity score is normalized in the rangewhich are perpendicular to the ﬁnger axis and their end-points by applying the normalization functionare on the polygon . Finger boundary estimates obtained using the abovemodel-based scheme are biased with respect to the trueoccluding boundary, since the proﬁle of the brightness functionacross ﬁnger boundaries is not the step function but rather de-cays more smoothly. The bias is also increased proportionally where and are the initial and normalized scores respec-to the width of the smoothing kernel, which is normally used tively (see also  for a discussion on different normalizationfor computing the image gradient. To compensate for this error, schemes). This requires, separately for each enrolled user, thethe initial estimate of the boundary is subsequently reﬁned, estimation of the mean and variance of the genuine transac-by ﬁtting a parametric edge model to the brightness values in tion score distribution. This is obtained using the Hampel the vicinity of the current boundary estimate ( pixels). The robust estimator.brightness proﬁle across the boundary is approximated with the Speciﬁcally, let be a set of gen-function uine transaction scores, obtained from a bootstrap set of im- ages of a given subject. Then, a robust estimate of their mean value is obtained by means of the iterative re-weighted least squares technique where are given by the Hampel inﬂuence function:where , and are the unknown parameters estimatedby minimizing the mean square error between and imagebrightness samples using the Levenberg–Marquard technique. has a ramp-like shape for and isﬂat outside this interval, taking values and on the left andright of the ramp respectively. Therefore the correction term is and are chosen as the 70th, 85th, and 95th percentiles ofgiven by (for left/right ﬁnger boundary respectively). An . is initially set equal to the median of the scores.example of boundary reﬁnement is illustrated in Fig. 8. Convergence is usually attained after a few (less than ten) iter- Then, for each ﬁnger we deﬁne two signature functions, ations. For the standard deviation the value of above was , which are parameterized by the 3-D distance shown to be a fairly robust estimate.from the ﬁnger tip computed along the ridge of each ﬁnger.For each such measurement the distance from the ﬁnger-tip VIII. EXPERIMENTAL RESULTSis computed as wherethe vector represents the 3-D coordinates of the segment A database containing several hand appearance variationsmid-point. The ﬁrst function corresponds to the width of the was recorded as described in Section III and used for ex-ﬁnger in 3-D. This is computed by ﬁtting a 3-D line on the perimental evaluation of the full authentication chain under3-D points corresponding to each segment , projecting the different conditions. The database contains images from 73end-points of this segment on this line and computing their volunteers and is separated into two recording sessions withEuclidian distance. The second signature corresponds to the at least one week lapse between the recordings. The ﬁrstmean curvature of the curve that is deﬁned by the 3-D points database session was used for training and the second one forcorresponding to each segment. testing. In order to minimize the training bias, we have used
18 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 1, NO. 1, MARCH 2006Fig. 9. Receiver operating characteristic curve showing false acceptance rate (FAR) versus veriﬁcation rate (VR) for M -tuples of probe images and varying M .for training only images depicting “canonical” cases (hand ap- matching every image in the test set with all images in the galleryproximately parallel and close to the camera, extended ﬁngers, set. This implies that a matching score is computed for each probeno rings worn). Also, we have performed several experiments image in the test set and for each claimed identity (1 to 73) giving aby varying the training set. For each experiment we select table (2880 73) of genuineand impostormatching scores.Froma subset of the training images and use this for training the this table we can subsequently draw Receiver Operator Charac-algorithms. Speciﬁcally, we randomly select 50 persons (totally teristic curves (false acceptance rate versus veriﬁcation rate) by20 such samplings), and four image pairs from the images varying the authentication threshold from 0 to 1 and Cumulativecorresponding to each person in the sampling (ten such sam- Match Characteristic curves by computing the rank of genuineplings), leading to 100 experiments. The results presented in transaction scores (identiﬁcation).the sequel are averages over all experiments. For each training We have also noticed that the performance of the system mayimage pair we applied the proposed algorithms and extracted a be signiﬁcantly improved by combining the scores computed onfeature vector containing 3-D ﬁnger shape measurements. images of the same individual. The best results were obtained In the following we evaluate the performance of the system by computing the average of the matching scores. In practiceunder various operating conditions and also describe its limita- this may be achieved by acquiring a sequence of hand imagestions and breakdown points. instead of a single image and then computing matching scores for a subset of the acquired frames. Averaging of the scores hasA. Accuracy the effect of reducing the noise in ﬁnger shape measurements. The execution time of the algorithm including 3-D image ac- The test set contains all images of the second recording ses- quisition, hand detection and feature extraction is 0.2 s on a Pen-sion (totally 2880 image pairs). The matching score for a probe tium 4, 3 GHz processor. In particular hand detection and globalimage is then computed as follows. Hand detection, localization feature extraction is executed with a rate of 10 frames/s. So, inand feature extraction algorithms are applied on the pair of color a practical application, feedback to the user may be provided inand depth images and a feature vector is extracted. Then, the real-time regarding the quality of recorded images using priordistance between this vector and the four previously estimated knowledge of hand geometry (e.g., palm radius, lengths of thegallery feature vectors corresponding to the claimed identity are ﬁngers). Thus, low quality images may be discarded.computed. The matchingscore isthensettotheminimumdistance Figs. 9 and 10 demonstrate the veriﬁcation and identiﬁcationand normalized in the range [0–1] as described in Section VII. results obtained for various values of , while the matching We have subsequently performed several experiments under scores were computed by randomly generating -tuples of thedifferent variations of the test set. Each experiment consists of probe images corresponding to the same individual.
MALASSIOTIS et al.: PERSONAL AUTHENTICATION USING 3-D FINGER GEOMETRY 19Fig. 10. Cumulative Match Characteristic curve showing identiﬁcation rate (IR) versus identiﬁcation rank for M -tuples of probe images and varying M . From the graphs it is evident that the performance improves as fails to ﬁnd a separating plane and crops part of the ﬁngers. Also gets larger; however after the relative improvement the hand should be located inside the working volume of the 3-Dbecomes very small. For the equal error rate is 5.4% and sensor. This is a limitation of the current setup since the 3-Dthe rank-1 identiﬁcation rate is 90%. For the equal error working volume is rather limited (see Section III), and it mayrate becomes 3.6% while the rank-1 identiﬁcation rate rises to be partially lifted by automatically detecting the center of the98%. Of course the identiﬁcation performance is a function of hand (as described in Section IV) and providing feedback to thethe database size. Using the extrapolation formula in  user. The accuracy of the system is obviously a function of the image resolution, and the size of the hand on the image and therefore it depends on the distance of the hand from the camera. We have tested the effect of the distance from the camera by splitting the test set into two subsets. The ﬁrst subset containedwhere and are the false rejection rate and false images with the hand close to the camera and the other set con-acceptance rate as a function of the threshold , and is the tained images with the hand further from the camera (15 cm ongallery size, the extrapolated identiﬁcation rate is equal to 89% average). The average hand size in the ﬁrst set is approximatelyfor and 85% for . 50% of the image area while in the second set is about 38%. We have also compared our results ( and ) with The equal error rate corresponding to the ﬁrst test set was 3.2%those obtained by other authors –,  and similar perfor- while for the second set was 3.7%.mance was obtained. Since the conditions of these experiments The proposed system was shown to work reliably with palmvary greatly (e.g., size of the data set, acquisition setup, experi- orientations up to 15 degrees with respect to the camera. Formental protocol, imagequality etc.) wehaveomitted these results. larger angles the accuracy was shown to deteriorate rapidly, mainly due to ﬁnger occlusion and self-occlusion. The deterio-B. Hand Placement and Pose ration in veriﬁcation accuracy between images approximately The placement of the hand with respect to the camera and parallel to the camera plane and those with an orientationthe conﬁguration of the ﬁngers have an effect on the classiﬁca- angle (with respect to the Y axis) greater than 10 was abouttion accuracy. The system is designed to operate with the hand 14%. We believe that there is room for improvement of theplaced in front of the body. The distance of the hand from the results with respect to the hand pose, but this relies mostly onbody can be as small as 10 cm. For smaller distances there are a the improvement of 3-D acquisition in the vicinity of ﬁngerfew cases (usually exhibiting ﬁnger bending) that the algorithm boundaries. Obviously the accuracy of authentication systems
20 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 1, NO. 1, MARCH 2006based on hand geometry relies on the accuracy of hand sil- those required in security applications, there are several otherhouette extraction and the best results were obtained using emerging applications such as personalization of services andhigh resolution document scanners. In our case, cross-sectional attendance control that may beneﬁt from the unobtrusive userﬁnger measurements are computed from the occluding bound- authentication achieved by the proposed system. Furthermore,aries localized on the color image and the ﬁnger orientation if the proposed system is combined with other authenticationobtained from the depth image. This leads to fairly accurate modalities such as face recognition, the overall performanceresults when the hand is approximately parallel to the 3-D of the multimodal system is expected to be superior since 3-Dsensor plane, but if there is a slant (e.g., more than 10 ) the hand geometry is not affected by variations in illumination, age,measurements will be biased. In the future we plan to cope obstructions, etc. In particular the same 3-D sensor may be usedwith this problem by using a shape-from-shading approach to to capture face and hand images and therefore the proposedreconstruct the 3-D structure of the ﬁnger surface over regions technique is ideal for fusion with 3-D face biometrics , .where such information is missing. Then it would be possible This is expected to lead to a low-cost solution offering highlyto obtain more accurate measurements even under relatively reliable authentication without sacriﬁcing user convenience.large hand pose variations.C. 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MALASSIOTIS et al.: PERSONAL AUTHENTICATION USING 3-D FINGER GEOMETRY 21 Sotiris Malassiotis was born in Thessaloniki, Michael G. Strintzis (S’68–M’70–SM’80–F’04) Greece, in 1971. He received the B.S. and Ph.D. received the Diploma in electrical engineering from degrees in electrical engineering from the Aristotle the National Technical University of Athens, Athens, University of Thessaloniki in 1993 and 1998, re- Greece, in 1967, and the M.A. and Ph.D. degrees spectively. in electrical engineering from Princeton University, From 1994 to 1997, he was conducting research Princeton, NJ, in 1969 and 1970, respectively. in the Information Processing Laboratory of Aristotle He then joined the Electrical Engineering De- University of Thessaloniki. He is currently a Senior partment at the University of Pittsburgh, Pittsburgh, Researcher in the Informatics and Telematics Insti- PA, where he served as Assistant (1970–1976) and tute, Thessaloniki. He has participated in several Eu- Associate (1976–1980) Professor. Since 1980, he is ropean and National research projects. He is the au- Professor of electrical and computer engineering atthor of more than 20 articles in refereed journals and more than thirty papers the University of Thessaloniki, and, since 1999, Director of the Informaticsin international conferences. His research interests include stereoscopic image and Telematics Research Institute, Thessaloniki. His current research interestsanalysis, range image analysis, pattern recognition, and computer graphics. include 2-D and 3-D image coding, image processing, pattern recognition, biomedical signal and image processing and DVD and Internet data authenti- cation and copy protection. Dr. Strintzis has served as an Associate Editor of the IEEE TRANSACTIONS Niki Aifanti received the Diploma in electrical and ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY. In 1984, he was awarded computer engineering in 1999 from the Electrical one of the Centennial Medals of the IEEE. and Computer Engineering Department, University of Thessaloniki, Thessaloniki, Greece, and the M.Sc. degree in multimedia signal processing in 2001 from the University of Surrey, U.K. She is currently pursuing the Ph.D. degree in the same department, where she holds research and teaching assistantship positions. She is a Graduate Research Assistant with the Informatics and Telematics Institute, Thessaloniki,Greece. Her research interests include face and gesture recognition, computervision, pattern recognition, image processing. Ms. Aifanti is a member of the Technical Chamber of Greece.