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where M wm = 1 . The weights wm are assigned to the individual classi ers so m=1 that the total equal error rate (EER) is minimized. This way, more robust classi ers are assigned higher weights, while less accurate classi ers are assigned lower weights. The above normalization-fusion scheme was applied to different modality combinations, that is, FC + FD and FC + FD + H. For the unimodal classi ers no normalization was required.
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10.6 Experimental Evaluation
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The face test database consists of 3457 face image pairs of 50 persons, while the hand test database consists of 24,898 4-tuples of hand image pairs of the same individuals. Face and hand probe images were selected from the second recording session. For each probe (face and/or hand) image the identity of all enroled users is claimed in turn, thus resulting in one genuine (user to whom this image actually belongs to) and 49 impostor claims per image. In total, 3457 genuine and 169,393 (3457 49) impostor matching scores are computed from the face test database and 24,898 genuine and 1,220,002 (24,898 49) impostor scores from the hand database. For the evaluation of the proposed face + hand multimodal system, each pair of probe face images (depth + color) is associated with ve randomly selected pairs of hand images belonging to the same person, thus resulting in 17,285 (3457 5) pairs of hand + face images that is, 17,285 score vectors. A score vector is a triplet sFC , sFD , sH , where sFC , sFD , and sH are the matching scores obtained by the FC, FD, and H classi ers, respectively. From each score vector, a multimodal score is computed in the following way: First we normalize the matching scores provided by the unimodal classi ers using the QLQ normalization. Then, we consolidate the normalized scores using the weighted-sum fusion technique. Using the above procedure, 17,285 genuine and 846,965 (17,285 49) impostor fusion scores were produced for evaluating the performance of the FC + FD + H authentication system. For the evaluation of the 2D + 3D face authentication system, the 3457 image pairs of the face database were used, resulting in 172,850 (3457 50) fusion scores (QLQ normalization and WS fusion were also applied). The performance of the proposed authentication system is presented in terms of the equal error rate (EER) values, the receiver operating characteristics (ROC) curves, and the rank-1 identi cation rates. Table 10.1 summarizes the EERs of the unimodal 2D and 3D face classi ers, the 2D + 3D face authentication system (FC + FD) and the proposed face and hand multimodal system (FC + FD + H) for different appearance variations of facial images. The corresponding identi cation rates (IR) are also shown. It is clear that the multimodal classi er combining facial and hand data exhibits better authentication rates (lower error rates) than do the unimodal systems or the combination of 2D and 3D facial data for all facial variations. Obviously, combining facial features with hand geometry features can be more ef cient, since these features are considerably less correlated than, for example, 2D and 3D facial data. The superiority of the proposed multimodal scheme is more clearly demonstrated in the case of expressions or wearing eyeglasses. For images depicting different expressions (smile, laugh), the EER reported for the FC and FD classi ers is about 10%. By combining 2D and 3D facial data, the EER decreases to 8%. An EER of 1% is nally obtained when fusing color and depth facial data with hand geometry data. Similar statistics are observed for images with subjects wearing glasses, although in this case the decrement of the EER is smaller. It is also interesting to observe that in the case of the unimodal face classi ers or the 2D + 3D face classi er, the EERs obtained for probe images with pose or
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Facial Variations Expression 10.14 (95.18) 10.73 (92.96) 8.00 (96.43) 1.07 (100.00) 5.79 (98.14) 4.42 (99.00) 2.57 (98.93) 0.50 (100.00) 3.61 (98.36) 2.53 (98.55) 2.00 (98.76) 0.80 (100.00) Pose Illumination Glasses 5.03 (97.96) 6.49 (98.95) 3.36 (98.59) 1.32 (100.00) All 6.46 (97.75) 7.55 (97.85) 4.39 (98.51) 0.82 (100.00)
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