3D Face Authentication System in .NET

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10.4 3D Face Authentication System
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Figure 10.7. Illumination compensation examples. (a) Original image, (b) R(Id , L, u),
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(c) R(Id , L0 , u), (d) R(Id , L0 , u)/R(Id , L, u), (e) novel image relit by frontal light.
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where Id is the pose compensated depth image, A is the unknown surface albedo, and R is a rendering of the surface with constant albedo. Likewise, the illumination compensated color image I c can be written as I c (u) = A(u)R(Id , L0 , u). From the above, it is easily drawn that the illumination compensated image I c can be simply computed by multiplication of the input image with a ratio image R(Id , L0 , u) I c (u) = Ic (u) . R(Id , L, u) (10.6)
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An important advantage of our technique is the exibility in coping with complex illumination conditions by adapting the rendering function R. For example, accounting for attached shadows may be easily achieved by activating shadowing in the rendering engine. Nonetheless, we have observed that relatively simple renderings, such as the Lambertian re ection model, where R(u) = n(u)T L and n(u) is the surface normal at u, also give good results. Figure 10.7 illustrates the relighting of side illuminated images.
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Face Classification
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The pair of images generated after pose and illumination compensation is subsequently used as input to the face classi er. Note that the same normalization procedure was applied to gallery images as well. Color pixel values are normalized to have zero mean and unit variance. Several state-of-the-art face classi cation techniques have been examined including classic eigenfaces, probabilistic matching, embedded hidden Markov models, and elastic graph matching. A simpler version of the probabilistic matching algorithm [56] based on extra-personal eigenfaces was nally adopted because of its good performance and computational ef ciency. The PM algorithm is applied to both color and
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A Novel Unobtrusive Face and Hand Geometry Authentication System
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depth images, independently. The two resulting matching scores are fused together to provide a single score using classic fusion techniques, as will be described in Section 10.6.3.
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3D HAND GEOMETRY AUTHENTICATION
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In this section we outline the algorithms employed by the hand geometry authentication system. First, the hand is segmented from the body using 3D moments. Then, the position of the palm and ngers is accurately localized in the 3D image. Twodimensional information is subsequently used to localize nger boundaries using a model-based approach. Finally, we extract a set of 3D nger measurements including width and curvature information [2].
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Hand Detection
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According to the authentication scenario described in Section 10.3, the user stands in front of the sensor with her hand in front of the face and the back of the hand facing the sensor. Segmentation of the hand from the body is achieved by assuming that the hand does not move. Thus, we may exploit the results of face detection to form a plane that separates the face from the hand and arm. In practice, however, this may not be ef cient, since the user may have moved her body. Thus, hand segmentation relies on statistical modeling of the hand, arm, and head plus torso points using a knowledgebased 3D blob approach, similar to the face segmentation algorithm described in Section 10.4.1. Similarly to Eq. (10.1), the probability distribution of a 3D point x can be modelled as a mixture of three Gaussians: P(x) = P(head + torso)P(x|head + torso) + P(hand)P(x|hand) + P(arm)P(x|arm) = 1 N(x;
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1, 1 ) + 2 N(x; 2, 2 ) + 3 N(x; 3, 3 ),
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(10.7) (10.8)
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where 1 , 2 , 3 are the prior probabilities of the head/torso, hand, and arm blobs, respectively. Initialization of blob parameters is obtained in a fashion similar to that in Section 10.4.1 using prior knowledge of the relative con guration of body parts [2] (see Figure 10.8). The parameters 2 and 2 that result after EM convergence correspond to the center of mass and the pose of the hand. Hand segmentation is achieved by de ning a plane (p 2 )T n = d that separates the hand from the face. n is the eigenvector of 2 corresponding to the smallest eigenvalue, and it is approximately perpendicular to the hand surface plane. d is the distance of the hand plane from the cutting plane. Three-dimensional points lying in front of this plane form a mask corresponding to the hand and forearm, while the rest are discarded (see Figure 10.9a,b). The value of d is chosen in accordance to allowed closeness of the hand to the face. For our experiments, the distance of the hand from the body can be as small as 10 cm. For smaller distances there are a few cases (usually exhibiting nger bending) where the algorithm fails to nd a separating plane and crops part of the ngers.
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