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PREVIOUS WORK 3D Face Recognition
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Public face recognition tests demonstrated that the performance of the best 2D face recognition systems is similar to that of ngerprint recognition, when frontal neutral views recorded under controlled conditions are used, but degrades signi cantly for images subject to pose, illumination, or facial expressions variations [3]. These dif culties may be alleviated using the 3D geometry of the face, which is inherently insensitive to illumination changes or face pigmentation. In addition, using 3D images makes it considerably easier to cope with pose variations [8] or facial expressions [9]. Three-dimensional face recognition techniques can be roughly divided into three categories: surface-based, appearance-based, and model-based [10]. These are brie y discussed in the following. Surface-Based Methods
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This class of techniques approach the problem of face recognition as one of measuring the similarity between surfaces. The similarity may be computed by means of local or global surface attributes. In many techniques, surface curvature is used to localize facial features invariant to rigid transformations (e.g., eyes, eyebrows, nose, mouth, etc.) by making use of prior knowledge of face anatomy [11]. Face classi cation is usually based on the comparison of feature vectors representing the spatial relationships (distances, angles, etc.) between extracted facial features [12]. More generic transformation invariant descriptors based on mean and Gaussian curvature were also proposed [13, 14]. In reference 15, the sign of the Gaussian and mean curvature is used to segment the face in various regions and construct extended Gaussian images (EGIs) of them. The EGIs represent the distribution of the surface normal vector over each region. Face matching is performed using rotation invariant correlation between the respective EGIs. A similar approach is followed in reference 16, where an EGI of the face is computed using the maximum and minimum principal curvature and their local extrema. A recognition rate of 100% was reported in a database of 37 people. In reference 17, the well-known point signatures method is applied for 3D face matching. Point signatures describe the structure of the face surface locally and are invariant to rigid transformations, but not to nonrigid ones, such as those caused by facial expressions. Thus, the rigid parts of the face should rst be identi ed, before this technique is applied. Face matching is based on establishing the correspondences between the two surfaces through correlation of their signature vectors and calculating a similarity measure. In reference 18, 3D geometry features described by point signatures are fused with 2D texture features described by Gabor lters. Experiments in a database of 50 people and 300 images with viewpoint and facial expressions variations report a recognition rate close to 92%. Although high recognition rates were reported for curvature-based techniques, in practice, these methods present several shortcomings. Their main disadvantage
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is that they are very sensitive to image noise (since the curvature is a second derivative) and occlusions of the face. Moreover, they are computationally expensive. The computation of curvature features may be avoided altogether using global surface alignment techniques such as the iterative closest point (ICP) algorithm [19]. Point-to-point correspondences are established simply by searching for each point on the surface, the closest point on the other surface. Then, a rigid transformation may be computed that minimizes the sum of distances of corresponding points. This is performed iteratively; after convergence, the resulting distance between the two registered surfaces is used as a measure of similarity. This technique was tested in reference 20, and an EER better than 2% was reported in a database of 100 people with 700 images representing different poses. The matching ef ciency of the ICP can be improved by considering additional features, such as color or curvature, or by using a weighted distance [21]. The main limitation of the ICP algorithm is that its convergence is not guaranteed, unless a good initial transformation is available. As a result, this approach fails when applied on faces exhibiting pose variations. Such an initial transformation may be recovered, however, by localization of feature points such as the eyes and the nose on both probe and gallery images [22]. In order to cope with nonrigid deformation, Lu and Jain [23] extended the work in reference 22 by subdividing the face in rigid and nonrigid parts. Rigid registration is based on the ICP, while registration of nonrigid parts is based on the thin-plate spline model. Signi cant gains are reported using such a scheme. A combination of ICP and curvature-based approaches is presented in reference 24. Alternative distance measures, such as the Hausdorff distance [25], the depthweighted Hausdorff distance (DWHD) [26] and 2D approximations of the 3D Hausdorff distance [27] were also proposed. To cope with facial expressions, many researchers have proposed the use of expression invariant representations of the face surface based on geodesic distances [28 30]. Such approaches rely on the assumption that the face is an approximately isometric surface and thus geodesic distances between face surface points are preserved with facial expressions. The intrinsic metric structure of the face surface is represented by embedding the surface into a low-dimensional 3D Euclidean space and replacing the geodesic distances by Euclidean ones [28]. Such representations are known as canonical forms and can be classi ed using classic rigid surface matching techniques. To address the problem of local nonisometric deformations caused by open mouths, topologically constrained Euclidean canonical forms and spherical canonical forms were also proposed in reference 29. A computationally more ef cient approach based on geodesic polar coordinates is presented in reference 30. The parameter space is built using a fast warping procedure, which avoids the embedding errors introduced by the multidimensional scaling (MDS) used in reference 29. Moreover, face matching is performed on 2D canonical images representing color or shape information, while the open-mouth problem is ef ciently handled by segmenting the face in three parts and merging the distinct canonical maps.
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