Recognition of Expression Variant Faces Using Weighted Subspace in .NET

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8.7 Recognition of Expression Variant Faces Using Weighted Subspace
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the lips and the eyes). Thus, in this case, similar RT are expected. This was indeed the case in our experiment (Figure 8.10b).
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Zhang and Martinez [67] applied the face recognition model presented above to the subspace approach for the recognition of identity under varying expressions in the appearance-based framework. By appearance-based, it is understood that the recognition system only makes use of the textural information of the face after this has been warped to a standard (prototypical) shape. Over the years, the success of appearancebased approaches, especially when applied to face recognition problems, has only increased. Appearance-based methods are attractive because the model of each class is directly de ned by the selection of the sample images of that object, without the need to create precise geometrical or algebraic representations [64]. The clear disadvantage is that any image condition not included in the learning set will cause incorrect recognition results. In the pattern recognition community, it is common practice to use a minimum number of independent sample vectors of 10 times the number of classes by the number of dimensions of our original feature space. Unfortunately, it is rarely the case where one has access to such a large number of training images per class in applications such as face recognition. And, even when one does have a large number of training images, these are not generally uncorrelated or independent from each other. Hence, other solutions must be de ned. The problem with subspace techniques is that some of the learned features (dimensions) represent (encode) facial expression changes. As shown above, this problem can be resolved if we learn which dimensions are most affected by expression variations and then build a weighted-distance measure that gives less importance to these. In this formulation, a fundamental question is yet to be addressed: Would a morphing algorithm solve the problem That is, rather than designing a weighted measure as we did in our model, one could utilize the motion estimation to morph the test face to equal in shape that of the sample face image. This would allow a pixel to pixel comparison. Unfortunately, morphing algorithms can fail due to occlusions (e.g., teeth and closed eyes), large deformations and textural changes due to the local deformation of the face. The last of these points is key. We note that when the face changes expression, the 3D position of several local areas also change, and therefore the re ectance angle will also change. This effect will obviously change the brightness of the image pixels (that is, the texture) in our image. The approach presented in this chapter solves this by assigning low weights to those areas with large deformations.
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Learning Linear Subspace Representation
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Principal component analysis (PCA), independent component analysis (ICA), and linear discriminant analysis (LDA) are three of the most popular linear subspace methods and have been largely used in face recognition applications.
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A Biologically Inspired Model
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PCA nds the optimal liner projection between the original space of d dimensions and a low-dimensional space of p dimensions (features), assuming the data are Gaussian [68]. To do this, PCA uses the rst and central moments of the data that is, the sample mean and the sample covariance matrix . While PCA only computes the rst and central moments of the data, ICA will use higher moments of the data to nd those feature vectors that are most independent from each other [69]. In contrast, and as already described earlier in this chapter, LDA selects those basis vectors that maximize the distance between the means of each class and minimizes the distance between the samples in each class and its corresponding class mean [61].
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