Part-based PCA for Facial Feature Extraction and Classification

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vertical position of the eyebrows as H1; set the second wave trough that corresponds to the vertical position of the eyes as H2. The starting vertical position of the eyes area is H1- 0.2 × VH, where VH=H2-H1; while the ending vertical position is H2+0.8× VH. Here, we get the extracted eyes area shown in Fig 8. Fig 5. Integral projection curves If we rotate the projection curve 90 degree, aligning the image with its vertical position, we could detect the position of eyes and mouth region by observing the horizontal graylevel projection curves. In horizontal gray-level integral projection, wave troughs of previous features are formed on the curves of the graphs due to the majority of black color in the areas of eyebrows, eyes, and mouths. By observing the wave trough, we could locate the position of the eyes and mouth areas. In horizontal gray-level projection, from the left to the right, the first minimum value represents the position of the eyebrow; the second minimum value represents the position of the eye. From the right to the left, the first minimum value represents the position of the mouth. Fig 6 shows the position of the eyebrows, eyes and mouth. Fig 8. The extracted eyes area We apply the same method for mouth area detection. Suppose the vertical length of the face image is H. Set the first wave trough from the top after 0.7H as H4, and the closest wave trough above H4 as H3. The starting vertical position of the mouth area is H3+0.4 × VH, where VH=H4-H3; while the ending vertical position is H4+0.7× VH. The extracted mouth area is shown in Fig 9. Fig 6. The position of the eyebrows, eyes and mouth However, due to image complexity and noise, there might be some small wave trough in the projection curve, which interferes with eyes and mouth location detection. Therefore, we need to smoothen the integral projection curves, filter minor wave troughs, and eliminate disturbing information. After smoothening, there will be four main wave troughs appearing, which represent eyebrows, eyes, nose and mouth respectively, see Fig 7. Fig 9. The extracted mouth area Based on the extracted eyes and mouth areas, we still need to refine the extracted eyes and mouth areas for future Gabor transformation. We apply integral projection once more with vertical projection. The vertical projection curves of eyes and mouth areas are shown in the following figure: Fig 7. Horizontal projection after smoothening The detail steps to detect eyes areas are: Considering the vertical length of the face image is H. Set the first wave trough from the top after 0.15H that corresponds to the Fig 10. Vertical projection curves of eyes and mouth areas The final extracted eyes area is the range from the left most maximum value W1 to the right most maximum value W2 (see Fig 11); while the final extracted mouth area is between: the right most maximum value W1 from the middle to the left and the left most maximum value W2 from the middle to the right (see Fig 12). 102
Fig 11. Final extracted eyes area image of each class, we can identify the expression class of the input image. We performed the experiments on the JAFF database [25] using image sequences and compared the results between traditional PCA and part-based PCA. By applying traditional PCA with neural networks, we achieve 89.10% on trained data and 69.76% on untrained data; while by applying partbased PCA with modified PCA reconstruction, we obtain 93.71% on trained data and 76.67% on untrained data. The results demonstrate that the part-based PCA outperforms traditional PCA in terms of higher recognition accuracy. Fig 12. Final extracted mouth area. 2.3 PCA Reconstruction for Facial Expression Classification Using the idea of multi-step integral projection we can extract the eyes and mouth regions and then apply part-based PCA on them. This can solve the problem of individual differences when applying whole face PCA. In order to solve the problem that the features extracted from PCA are not the best features suitable for classification but for expressing the data set, we propose a modified PCA reconstruction method [24]. The main idea of this method is: Instead of having a single training set for PCA reconstruction, we divide the training set into different classes according to different facial expressions. For the JAFFE database [25], we divide the training set into seven classes. Each class represents a facial expression and then perform PCAs on these classes respectively. Let V be the matrix whose columns are the first k eigenvectors of C. The projection of image τ i into its space is given by P = V( τ − ψ ) i The face image can be represented by P i . From this projection, we can get the reconstructed image R i T Ri = V Pi + ψ Since the input image is much similar to one expression training set than the others, the reconstructed image will have less distortion than the image reconstructed from other eigenvectors of training expressions. For an input happy expression image, if we reconstruct the eyes area and mouth area in each expression class independently, we could find that the happy class shows the best similarity with the input image (See Fig 13). By measuring the similarity (distance measure) between the input image and the reconstructed i Fig 13 Comparison between original eye and mouth image with reconstructed images 3. Error analysis Some of the incorrect facial expression recognitions are due to the difference of expression images in the database are not obvious. Another reason is that the boundaries between some expression, such as anger and disgust, disgust and sad, fear and sad, etc. are not very clear. The above two reasons cause most of the false recognition results. Table 1 lists some incorrect classification examples. a) list of the expressions that the images are supposed to be classified into; b) list of our classification results. We could see that some expressions 103
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Part-based PCA for Facial Feature Extraction and Classification

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