Gabor-based kernel PCA with doubly nonlinear mapping for face recognition with a single face image

In this paper, a novel Gabor-based kernel principal component analysis (PCA) with doubly nonlinear mapping is proposed for human face recognition. In our approach, the Gabor wavelets are used to extract facial features, then a doubly nonlinear mapping kernel PCA (DKPCA) is proposed to perform feature transformation and face recognition. The conventional kernel PCA nonlinearly maps an input image into a high-dimensional feature space in order to make the mapped features linearly separable. However, this method does not consider the structural characteristics of the face images, and it is difficult to determine which nonlinear mapping is more effective for face recognition. In this paper, a new method of nonlinear mapping, which is performed in the original feature space, is defined. The proposed nonlinear mapping not only considers the statistical property of the input features, but also adopts an eigenmask to emphasize those important facial feature points. Therefore, after this mapping, the transformed features have a higher discriminating power, and the relative importance of the features adapts to the spatial importance of the face images. This new nonlinear mapping is combined with the conventional kernel PCA to be called "doubly" nonlinear mapping kernel PCA. The proposed algorithm is evaluated based on the Yale database, the AR database, the ORL database and the YaleB database by using different face recognition methods such as PCA, Gabor wavelets plus PCA, and Gabor wavelets plus kernel PCA with fractional power polynomial models. Experiments show that consistent and promising results are obtained.