NUMERICAL ANALYSIS AND COMPARISON OF SPECTRAL DECOMPOSITION METHODS IN BIOMETRIC APPLICATIONS

Abstract

Face recognition is a challenging problem in computer vision and artificial intelligence. One of the main challenges consists in establishing a low-dimensional feature representation of the images having enough discriminatory power to perform high accuracy classification. Different methods of supervised and unsupervised classification can be found in the literature, but few numerical comparisons among them have been performed on the same computing platform. In this paper, we perform this kind of comparison, revisiting the main spectral decomposition methods for face recognition. We also introduce for the first time, the use of the noncentered PCA and the 2D discrete Chebyshev transform for biometric applications. Faces are represented by their spectral features, that is, their projections onto the different spectral basis. Classification is performed using different norms and/or the cosine defined by the Euclidean scalar product in the space of spectral attributes. Although this constitutes a simple algorithm of unsupervised classification, several important conclusions arise from this analysis: (1) All the spectral methods provide approximately the same accuracy when they are used with the same energy cutoff. This is an important conclusion since many publications try to promote one specific spectral method with respect to other methods. Nevertheless, there exist small variations on the highest median accuracy rates: PCA, 2DPCA and DWT perform better in this case. Also all the covariance-free spectral decomposition techniques based on single images (DCT, DST, DCHT, DWT, DWHT, DHT) are very interesting since they provide high accuracies and are not computationally expensive compared to covariance-based techniques. (2) The use of local spectral features generally provide higher accuracies than global features for the spectral methods which use the whole training database (PCA, NPCA, 2DPCA, Fisher's LDA, ICA). For the methods based on orthogonal transformations of single images, global features calculated using the whole size of the images appear to perform better. (3) The distance criterion generally provides a higher accuracy than the cosine criterion. The use of other p-norms (p > 2) provides similar results to the Euclidean norm, nevertheless some methods perform better. (4) No spectral method can provide 100% accuracy by itself. Therefore, other kind of attributes and supervised learning algorithms are needed. These results are coherent for the ORL and FERET databases. Finally, although this comparison has been performed for the face recognition problem, it could be generalized to other biometric authentication problems.