Weighted Sub-Gabor for face recognition

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Abstract

In this paper, we introduce a new face recognition approach based on the representation of each individual by a feature vector extracted through a bank of Gabor filters and Karhunen–Loeve transform. This method operates directly on sub-patterns of the whole image, extracting features from them. The features obtained by each sub-pattern are used to train a Parzen Window Classifier. Moreover, our method computes the contributions of each part in order to enhance the robustness to facial expression and illumination condition. Extensive experiments carried out on the FERET database of faces prove the advantages of the proposed approach when compared with other well-known techniques.

Introduction

Face images may be represented by feature vectors in a high dimensional vector space, obtained by a simple raster scanning the face image or by means of some more sophisticated feature extraction techniques such as Discrete Cosine transform (DCT) (Manjunath et al., 1992) or Gabor wavelet decomposition (Wiskott et al., 1997, Liu, 2004). The processing of vectors in such a space is usually a difficult task due the “dimensionality curse” problem. In the last few years, a variety of dimensionality reduction transforms have been applied in the context of face recognition: Karhunen–Loève (KL) transform (Turk and Pentland, 1991) (also known as Principal Component Analysis), Independent Component Analysis (Bartlett et al., 2002, Fortuna and Capson, 2004), and Discriminant Analysis (LDA) (also called Fisher Discriminant Analysis) (Zhao et al., 1998). Some extensions of Principal Component Analysis have been studied and applied to face recognition: Nonlinear Principal Component Analysis (Krame, 1991), Kernel Principal Component Analysis (Yang et al., 2000). A comparative performance analysis carried out in (Yang et al., 2000) among several subspace methods shows that the method based on Fisher transform performed significantly better than the others.

The methods based only on the global information of face images are not very effective under different facial expression, illumination condition and pose. The authors in (Gottumukkal and Asari, 2004, Tan and Chen, 2005) proposed two methods (mPCA and Aw-SpPCA) which try to overcome such ineffectiveness by exploring the face’s local structure. In mPCA a face image is first partitioned into several smaller sub-images, and then a single conventional PCA is applied to each of them. In Aw-SpPCA not only the spatially related information in a face image is considered and preserved in each sub-pattern, but also the different contributions made by different parts of the face are emphasized. The different contributions made by different sub-patterns are obtained classifying median and mean faces of the different individuals. Elastic grid matching described in (Wiskott et al., 1997) uses Gabor wavelets to extract features at grid points and graph matching for the proper positioning of the grid. In (Tefas et al., 2001) the authors propose an “improved” elastic graph matching, they propose to weigh the local similarity values at the grid nodes according to their discriminatory power. Yang et al. (2004) uses AdaBoost to select a small set of Gabor features. Both Tefas et al., 2001, Yang et al., 2004 need more images for each individual of the training set to weigh the local similarity values at the grid nodes or to train the AdaBoost. In (Heisele et al., 2003) the authors divide the face in ten fixed sub-windows and then train a Support Vector Machine (SVM) for each sub-window, finally, they combine these ten classifiers. Kim et al. (2002) proposes a method similar to Heisele et al. (2003) but instead of SVM they train, for each sub-window, a Linear Discriminant Analysis.

In this paper, we propose a new method that try to overcome ineffectiveness of Aw-SpPCA:

  • Better feature extraction, Gabor filters (with overlap between sub-patterns) + PCA instead of Gray Values (without overlap between sub-patterns) + PCA.

  • Better method to calculate the scores, Parzen Window Classifier (PWC) instead of nearest neighbour.

  • Method, based on Genetic Algorithm (GA), that permits to compute the contributions of the sub-patterns when we have few images for each individual (as in FERET database).

In this paper, we use as classifier the Parzen Window Classifier (PWC) instead of nearest neighbour. PWC is a one-class classifier and it is probabilistic (see Section 2.3). The problem in one-class classification is to make a description of a target set of objects. The difference with conventional classification is that in one-class classification only examples of one class are available. The objects from this class will be called the target objects. Using one-class classifier we can build a classifier for each individual without any knowledge of the others individuals. Since the output of PWC is a pdf it is easy to combine these classifiers (Duda et al., 2000).

The methods proposed in (Tefas et al., 2001, Yang et al., 2004) and in this paper are based on the Gabor filters and on weighing the local regions of the face, but there are some differences: our work selects a given region and then extract the features, while Yang et al. (2004) selects the features of a local-based Gabor approach. We want to stress that Tefas et al. (2001) needs more example of the same reference person to weigh the nodes, while Yang et al. (2004) needs intra-class examples in the training set (to create examples of the class genuine). Our method tries to find a weight for each local regions of the face and does not need more examples of the same person in the training (we do not need examples of the class genuine), we need to build a validation set to validate the weights find by GA, it is not important if in the training we have more than one intra-class example.

Moreover, our work is based on a one-class classifier, while Adaboost is a 2-class classifier (genuine vs impostor). Definitively, in our opinion, these methods are complementary (Kuncheva, 2004). In our opinion a fusion among our method, Tefas et al., 2001, Yang et al., 2004 permit to obtain an Equal Error Rate lower than that obtained by a single method (e.g. in Zana et al. is shown that a fusion between a 2-class classifier and nearest neighbour permits to improve the performance of the Face Recognizer).

Table 1 compares the Weighted Sub-Gabor, Aw-SpPCA and Heisele et al. (2003), highlighting the main differences.

The experimental results obtained on the most common database in this field (Zhao et al., 2000) show that our approach outperforms other methods reported in the literature. The results on FERET database are particularly interesting since they prove the effectiveness of our method in dealing with problems where only few poses are available for each individual (only one per person in FERET).

The paper is organized as follows: in Section 2 a description of the system architecture is given and the individual steps of the method are detailed, in Section 3 the experimental results are discussed and, finally, Section 4 draws the conclusions.

Section snippets

Proposed algorithm

There are three main steps, showed in Fig. 1, in Weighted Sub-Gabor algorithm: (1) image partition and feature extraction (2) computing contributions, and (3) classification.

Experiments

The FERET (Phillips et al., 1998, Phillips et al., 2000) database has been used in our experimentations, this database was introduced in the third evaluation (September 96) contains images of 1196 individuals (taken over a long period varying acquisition conditions) and consists of one training set (1196 frontal images, one for each individual) and four test sets:

  • FB probes: 1195 images of individuals taken on the same day with the same lighting.

  • FC probes: 194 images of individuals taken on the

Conclusions

In this paper, we propose a new Face Recognition method. In this method, the feature extraction is performed by using a bank of Gabor filters, the filters are applied at fixed positions, in correspondence of the nodes of a square-meshed grid superimposed to the face image. The features extracted by the Gabor filters that belong to the same row of the square-meshed grid are projected onto a lower dimensional space by KL, and than these features are used to train a classifier. We train a

Acknowledgements

This work has been supported by Italian PRIN prot. 2004098034 and by European Commission IST-2002-507634 Biosecure NoE projects. Portions of the research in this paper use the FERET database of facial images collected under the FERET program, sponsored by the DOD Counterdrug Technology Development Program Office.

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