A Statistical Nonparametric Approach of Face Recognition: Combination of Eigenface&Modified k-Means Clustering

Facial expressions convey non-verbal cues, which play an important role in interpersonal relations. Automatic recognition of human face based on facial expression can be an important component of natural human-machine interface. It may also be used in behavioural science. Although human can recognize the face practically without any effort, but reliable face recognition by machine is a challenge. This paper presents a new approach for recognizing the face of a person considering the expressions of the same human face at different instances of time. This methodology is developed combining Eigenface method for feature extraction and modified k-Means clustering for identification of the human face. This method endowed the face recognition without using the conventional distance measure classifiers. Simulation results show that proposed face recognition using perception of k-Means clustering is useful for face images with different facial expressions.


INTRODUCTION
Over the past 20 years [1], considerable amount of works have been carried out for automatic recognition of facial expression by different researchers using parametric as well as non-parametric techniques. The work proposed by M.A.Turk & A.P.Pentland [2,3], in "Eigenfaces for Recognition" the input images is projected onto the face space using principle component analysis called Eigenfaces. The recognition is performed using various distance classifiers and a correct distance-threshold. Sang-Jean Lee et al. [4] developed a system that can locate and track person's head in a complex background and recognization is done using pre-extracted face images on a feature space using PCA. Moon H. et al. [5] designed a generic PCA algorithm for experimenting on FERET image set with varieties of issues such as illumination Facial expressions convey non-verbal cues, which play an important role in interpersonal relations. Automatic recognition of human face based on facial expression can be an important component of natural humanmachine interface. It may also be used in behavioural science. Although human can recognise the face practically without any effort, but reliable face recognition by machine is a challenge. This paper presents a new approach for recognizing the face of a person considering the expressions of the same human face at different instances of time. This methodology is developed combining Eigenface method for feature extraction and modified k-Means clustering for identification of the human face. This method endowed the face recognition without using the conventional distance measure classifiers. Simulation results show that proposed face recognition using perception of k-Means clustering is useful for face images with different facial expressions. normalization, effect of compression with JPEG and Wavelet, eigenvectors selection etc. Further, Hyun-chul Kim et al. [6] deals with "face recognition using the mixtureof-eigenfaces method" uses more than one set of eigenfaces from the expectation maximization learning in the PCA mixture model for representation of face images with large variations. The research carried out by Yan Ma et al. [7] stated that during training process average projection vector of different images for each person is used. Recognition uses two thresholds (acceptance and rejection). The work done by M.A. Rabbani et al. [8] used Median instead of mean and with different distance measures in appearance-based statistical eigenface method.

Fig. 1 Schematic block diagram of the proposed face recognition system
In our proposed work we address a simple yet efficient method for face recognition that considered one of the hurdles of the Eigenface method that uses different distance classifiers. In our travail, deliberating different facial images of a single human face taken together as a cluster, then have applied concept of k-Means clustering for recognition that avoids that exploit a threshold value which is changed under different distance classifiers. This is very sophisticated face recognition algorithm and has comparable performance with conventional eigenface face recognition method.
where M = No. of images in training image set, Ψ= Mean face • Normalized images: where Ф i = i th normalized training image.
where u= [ u 1 ,u 2 ,…..u E ], E<=M, Ω i = face space training images, • Mean of each class: where Ω i k = i th face space image of k th class, £ k = mean of each k th class, C = no. of classes (each person belongs to a separate class), P = no. of images per class.

Recognition of a Probe Image
• Normalized test image: where Г test = vector form of test image, Ф test = normalized test image • Mapped test image: where u= [ u 1 ,u 2 ,…..u E ], Ω test = mapped test image in the face space • Mean with test image: (8) where µ k = mean of each class including test image, Ω i k = represents i th face space image of k th class, C = no. of classes (each person belongs to a separate class), P= no. of images per class.
• Difference of old and new mean : where D k = difference between old and new mean value of k th class • Minimum mean difference: D min = Min ( D k ) , k=1 to C (10) where D min = minimum value among all D k • If D min <= T (where, T is very small) => Ф test ε I

EXPERIMENTAL RESULT
In our experimental purpose, standard ORL face database is used which contains a set of 40 people with 10 images (representing different facial expressions) of each face. For all the cases a subset of images are used as training set and the rest of the images as testing set. Table 1 represents the result of average percentage of success when we have used one image per person of the training image set.

CONCLUSION
Under this new methodology we can avoid the use of various distance measurement technique and computation of correct threshold value which is the core parameter of existing eigenface method. Very little work has been done on avoiding the use of distance classifiers and threshold measurements in Eigenface based method. Previous work [9] has given emphasis on selecting the correct distance measure classifiers. When we apply our new methodology for both the case (Case Study 1 & 2), the success rates are satisfactory. This method provides a simple and fast solution while maintaining standard prediction accuracy.