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Fig.1 Radon transform of the image

ABSTRACT

This paper presents a new technique for face recognition using Radon transform. The technique captures the facial features from different directions. Proposed method which is robust to zero mean additive white noise derives local and directional information of the face images. The technique acts as low pass filter, enhancing low frequency components useful in face recognition which improves the recognition rate. The images are classified by using minimum distance 1 classifier. The feasibility of Radon transform based model has been successfully tested using ORL database. The effectiveness of the algorithm is shown in terms of absolute performance and compared with different existing popular algorithms for face recognition such as PCA, KPCA and Fisher classifier. This algorithm has outperformed the other algorithms.

KEY WORDS

Face recognition, Radon Transform, Principal Component Analysis (PCA), Fisher Discriminant Analysis (FDA).

1. Introduction

A wide variety of systems require reliable personal recognition schemes to either confirm or determine the identity of an individual requesting their services. The purpose of such schemes is to ensure that the rendered services are accessed only by a legitimate user and no one else. Examples of such applications include secure access to buildings, computer systems, laptops, cellular phones, and ATMs. In the absence of robust personal recognition schemes, these systems are vulnerable to the wiles of an impostor. Biometric recognition or, simply, biometrics refers to the automatic recognition of individuals based on their physiological and/or behavioral characteristics. By using biometrics, it is possible to confirm or establish an individual’s identity based on “who she is,” rather than by “what she possesses” (e.g., an ID card) or “what she remembers” (e.g., a password) [1].

Over the past few years, the person authentication is increasingly important because the security control is required everywhere. Traditionally, ID cards and passwords are popular for authentication although the security is not reliable and convenient. Recently biometric authentication technologies across voice, iris, fingerprint, palm, and face are playing a crucial role and attracting intensive interest of many researchers. Among them face recognition is an amicable alternative because the authentication can be completed in a hands free way without stopping user’s activities. In case of surveillance, the authentication is done without notice of the person.

Face recognition has received extensive attention within the past two decades because of its potential applications in many fields, such as identity authentication, information security, surveillance, human-computer interface, and so on. Face recognition depends heavily on the particular choice of features used by the classifier [2]. One usually starts with a given set of features and then attempts to derive an optimal subset of features leading to high classification performance with the expectation that similar performance can also be displayed on future trials using novel test data. Principal component analysis (PCA) is a popular technique used to derive a starting set of features for both face representation and recognition. Kirby and Sirovich [3] showed that any particular face can be economically represented along the eigenpictures coordinate space, and approximately reconstructed using just a small collection of eigenpictures and their corresponding projection. By PCA technique to face recognition, Turk and Pentland [4] developed a well-known Eigenfaces method. The PCA, however, does not consider the classification aspect, as it is based on the optimal representation criterion in the sense of mean square error. To improve the PCA standalone classification performance, one needs to combine further this optimal representation criterion with some discrimination criterion.

One widely used discrimination criterion in the face recognition is the Fisher linear discriminant (FLD) or linear discriminant analysis (LDA), which defines a projection that makes within-class scatter small and the between-class scatter large. As a result, FLD derives compact and well-separated clusters. As the original image space is high dimensional, most of these methods apply PCA first for dimensionality reduction. Subsequent FLD transformation is used to build the most discriminating features (MDF) space for classification [3]. The drawback of FLD is that it requires large training sample size for good generalization. For a face recognition problem, however, usually there are a large number of faces (classes), but only a few training samples per face. To cope with these problems, a new technique is developed.

This paper presents a Radon transform based model for face recognition which is robust to zero mean additive white noise. The technique utilizes Radon transform to convert the rotation to translation and derive the facial features with different orientations. The images are classified on the basis of distance measure using minimum distance classifier.

2. Radon Transform

Numbers of methods are available to extract the facial features. In the proposed method, Radon transform, which is conceptually similar to Hough transform, is used to derive the linear features. It is based on the parameterization of straight lines of the image domain, and on the evaluation of the integrals of the image along these straight lines. Due to inherent properties of Radon transform, it is a useful tool to capture the directional features of the images. It enables the implementation of very effective detection algorithms.

The Radon transform of a two dimensional (2-D) function is defined as

. (1)

where is the Dirac function, is the perpendicular distance of a line from the origin and is the angle formed by the distance vector as shown in fig. 1.

Radon transform is defined for an image with unlimited support. In practice, the image is confined to [-L, L] x [-L, L]. According to Fourier slice theorem, this transformation is invertible. Fourier slice theorem states that for a 2-D function, the 1-D Fourier transforms of the Radon transform along r, are the radial samples of the 2-D Fourier transform of at the corresponding angles. Rotation of the input image corresponds to the translation of the Radon transform along [5], [6].

The shifted Radon transform along , corresponds to an image significantly different from the original image. The important issue in using the Radon transform is finding the optimal number of projections to get the minimum classification error. By changing the number of projections, the Radon transform along is compressed or expanded. These scale the Fourier transform of the signal along and affects the extracted features. It is necessary to find the optimal number of projections that leads to most discriminative features with reasonable calculations.

For an increment of along , a point with a distance of from the origin has a displacement of . For all the points inside a circle with radius R, the average displacement for a constant increment of along is

. (2)

Fig.1 Radon transform of the image

To make the sampling rate consistent in the and directions, the Radon transform along is scaled by a factor of. If the number of samples for values from 0 to is, then

. (3)

(4)

The number of samples along is

. (5)

This is a good approximation of the sampling rate. In the proposed algorithm, the Radon transform calculates the projections of the image in different orientations. The maximum recognition rate is obtained by varying number of projections.

The line integral of an image during the calculation of the Radon transform acts like a low pass filter. This amplifies low frequency components in the face image. Earlier studies show that, information in low spatial frequency bands play a dominant role in face recognition. The low frequency components contribute to the global description, while the high frequency components contribute to the finer details required in the identification process. Sex judgment task is successfully accomplished using low frequency components only, while the high frequency components contribute the finer details required in the identification process [7]. This property of Radon transform is helpful in deriving the directional facial features.

The advantage of the proposed approach is its robustness to zero mean additive noise. Suppose an image is represented as

. (6)

where is white noise with zero mean and variance . Then its Radon transform is

(7)

As the Radon transform is line integral of the image, the Radon transform of noise is constant for all of the points and directions and is equal to mean value of the noise, which is assumed to be zero. Therefore

. (8)

This is same as (1). This means zero mean white noise has no effect on the Radon transform of the image. Thus the method is very robust to noise.

3. Feature Extraction

The directional information of face images is captured by the projection of the image in different orientations with the Radon transform. In each projection, the variations of the pixel intensities are preserved even if the pixels are far from the origin. For each projection, a vector, which is the projection of the image intensity along a radial line oriented at a specific angle, is computed. The radial coordinates returned in a vector are the values along the, which is oriented at theta degrees counterclockwise from the x-axis. The origin of both axes is the center pixel of the image. Radon transform projection of an image for different angles is computed. All the projections of one image are concatenated to form one vector. This vector represents the facial features. Such feature vectors for all training images as well as test images are computed. The Euclidean distance between test and training images is computed. The images are classified by using minimum distance classifier.

4. Experimental Result

The feasibility and performance of Radon transform based face recognition model is tested using AT&T (formerly ORL (Olivetti Research Laboratory)) database. The effectiveness of this method is tested against some popular existing face recognition schemes such as PCA, Kernel PCA (KPCA) and Fisher classifier.

1. Database

There are many facial databases available for evaluating face recognition algorithms. We have tested all the algorithms using ORL database. The ORL face database (developed at Olivetti Research Laboratory, Cambridge, U.K.) is composed of 400 images with ten different images for each of the 40 distinct subjects. The variations of the images are across pose, size, time and facial expression. All the images were taken against a dark homogeneous background with the subjects in an upright, frontal position, with tolerance for some tilting and rotation of up to about 20⁰. The spatial resolution is of 92 x 112, while gray level resolution is 256. Fig. 2 shows sample images of ORL database.

Fig.2. Sample images with spatial resolution of 92 x 112 from ORL database. The images vary in pose, size and facial expression.

2. Experimental result

In all the experiment, three images of each subject were used for training. The system was trained for 120 images. The percentage of correct classification was computed by varying number of features. In our study following sets of experiment were carried out.

1. The first set of experiment was carried out for Principal Component Analysis (PCA) method. For 120 features, the method yields 82% recognition rate.

2. In the second set of experiment, Kernel PCA (KPCA) method using a polynomial kernel with d equal to 3, 2, 1, 0.8, 0.7, and 0.6 was implemented. With integer degree of polynomial, highest recognition rate is obtained for d = 1. This special case of KPCA is equivalent to PCA. Hence PCA method performs better than KPCA method with second, third order polynomial. Fractional power polynomial model performed better than the integer power polynomial kernel.

3. The third set of experiment evaluated Fisher Discriminant Analysis (FDA). The recognition rate for Fisher classifier was 84%.

4. In the last experiment, Radon transform is used to derive the directional features. Fig. 3 shows the two images and their corresponding Radon transform for 0 to 180⁰ angle. The number of features is the number of projections of image using Radon transform in different directions. All such projections are concatenated to form the feature vector of an image. By varying the number of projections, (features) recognition rate is computed. Fig. 4 compares the performance of this algorithm with other approaches of face recognition. This method yields the recognition rate of 95.5%.

(a) (b)

3. (d)

Fig. 3 (a) And (c) shows the training images, while (b) and (d) shows their respective Radon transform

Fig.4 Comparison of different methods of face recognition with Radon transform model.

5. Conclusions

The results of the experiments described in Section 4 confirm that the Radon transform based algorithm performs better than the other methods. The results indicate that Radon transform based algorithm captures the recognition rate of more than 95%. Radon transform first derives desirable directional facial features. This transform is the line integral and hence acts as low pass filter. The low frequency components which play significant role in identification process are amplified and recognition rate is improved. The feasibility of this model has been successfully tested on ORL database. The algorithm outperformed the other methods of face recognition.

6. References

[1] Anil K. Jain, Arun Ross, and Salil Prabhakar, An introduction to biometric recognition, IEEE Transaction on Circuits and Systems for Video Technology, vol.14, no. 1.January 2004.

[2] C. Liu and H. Wechsler, Evolutionary pursuit and its application to face recognition, IEEE Transaction on Pattern Analysis and Machine Intelligence. vol. 22, June 2000, 570–582.

[3] M. Kirby and L. Sirovich, Application of the Karhunen-Loeve procedure for the characterization of human faces, IEEE Transaction on. Pattern Analysis and Machine Intelligence, vol. 12, no. 1, 1990, 103–108.

[4] M. Turk and Alex Pentland, Eigenfaces for recognition, Journal of Cognitive Neuroscience, vol. 13, no. 1, 1991, 71-86.

[5] Kourosh Jafari – Khouzani and Hamid Soltanian-Zadeh, Rotation invariant multiresolution texture analysis using Radon and Wavelet transform, IEEE transactions on signal processing, vol. 14, no. 6, June2005.

[6] E. Magli, G. Olmo and L. Lo Presti, Pattern recognition by means of the Radon transform and the continuous wavelet transform, Signal processing, vol. 73, Elsevier, 1999,277-289.

[7] Rama Chellappa, Charles L. Wilson, and Saad Sirohey, Human and machine Recognition of Faces: A Survey, Proceeding of IEEE, vol. 23, no. 5, 1995, 705-740.

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