Snowflake Logarithmic Metrics for Face Recognition in the Zernike Domain

Transcription

1 Global Journal of Pure and Applied Mathematics. ISSN Volume 3, Number 3 (27), pp Research India Publications Snowflake Logarithmic Metrics for Face Recognition in the Zernike Domain Ahmed J. Ali Faculty of Computer Science & Mathematics, University of Kufa, Najaf, Iraq. Zahir M. Hussain Faculty of Computer Science & Mathematics, University of Kufa, Najaf, Iraq. Professor, School of Engineering, Edith Cowan University, Joondalup, Australia. Mohammed S. Mechee Faculty of Computer Science & Mathematics, University of Kufa, Najaf, Iraq. Abstract Five power transform (a.k.a snowflake) distance metrics are constructed for the purpose of defining similarity measures for holistic face recognition. The power transform metrics are based on the logarithm of five distance metrics: Euclidean, City-Block, Soergel, Lorentzian and Minkowski metrics. The constructed power logarithmic metrics have been called, PL-City-Block, PL-Soergel, PL-Lorentzian and. Distance is considered in the Zernike domain of face images, a domain that contains a vector of Zernike moments for each face image. These distance metrics are further modified as similarity measures then normalized to be restricted over the range (,) so that a fair comparison could be made with the well-known image structural similarity measure () and Feature Similarity Index for Image Quality Assignment (). The purpose is discovering the similarity of a given face image with a face-database to check for best match. A measure for quality of recognition is proposed. This confidence is based on the difference between similarities given by the most likely match with that given by Corresponding author. zmhussain@ieee.org; z.hussain@ecu.edu.au

2 the second-likely confusing face. Simulation results show that the proposed distance measures have superior performance as compared to classical metrics, and the proposed similarity measures are all superior to the well-known and. AMS subject classification: Keywords: Computer vision, face recognition, Zernike moments, power transform, image similarity.. Introduction Face recognition has become a fundamental application after the advent of high performance computing. It is a multidisciplinary filed with many unresolved problems that involve several other fields especially mathematics, numerical analysis, statistics, computer science, and electronic engineering []-, [4]. One of the main streams in face recognition is to recognize a given face image in the sense of similarity with some image in a large face-database. This process involves a lot of unresolved difficulties [5]-, [7]. A powerful approach for image analysis and face recognition is through the use of image moments [8]-, [2], among which Zernike moments is the most important. Zernike moments has been proposed in 934 by Zernike [3], and the use of Zernike moment in image analysis was introduced by Teague [4]. Some researchers have proved Zernike moments to be robust under the presence of Gaussian noise. Due to the fact that Zernike moment functions have been designed using polar coordinates to represent image space, they have been used successfully in image recognition tasks which require rotation invariance. Zernike moments have some advantages over other moments like providing good feature representation of the image, providing more information about facial details, and reducing the dimension of the feature vector which improves computational complexity and accuracy of results [5, 6]. Despite the powerful features given by Zernike moments, they may not be decisive in recognizing a face image from a large face-database. However, this may be due to the inefficient exploitation of hidden features in Zernike moments. In this paper the distance features of Zernike moments are explored, where new similarity measures are designed to reveal the hidden powers of Zernike moments in face recognition. Power transform (a.k.a snowflake) metric is considered [7], from which five distance metrics are designed. Distance is measured in the Zernike domain of the face images. This domain is constructed using vectors of Zernike moments for face images. The power transform metrics are extensions for five well-known distance metrics: Euclidean, City-Block, Soergel, Lorentzian and Minkowski. Using the proposed definition for recognition confidence, numerical simulation of the proposed approach revealed excellent performance in face recognition with high confidence. The paper is organized as follows. In Section 2 some background theoretical basics of Zernike moments, metric distances, structural similarity and feature similarity are briefly reviewed. In Section 3 the proposed measures

3 Snowflake Logarithmic Metrics for Face Recognition 923 are designed, along with a definition of recognition confidence. In Section 4 simulation results are presented and compared to well-known methods. 2. Background In this section some related theoretical principles are explained. First, a brief on Zernike moments is presented, then the notions of metric space and metric distance are summarized. The structural distance between 2D objects is handled through the well-known structural similarity index (). 2.. Zernike Moments Zernike polynomials are a set of orthogonal polynomials defined over the interior of the unit circle. The two-dimensional Zernike moments of order p with repetition q of an image f with intensity function f(r,θ)are defined as follows [5, 8]: Z pq = p + π 2π R pq (r)e jqθ f(r,θ)rdrdθ, r (2.) where the radial polynomial R pq (r) is defined by the following form: R pq (r) = p q 2 k= ( )(p k)!r p 2k k!( p+ q 2 k)!( p q 2 k)! (2.2) Zernike moments have been designed using the polar coordinates (r, θ) R 2 inside the unit circle defined by {(r, θ) : r }. To approximate and compute these moments in discrete Cartesian form, a linear transformation of the image Cartesian coordinates (i, j) from the inside of the square {(i, j) : i, j =,,...,N } to the inside of the unit circle {(r, θ) : r } should be applied to get the following discrete Cartesian form: where r ij = x 2 i + y 2 i ; y i = Z pq = p + N N j= N i= 2j N ; x i = R pq (r ij )e jqθ f(i,j) (2.3) 2i N ; θ ij = tan ( y i x i ) (2.4) Table 2. shows low-order Zernike moments for different orders p and repetition q satisfying the conditions q p such that p q is an even integer. Features of an image f are represented by an n-dimensional vector of selected Zernike moments, V f (details in Section 3). In this work these moments are used to design similarity measures for face recognition; although they have other applications in face emotion recognition [9].

4 924 Ahmed J. Ali, Zahir M. Hussain, and Mohammed S. Mechee Table : Low-order Zernike moments p Dimensionality) Zernike moments (Z pq ) Z 2 Z 2 4 Z 2 Z Z 3 Z Z 4 Z 42 Z Z 5 Z 53 Z Z 6 Z 62 Z 64 Z Z 7 Z 73 Z 75 Z Z 8 Z 82 Z 84 Z 86 Z Z 9 Z 93 Z 95 Z 97 Z Z, Z,2 Z,4 Z,6 Z,8 Z, 2.2. Metric Distance In this subsection we consider five metrics (distance measurements) for the vectors in R n space. These metrics will be used later to design similarity measures Metric Space Let X be a set. A function d : X X R is called metric on X if, for all x,y,z X, the following properties hold:. d(x,y) (non-negativity); 2. d(x,y) = if and only if x = y (separation or self-identity axiom); 3. d(x,y) = d(y,x) (symmetry); 4. d(x,y) d(x,z) + d(z,y) (triangle inequality). A metric space (X, d) is a set X together with a metric d on X [7]. Important distance metrics considered in this study are Euclidean, Minkowski, City-Block, Soergel and Lorentzian. Let X and Y be vectors R n space, where X ={x,x 2,x 3,...,x n } and Y ={y,y 2,y 3,...,y n }. The above metrics are defined as follows [2, 2]: Classical Distance Measures The Euclidean distance between vectors X, Y is computed by: d Euc (X, Y ) = n (x i y i ) 2 (2.5) i=

5 Snowflake Logarithmic Metrics for Face Recognition 925 The Cityblock distance between two vectors X, Y vectors is computed by: d CB (X, Y ) = n x i y i (2.6) The Soergel distance between two vectors X, Y vectors is defined by the following form: ni= x i y i d Sg (X, Y ) = ni= (2.7) max(x i,y i ) The Lorentzian distance between two X, Y vectors is defined by the following form: d Lor (X, Y ) = i= n ln( + x i y i ) (2.8) i= The Minkowski distance between two vectors X, Y is defined by the following form: d MK (X, Y ) = n t (x i y i ) t ; t (2.9) i= The above measures can be used to investigate similarity between images through mean-squared error, however, this is a weak tool for image similarity (see [22]). A more powerful tool for similarity is explained below Image structural similarity measure () Wang et al. (24) [23] introduced a new image quality index named structural similarity index measure () based on the statistical structure of pixel intensities. The measure between two images X and Y is defined as follows: (X,Y) = (2µ xµ y + C )(2σ xy + C 2 ) (µ 2 x + µ2 y + C )(σ 2 x + σ 2 y + C (2.) 2) where µ x and µ y represent the local means of images X and Y, respectively, σ x and σ y represent the standard deviations, σ xy is the covariance of the two images, σ 2 x and σ 2 y represent the variances, respectively, while the constants C and C 2 are defined as C = (K L) 2 and C 2 = (K 2 L) 2 with K =.,K 2 =.3 and L = 255 [24] Feature Similarity Index for Image Quality Assignment () Zhang et al. (2) [25] proposed a novel image quality index called feature similarity index measure based on the phase congruency (PC) and the gradient magnitude (GM). The between images f (p) and f 2 (p) is defined as follows: p = S L(p)P C m (p) p PC (2.) m(p)

6 926 Ahmed J. Ali, Zahir M. Hussain, and Mohammed S. Mechee where p represents position in the image, PC m (p) = max(p C (p), P C 2 (p)) is the maximal phase congruency (P C) value at the position p between f (p) and f 2 (p), S L (p) = S PC (p) S G (p), S P C(p) is the similarity measure for PC (p) and PC 2 (p), S G (p) is the similarity measure for two gradient magnitude values at the position p between f (p) and f 2 (p); and is the whole image spatial domain [25, 26]. 3. Snowflake Logarithmic Distance Metrics In this section we will construct distance metrics based on the power transform metric (also known as snowflake metric). Power transform metric [7]: Given a metric space (X, d) and <α then, the power transform metric is a functional transform metric defined on on X by [d(x,y)] α. Theorem 3.. If (X, d) is a metric space, then (X, d) is also metric space with a new metric d(x,y) = ln( + d(x,y)). Proof. i. To show d(x,y) for all x,y X, since d is metric distance then, we have d(x,y) for all x,y X this implies to + d(x,y). Therefore, the new metric satisfies d(x,y) = ln( + d(x,y)). ii. d(x,y) = iffx = y; d(x,y) = ln( + d(x,y)) = d(x,y) = x = y. iii. d(x,y) = ln( + d(x,y)) = ln( + d(y,x)) = d(y,x). iv. To prove the triangle inequality, the monotone increasing property of the logarithmic function will be utilized as follows. Let x,y,z X, then d(x,z) = ln( + d(x,z)) ln( + d(x,y) + d(y,z)) ln( + d(x,y) + d(y,z) + d(x,y)d(y,z)) = ln(( + d(x,y))( + d(y,z)) = ln( + d(x,y)) + ln( + d(y,z)) = d(x,y) + d(y,z). Power logarithm metrics: Using the Theorem and definitions above, five metric distances are designed as follows. Power logarithm Euclidean distance: For <α, the distance between vectors X, Y is defined by: d PL Euc (X, Y ) = ln( + n (x i y i ) 2 ) i= α (3.2)

7 Snowflake Logarithmic Metrics for Face Recognition 927 Logarithm Cityblock distance: For <α, the PL-Cityblock distance between vectors X, Y is defined by: [ ( α n d PL CB (X, Y ) = ln + x i y i )] (3.3) Power logarithm Soergel distance: For <α, the PL-Soergel distance between two vectors X, Y vectors is defined by the following form: [ ( ni= α x i y i d PL Sg (X, Y ) = ln + ni= (3.4) max(x i,y i ))] Power logarithm Lorentzian distance: For < α, the PL-Lorentzian distance between two vectors X, Y is defined by the following form: [ ( α n d PL Lor (X, Y ) = ln + ln( + x i y i ))] (3.5) Power logarithm Minkowski distance: For <α, the distance between two X, Y vectors is defined by the following form: i= i= n d PL MK (X, Y ) = ln + t (x i y i ) t 3.. Normalized Distance Similarity in the Zernike Domain i= α ; t (3.6) Given a distance metric d between two n-dimensional feature vectors V x and V y, each vector is assumed here to contain a specific number of selected Zernike moments of the two images X and Y, the normalized similarity vector s is defined using doublenormalization of the distance vector d as follows: s = d o max(d o ) ; with d o = d max(d) (3.7) which has the property that s i s i s. The above normalization process is necessary for a fair comparison with and other similarity measures A Measure for Recognition Confidence A performance measure is an importance tool for comparison. Here a measure for the quality of recognition is designed based on the confidence provided by the face recognition approach. The confidence is defined as the complement of confusion between the recognized face and the second-likely face measured by how much near are there similarities with the test image.

8 928 Ahmed J. Ali, Zahir M. Hussain, and Mohammed S. Mechee Applying a similarity formula between a test image and a database of N face images will produce N similarity numbers ranging between and. Nearby numbers are confusing as they reduce confidence in recognition. Most important is the maximum similarity number, which gives the best match, and the second maximum number, which gives a measure of the amount of confusion. After normalization the maximum is always, while the difference m with the second maximum would vary according to the seriousness of confusion. See Figure. Now confidence in face recognition at level k of similarity with a specific test image is defined as follows: C k = where n k is the number of with k-level similarity s k >k. ( k) m n k (3.8) Figure : Similarity confidence. While testing a reference face image x versus a number of other faces, the confusion at decision (similarity) level k(k<) is defined as the number of faces giving similarities above k with the face x under test. 4. Implementation and Results 4.. Test environment The ORL database [27] contains faces of 4 people, each having different images. Some images were taken at different times. The facial expressions (e.g., open or closed eyes, smiling or non-smiling) and occlusion (glasses or no glasses) were included in some subjects. The tolerance for tilting and rotation is considered up to 2 degrees. Some variation in the scale of up to % is included. All images are grayscale and unified to the size of 2 92 pixels.

9 Snowflake Logarithmic Metrics for Face Recognition 929 The face94 database consist of 53 individuals; it contains 2 females, 3 male and 2 male staff images. The background of images is plane green. The images vary with intensity of expression, lighting and glasses [28]. The FEI face database has also been chosen: it contains a set of faces taken over the period from June 25 to March 26 at the Artificial Intelligence Laboratory of FEI in São Bernardo do Campo, São Paulo, Brazil. There are 2 people, with 4 face images for each individual, hence a total of 28 face images. The FEI face images are all colored, taken against a white background in an upright frontal position. A profile rotation of up to 8 degrees is included. Scale variation reaches %. The size of each face image is unified to pixels. The FEI database includes only faces of students and staff at FEI, whose ages range from 9 to 4 years, with distinct appearance, hairstyle, etc. There is equal numbers of males and females, each [29] Simulation Results The Face94, ORL and FEI databases contain 53, 4 and 2 face images, respectively. For the reference person, three images with three different poses have been used: two of them used as a test image, and one as a part of the training database (see Figure 3). In these experiments, best results are obtained with parameters α =. and t =.8 in Equations (2.9)-(3.5). Optimal results are obtained by using the following vector of Zernike features for an image f: V f ={ Z 2, Z 22, Z 3, Z 33, Z 4, Z 42, Z 44,..., Z 9, Z 93, Z 95, Z 97, Z 99 } (4.9) The implementation proceeds in three main parts; the diagram in Figure 2 explains the main steps. Figure 2: The proposed recognition process.

10 93 Ahmed J. Ali, Zahir M. Hussain, and Mohammed S. Mechee Figure 3: Examples of testing using face databases (a) face94 database (b) ORL database (c) FEI database.

11 Snowflake Logarithmic Metrics for Face Recognition 93.9 Person E Lor PL-Lor.9 Person E CBD PL-CBD (a) Lorentzian vs. PL-Lorentzian (b) Cityblock vs. PL-Cityblock.9 Person E Sg PL-Sg.9 Person E Euc PL-Euc (c) Soergel vs. PL-Soergel. (d) Euclidean vs.. Figure 4: Distance-based similarity metrics: Top left: Lorentzian metric vs. PL- Lorentzian; top right: Cityblock metric vs. PL-Cityblock; bottom left: Soergel metric versus PL-Soergel; bottom right: Euclidean metric versus. The first part presents a comparative study to test the performance of proposed distance metrics versus existing metrics. A person E is chosen as shown in Figure 3 to be a reference. Numerical results in Figure (4-5) show that the proposed metrics are more efficient than classical five distance metrics, where they give less confusion or more distance between the most likely face and the second-most likely face. The second part represents a comparative study on the performance of the proposed similarity metrics versus:

12 932 Ahmed J. Ali, Zahir M. Hussain, and Mohammed S. Mechee.9 Person E MK PL-MK Figure 5: Minkowski metric versus PL- Minkowski metric. i) the classical. ii) Feature Similarity Index Measure (). iii) Zernike moment with Euclidean distance, introduced by Singh et al. (2) [3]. The proposed metric measures are much more robust, with larger confidence. In addition, the metric is more efficient than other metrics in the sense of giving less confusion as shown in Figures (6 8). To test the confidence in recognition, the confidence measure given by Equation (3.8) has been implemented and applied. Figure 9 shows higher confidence for the proposed metrics as compared to other methods. Table 4.2 shows recognition rate for the proposed metrics versus other methods. Table 4.2 shows the time complexity of the proposed method versus other methods, where the laptop used here is hp EliteBook workstation 856w with Intel Core i7 272 QM CPU@2.2GHz (8 CPUs) and 8G RAM. Note that the actual time required for recognition using the proposed method can be much less than that in Table 4.2, as Zernike features for the database faces can be calculated offline. The third part represents a comparative study on the performance of Zernike MSE method (with measure based on features in Equation (4.2) under MSE) versus and under Gaussian noise. Peak Signal to Noise Ratio (PSNR) has been used in this test and defined as follows: PSNR = L2 P n (4.2) where p n is the Gaussian noise variance (power). A test image and a noisy version of the same image are shown in Fig., while Fig. shows the proposed method versus and under noise. It is clear that Zernike MSE can detect similarity at very

13 Snowflake Logarithmic Metrics for Face Recognition Person B.9 Person B Zernike[3] Zernike[3] (a) Person B (b) Person B2.9 Person B3.9 Person B Zernike[3] Zernike[3] (c) Person B3 (d) Person B4 Figure 6: Snowflake logarithmic similarity measures versus other methods using different faces from face94 database. low PSNR values, while and fail. For example, at the similarity level of.6, Zernike MSE works under PSNR = 2 db, while and cannot give such a level of similarity until PSNR is 8 db and 3 db, respectively. 5. Conclusion In this paper, five efficient similarity measures have been proposed for the purpose of holistic face recognition. Design of these measures is based on defining a measure of

14 934 Ahmed J. Ali, Zahir M. Hussain, and Mohammed S. Mechee.9 Person C.9 Person C Zernike[3] Zernike[3] (a) Person C (b) Person C Person C Zernike[3] Person C Zernike[3] (c) Person C3 (d) Person C4 Figure 7: Snowflake logarithmic similarity measures versus other methods using different faces from ORL face database. distance in the Zernike domain between a test image and a database of face images. It is shown that the choice of the relevant distance metric has a significant effect on the performance of the similarity metric. Classical distance metrics have been modified for this purpose using power transform (snowflake) metric. A measure for recognition confidence is also proposed. Various comparisons have been made using ORL, face94 and FEI face databases. Results show that the proposed similarity measures based on the proposed distance metrics outperform well-known existing methods like structural similarity measure () and Feature Similarity Index Measure () in recognition

15 Snowflake Logarithmic Metrics for Face Recognition Person E.9 Person E Zernike[3] Zernike[3] (a) Person E (b) Person E2.9 Person E3.9 Person E Zernike[3] Zernike[3] (c) Person E3 (d) Person E4 Figure 8: Snowflake logarithmic similarity measures versus other methods using different faces from FEI face database. rate and confidence. It is worth mentioning that the proposed similarity measure outperforms all other distance measures in giving larger distance between dissimilar vectors. Acknowledgements The Authors would like to thank the Ministry of Higher Education & Scientific Research (Iraq) and the School of Engineering, Edith Cowan University (Australia) for financial support of this project.

16 936 Ahmed J. Ali, Zahir M. Hussain, and Mohammed S. Mechee Confidence in Recognition Person E Zernike[3] Similarity Level, k Figure 9: Recognition confidence versus similarity level for various measures. Table 2: Recognition rate for the proposed method versus other methods. Method Recognition rate% ORL FEI database Face94 database Zemike moments[3] Proposed method with Proposed method with PL-Lorentzian Proposed method with PL-Cityblock Proposed method with Proposed method with PL-Soergel Table 3: Running time for the proposed method versus other methods. Method Running time (seconds) ORL database FEI database Face Zemike moments[3] Proposed method

17 Snowflake Logarithmic Metrics for Face Recognition 937 Figure : Original Image, Noisy Image, PSNR (db) = 2..8 Similarity Measures: A Comparison Zernike MSE PSNR (db) Figure : Zernike MSE measure versus classical similarity measures and under Gaussian noise.

18 938 Ahmed J. Ali, Zahir M. Hussain, and Mohammed S. Mechee References [] D. N. Parmar, B. B. Mehta, Face recognition methods and applications, International Journal of Computer Technology and Applications (IJCTA) 4 () (23). [2] L. G. Vu, A. Alsadoon, P. W. C. Prasad, A.Monem, A. Elchouemi, Face recognition template in photo indexing: A proposal of hybrid principal component analysis and triangular approach (pcaata), IEEE Southwest Symposium on Image Analysis and Interpretation (SSIAI) (26). [3] J. Nagi, S. K. Ahmed, F. Nagi, A matlab based face recognition system using image processing and neural networks, International Colloquium on Signal Processing and its Applications (28). [4] M. Alwakee, Z. Shaaban, Face recognition based on haar wavelet transform and principal component analysis via levenberg-marquardt back-propagation neural network, European Journal of Scientific Research 42 () (2). [5] R. Jafri, H. R. Arabnia, A survey of face recognition techniques, Journal of Information Processing Systems 5 (2) (29). [6] G. Sang, J. Li, Pose-invariant face recognition via rgb-d images, Computational Intelligence and Neuroscience (26). [7] S. D. Kakade, A review paper on face recognition techniques, International Journal for Research in Engineering Application & Management (IJREAM) (26). [8] C. H. The, R. T. Chin, On image analysis by the methods of moments, IEEE Transactions on Pattern Analysis and Machine Intelligence (4) (988). [9] A. Fathi, P. Alirezazadeh, A new global-gabor-zernike feature descriptor and its application to face recognition, J. Visual Communication and Image Representation (26). [] S. M. Imran, M. Rahman, D. Hatzinakos, Differential components of discriminative 2d gaussian-hermite moments for recognition of facial expressions, Pattern Recognition (26). [] S. M. M. Rahman, T. Howlader, D. Hatzinakos, On the selection of 2d krawtchouk moments for face recognition, Pattern Recognition (26). [2] F. Hajati, A. A. Raie, Y. Gao, 2.5d face recognition using patch geodesic moments, Pattern Recognition (22). [3] F. Zernike, Beugunstheorie des schneidenverfahrens und seiner verbesserten form, der phasenkonstrastmethode, Physica (934). [4] M. Teague, Image analysis via the general theory of moments, J. Opt. Soc. Amer. 7 (8) (98). [5] A. M. Hashim, Z. M. Hussian, Local and semi-global feature-correlative techniques for face recognition, Journal of Advanced Computer Science and Applications 5 (8) (24).

19 Snowflake Logarithmic Metrics for Face Recognition 939 [6] S. M. Lajevardi, Z. M. Hussain, Zernike moments for facial expression recognition, Proceedings of the 29 International Conference on Communication, Computer and Power (ICCCP 9) (29). [7] M. M. Deza, E. Deza, Encyclopaedia of distances, Springer (29). [8] K. Sharma, G. Joshi, M. Dutta, Analysis of shape and orientation recognition capability of complex zernike moments for signed gestures, IEEE International Conference on Signal Processing and Integrated Networks (SPIN) (25). [9] S. M. Lajevardi, Z. M. Hussian, Higher order orthogonal moments for facial expression recognition, Digital Signal Processing 2 (6) (2). [2] S. H. Cha, Comprehensive survey on distance/ similarity measures between probability density functions, International Journal of Mathematical Models and Methods in Applied Sciences (4) (27). [2] C.-C. Chen, H.-T. Chu, Similarity measurement between images, IEEE Proceedings of the 29th Annual International Computer Software and Applications Conference (COMPSAC 5) (25). [22] Z. Wang, A. Bovik, Mean squared error: Love it or leave it? a new look at signal fidelity measures, IEEE Signal Processing Magazine 26 () (29). [23] Z. Wang, A. Bovik, H. Sheikh, E. Simoncelli, Image quality assessment: From error visibility to structural similarity, IEEE Transactions on Image Processing 3 (4) (24). [24] D. Dosselmann, X. D. Yang, A comprehensive assessment of the structural similarity index 5 () (2). [25] L. Zhang, Zhang, L. X. Mou, D. Zhang, Fsim: A feature similarity index for image quality assessment, IEEE Transactions on Image Processing 2 (8) (2). [26] A. Li, X. She, Q. Sun, Color image quality assessment combining saliency and fsim, International Conference on Digital Image Processing (23). [27] AT & T Laboratories Cambridge, AT & T face database (formerly the ORL Database of Faces ), facedatabase.html (22). [28] L. Spacek, University of essex, department of computer science, essex.ac.uk/mv/allfaces/faces94.html. [29] Fei face database, image processing laboratory, department of electrical engineering, centro universitario da fei, sao bernardo do campo, sao paulo, brazil, cet/facedatabase.html. [3] C. Singh, N. Mittal, E. Walia, Face recognition using zernike and complex zernike moment features, Pattern Recognition and Image Analysis 2 () (2).