Face recognition using complex wavelet moments

Optics & Laser Technology 47 (2013) 256–267

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Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec

Face recognition using complex wavelet moments Chandan Singh n, Ali Mohammed Sahan Department of Computer Science, Punjabi University, Patiala 147002, Punjab, India

a r t i c l e i n f o

a b s t r a c t

Article history: Received 27 May 2012 Received in revised form 20 August 2012 Accepted 5 September 2012 Available online 12 October 2012

The wavelet moments are very useful image descriptors which contain both global and local characteristics of an image. Its usefulness is further characterized by rotation invariant property of its magnitude. The phase information is, however, left out because it changes with image rotation. In this paper, we incorporate phase information and use both the real and imaginary components of wavelet moments to describe an image and develop a similarity measure which is invariant under image rotation. The proposed framework is applied to face recognition. Extensive experimental results are provided to demonstrate the enhanced performance of the proposed framework as compared to the magnitude only framework. The results are also compared with many other state-of-the-art techniques used for face recognition. & 2012 Elsevier Ltd. All rights reserved.

Keywords: Face recognition Wavelet moments Complex wavelet moments

1. Introduction Since more than two decades face recognition problem has been receiving more attention due to its complexity and its wide range of applications in many fields [1–2] such as human– computer intelligent interaction, digital library, control access, real time matching of surveillance video images, building or office security, criminal identification and authentication in secure systems like computers or bank teller machines. Face recognition problem remains a difficult and complex pattern recognition task since the human face image contains many variations such as facial expression, pose, illumination, and aging. There are three stages in face recognition problem [3], namely, face segmentation from an image, feature extraction and classification. The stage of feature extraction is very important as it ultimately determines the performance of a recognition system. Existing face recognition methods rely on two broad approaches: global feature extraction methods and local feature extraction methods. The global feature extraction methods extract the features from the whole image and each component of the feature vector represents the complete image. Thus they provide the holistic view of the face images. Their major advantages are that they are less sensitive to image noise. However, they are affected by local variations in the image such as pose and expression. The local feature expression methods represent the local structures such as eyes, nose and mouth. They also represent the facial expression in a better way. However, they are sensitive to image noise, unpredictability of face appearance and environmental conditions [4]. The global

n

Corresponding author. E-mail address: [email protected] (C. Singh).

0030-3992/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.optlastec.2012.09.004

based methods are further categorized into two groups: the sub space based methods and the frequency based methods. The subspace based methods have been the dominant successful methods and many existing practical face recognition systems use them as major feature extractors. These methods represent images as a linear combination of basis images and need a training process to derive the basis images. Although, they are very effective, they are computation intensive and many classification processes employing these methods require retraining once new face images are added in the image databases. In the category of subspace based methods, some of the popular and most frequently used methods are principal component analysis (PCA), Fisher’s linear discriminant (FLD), two-dimensional PCA (2DPCA), two-dimensional twodimensional PCA (2D2PCA) [5–9]. In the second category of methods, face images are transformed to frequency domain and low frequency components are used to represent them. The high frequency components are discarded as they are affected by image noise. Fourier transform [10–11] and discrete cosine transform [12–13] are well known transform based method. The major problems with these methods are that they are not invariant under geometric transformation. To deal with in-plane rotation of face images, moment invariants such as Zernike moments (ZMs) [14–15] and pseudo-Zernike moments (PZMs) [16–17] are used as global methods in face recognition. The local feature extraction methods can be classified into two categories: the sparse descriptors and the dense descriptors. The sparse descriptors initially divided face image into patches and then determine its invariant features. The scale invariant features transform (SIFT) introduced by Lowe [18] and its variant discriminative SIFT (D-SIFT), applied by Soyel and Demirel [19] in facial expression recognition, is such a descriptor. In face recognition technology, Gabor wavelet is one of the most frequently used

C. Singh, A.M. Sahan / Optics & Laser Technology 47 (2013) 256–267

and successful local image descriptors. It analyzes spatial frequency distribution of the intensity variations on different scales, orientations and positions. Despite its excellent performance in face recognition, Gabor based methods suffer from a huge computational load [20]. Among the dense descriptors, local binary pattern (LBP) and its variants are the most widely used approaches in representing local features in face recognition [21–23]. A recent survey on LBP and its application to facial image analysis is presented by Huang et al. [24]. One of the most important properties of LBPs is its tolerance to illumination change. Also, the computational simplicity of the operator is a significant advantage over other approaches. Its disadvantages are that it is sensitive to noise, since the operator thresholds exactly at the value of central pixel, and its small 3  3 neighborhoods cannot capture dominant features with large-scale structures. In complex applications, like face recognition, it is observed that one category of features, global or local, cannot effectively represent the entire face information. A combination of complementary feature sets, as in the case of global and local features, is needed to capture both the holistic and the local fine details of facial images. Thus finding and combining the complementary feature sets have become an active research area in face recognition. Most of the works belonging to this category use a global descriptor and a local descriptor and the fusion of these features is performed either at the classification stage or at the score level. A survey of such methods is given by Su et al. [25] who have proposed Fourier transform as a global descriptor and Gabor wavelets as a local descriptor. Combining the features from more than one modality becomes one of the major issues in deriving final score from heterogeneous methods. Normally, equal weights are provided as a simple solution in deriving the final result. An alternative solution to this problem is to use a hybrid descriptor which combines the traits of both the global and local changes in faces images. Wavelet moments (WMs) proposed by Shen and Ip [26] is one of such descriptors. In their extensive experiments on character recognition they observed the performance of WMs to be far superior than ZMs. They further observed that WMs have the ability to differentiate between two similar images with subtle differences. Since WMs combine the characteristics of multi-resolution analysis and moment invariant traits, it has been employed in many applications, for instance, image watermarking [27–29], PET image reconstruction [30], image recognition [31–33], character recognition [34–35], steganalysis [36], gait recognition [37], hand posture classification [38]. In audio image watermarking, a new algorithm is presented by Wang et al. [29] based on WMs synchronization code, which provided good auditory quality and reasonable resistance against most common audio signal processing attacks. The performance analysis tests reveal that the results of WMs are better compared PZMs based method. Rodtook and Makhnov [39] performed experiments for the recognition of various patterns and observed better performance of WMs invariants in comparison to orthogonal radial moments invariants, especially, under noisy condition. A substantial improvement in the accuracy of Farsi character recognition was observed by combining features from ZMs and WMs [35]. Fourier-wavelet moments are used to achieve good quality reconstructed images in positron emission tomography (PET) [30]. In video based gait recognition [37], it is observed that the combined features of fractal scale and WMs improve the results of gait recognition. The proposed method is computationally simple and improves the flexibility of wavelet moments. The WMs have a distinct characteristics of representing subtle variations in images. These characteristics of WMs coupled with features of ZMs which represent global variations in the images, is exploited by Sriboonruang et al. [38] in hand posture classification. The combined

257

features along with the fuzzy classification algorithm provide good discriminatory power for seemingly similar hand postures. In face image analysis, WMs were successfully applied for facial expression recognition by Zhi and Ruan [40]. In order to improve the performance of the system, AdaBboost was used to select most effective features. The performance of WMs in face recognition is significantly enhanced when combined with Delaunay method based on Voronoi graph along with the Hu’s moment invariants [41]. Sahan [42] used WMs and wavelet transform to combine the features of the two image descriptors to enhance the performance of face recognition system. The above discussion leads to the conclusion that WMs are among the most prominent image descriptors which are used in numerous image processing applications. Perhaps it is the only image descriptor which embodies the traits of both global and local characteristics of image and whose magnitude is invariant to image rotation. They are different from radial moments (RMs) invariants because RMs do not incorporate the local changes in image. Moreover, many RMs, for instance, ZMs, PZMs, and Orthogonal Fourier-Mellin moments (OFMMs), are computation intensive as their kernel functions consist of polynomials of the same degree as the order of the moment. The computation complexity of ZMs and PZMs is of cubic order with respect to the order of moments. On the other hand, the computation complexity of WMs increases linearly with the increase of the order of the moment. In addition RMs are unstable for high orders, whereas the numerical stability of the WMs remains unaffected, therefore, the size of feature set of WMs can become large, providing a large number of features. The WMs are complex numbers. The magnitude of the WMs is rotation invariant. Thus, if an image is rotated, then the magnitude of the WMs does not change, whereas the phase angle undergoes a change. There exists a relationship between the phase angles of the non rotated and the rotated images. All applications involving WMs features including the original work on WMs by [26], presented in the literature so far, use the magnitude of the moments but avoid the phase relationship for the comparison purpose. It is observed recently in pattern recognition problems using ZMs features that the phase component also carries equally significant information as the magnitude component does [43,44]. As a consequence of this, there is an increasing trend in the use of phase components along with the magnitude of RMs in pattern recognition problem, including the face recognition application [45,46]. In [43], the complex ZMs are used as features by estimating rotation angle between the query and the database images and after making phase correction by incorporating rotation angle, the magnitude of the ZMs are compared. The method is fine but it requires the estimation of the rotation angle which may not turn out to be correct because the rotation angle is estimated by one moment. In [44], only the phase components of the moments are used as features not their magnitude. Therefore, the combined advantages of magnitude and phase are not realized. The phase information using Gabor wavelets is successfully used by Zhang et al. [47] in face recognition. It is observed by them that the histogram of phase patterns improve the face recognition performance significantly on various databases. Motivated by these observations, in this paper, we use the complex moments in face recognition as features called complex wavelet moments (CWMs). Thus the characteristics of CWMs of embedding both the global and the local features simultaneously are exploited not only in its magnitude but also in its phase. The proposed method assumes that the query image (test image) is a rotated version of the database image (training image) or vice-versa and then uses phase relationship between the query image and the database image to incorporate correction in the moments of one of the two images. If the images are the

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same, that is, one of the two images is a rotated version of another, then the real and imaginary parts of the WMs of the two images will be the same. On the other hand, if the two images are different, then these components will be different. L1-norm based similarity measure is used to measure the similarity between images. The proposed similarity measure combines the contribution of WMs magnitude and phase in a homogenous manner. Detail experimental analysis supports the enhanced performance of the hybrid system. The rest of the paper is organized as follows. An overview of the WMs is discussed in Section 2. The proposed system of deriving the features based on the complex wavelet moments is presented in Section 3. In this section, a method for the fast computation of WMs is also discussed. The database construction is explained in Section 4. Detail of experimental results showing the improvement in performance of the proposed system is given in Section 5. The paper is concluded in Section 6.

Thus the wavelet function defined by Eq. (2) assumes the form

cm,n ðrÞ ¼ 2m=2 cð2m r0:5nÞ

ð7Þ

In digital image processing the image function f(r,y) is discrete and defined in a rectangular domain. A pixel is represented by (i,k) with ith row and kth column. If the size of an image is N  N pixels, then we perform a mapping from the domain [0,N  1]  [0,N  1] to the unit circle: D ¼ fðxi ,yk Þ9x2i þ y2k r1g, with xi ¼

2iþ 1N 2kþ 1N ; yk ¼ ; i, k ¼ 0, 1, :::, N1, N N

ð8Þ

Such a choice of the coordinates enables us to perform the computation of moments in Cartesian coordinates in unit disk. The zeroth order approximation of Eq. (2) is given by Mm,n,q ¼

N 1 X

N 1 X

i¼0

k¼0

f ði,kÞcm,n ðxi ,yk Þejqyik Dxi Dyk ,

x2i þ y2k r1

where Dxi ¼ Dyk ¼ 2=N, yik ¼ tan1 ðyk =xi Þ and r ¼

ð9Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2i þ y2k .

2. Wavelet moments WMs are derived from the general moment M of a continuous function f(r,y) in polar coordinates defined over a unit disk Z 2p Z 1  n f ðr, yÞ Fðr, yÞ rdrdy, ð1Þ M¼ 0

0

where F(r,y) is called the kernel function and ‘*’ denoted the complex conjugate. In rotation invariant moments, the kernel function F(r,y) ¼R(r)w(y), i.e. the kernel function consists of the jqy radial where pffiffiffiffiffiffiffiand angular functions and normally w(y) ¼e j ¼ 1 and q is usually an integer which is called the angular order. Such a choice of w(y) makes the magnitude of the moments rotation invariant. In the case of the wavelet moments, Shen and Ip [26] proposed wavelet basis functions given by   1 rb RðrÞ ¼ ca,b ðrÞ ¼ pffiffiffi c , ð2Þ a a where a is the scale parameter (or the scale index) and b the shifting (translation parameter). The function c(r) is the mother wavelet. Let the wavelet moment be defined by Mm,n,q, then Z 2p Z 1 f ðr, yÞcm,n ðrÞejqy rdrdy: ð3Þ M m,n,q ¼ 0

0

where p ¼3, s¼ 0.697066, f0 ¼0.409177 and s2w ¼ 0:561145. The scale and translation parameters, a and b, are such that aAR þ and bAR where R þ and R denote the set of positive real numbers and the set of all real numbers. Since we restrict our domain of moment computation within unit disk (r r1), the values of a and b are normally taken to be as follows: ð5Þ

and b ¼ 0:5:n:0:5m , n ¼ 0, 1, :::, 2m þ 1 :

The WMs are complex numbers. The existing applications of WMs use its magnitude in pattern recognition problem for rotation invariance features. It is because of the fact that if Mm,n,q represents the WMs of an image, then it can be proved that the WMs of the image rotated by an angle a denoted by M rm,n,q , are given by jqa

Mrm,n,q ¼ M m,n,q e

:

ð10Þ

9Mrm,n,q 9 ¼

9M m,n,q 9: Therefore, the existing methods use Thus, the equality relationship of magnitudes to test the similarity/ dissimilarity of two images. The important information contained in the phase angles of WMs is lost. In some applications, the phase information of a signal is more informative than the magnitude information [44]. In the proposed method, we consider both magnitude and phase angle in the feature description using WMs. The moments Mm,n,q can be expressed as M m,n,q ¼ M Rm,n,q þjM Im,n,q , where M Rm,n,q and MIm,n,q represent the real and imaginary parts of Mm,n,q, respectively. Thus Mm,n,q ¼ 9M m,n,q 9ejfm,n,q ,

ð11Þ

where

The selection of the mother wavelet function c(r) is an important task because the effectiveness of the features is heavily dependent on it. The cubic B-spline wavelet [26] is a preferred choice which is optimally localized in space-frequency domain and close to the forms of Li’s (or Zernike’s) polynomial moments. The mother wavelet c(r) of the cubic B-spline in Gaussian approximation form is [48] ! 4sp þ 1 ð2r1Þ2 cðrÞ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sw cosð2pf 0 ð2r1ÞÞ  exp  2 , ð4Þ 2sw ðn þ1Þ 2p ðp þ 1Þ

a ¼ 0:5m , m ¼ 0, 1, 2, 3,

3. The proposed method based on CWMs

ð6Þ

h i1=2 Mm,n,q ¼ ðM Rm,n,q Þ2 þ ðM Im,n,q Þ2 ,

ð12Þ

and M Im,n,q

fm,n,q ¼ tan1

M Rm,n,q

! :

ð13Þ

Substituting Eq. (11) in Eq. (10), we get r 9M rm,n,q 9ejfm,n,q

¼ 9M m,n,q 9ejðjm,n,q qaÞ ,

ð14Þ

where the superscript ‘‘r’’ denotes the values for the rotated images which will be henceforth used for the said purpose. Therefore, the phase relationship is expressed by

frm,n,q ¼ fm,n,q qa,

ð15Þ

or, r

qa ¼ fm,n,q fm,n,q :

ð16Þ

The phase relationship between two images expressed by Eq. (16) is useful in determining similarity between two images. If we compare two images P and Q, and if the two images P Q are the same, then fm,n,q ¼ fm,n,q , yielding qa ¼0. If the image Q is

C. Singh, A.M. Sahan / Optics & Laser Technology 47 (2013) 256–267

a rotated version of P, then we can determine the value of qa using Eq. (16) and correct the real and imaginary components of the WMs of the image Q using the following equations: C M Qm,n,q ¼ MQm,n,q ejqa ,

ð17Þ

where the superscript ‘‘QC’’ denotes the corrected value of M Qm,n,q . Rewriting Eq. (17), we get QC Q Q RðM QC m,n,q Þ þ jIðM m,n,q Þ ¼ ½RðM m,n,q Þ þ jIðM m,n,q Þ½cosðqaÞ þjsinðqaÞ,

ð18Þ where R(U) and I(U) denote the real and imaginary parts of a real number. After separating the real and imaginary parts, we get Q RðM QC m,n,q Þ ¼ RðM m,n,q Þcosðq

ÞIðM Qm,n,q Þsinðq

a

aÞ,

Q Q IðM QC m,n,q Þ ¼ IðM m,n,q ÞcosðqaÞ þ RðM m,n,q ÞsinðqaÞ:

Let RðM Pm,n,q Þ, and IðM Pm,n,q Þ denote the real and imaginary parts of WMs for the image P. If Q is a rotated version of P, then P QC P RðM QC m,n,q Þ ¼ RðM m,n,q Þ, and IðM m,n,q Þ ¼ IðM m,n,q Þ,

and

C IðM Qm,n,q Þ a IðMPm,n,q Þ:

ð22Þ

The similarity between two images P and Q is determined by a suitable distance measure. Normally, two distance measures, L1-norm and L2-norm, are most common. In the proposed framework, we use L1-norm, also called the City Block or Manhattan distance measure. The L2-norm which is the Euclidean distance measure is not used in the proposed framework, because it is observed that L2-norm cancels the effect of phase angle as it turns out to be the same as the Euclidean distance between the magnitudes of the two images. Which can be verified as follows. Let dE denote the Euclidean distance between the images P and Q, then 2

dE ¼

m max n max q max X X X



RðM Pm,n,q ÞRðM QC m,n,q Þ

2

 2  C : þ IðM Pm,n,q ÞIðM Qm,n,q Þ

m¼0n¼0q¼0

ð23Þ After simplifying, we observe that 2

dE ¼

m max n max q max X X X m¼0n¼0q¼0

2  P M m,n,q  M Qm,n,q ,

ð24Þ

which is the same as the L2-norm of the magnitudes of the WMs of the images P and Q. Therefore, we use the L1-norm measure which includes the contribution to the distance from the real and imaginary parts of the WMs and thus preserves the contribution of both the magnitude and the phase. The L1-norm distance measure, denoted by dC, is given by dC ¼

m max n max q max X X X m¼0n¼0q¼0

Step 1: Find the WMs of the images P and Q which are denoted by M Pm,n,q and M Qm,n,q , respectively. It is computationally more efficient to compute the WMs of the database images offline. P Q Step 2: Find the phase angles fm,n,q and fm,n,q ,

fPm,n,q

1

¼ tan

IðMPm,n,q Þ

  C C Þ þ IðM Pm,n,q ÞIðM Qm,n,q Þ : RðM Pm,n,q ÞRðM Qm,n,q ð25Þ

3.1. The overall algorithm The above procedure is explained in algorithmic form in order to facilitate the process of implementation of the proposed framework. Let P and Q denote the test and database images,

! P

RðMPm,n,q Þ

, fm,n,q A ½0,2pÞ,

ð26Þ

and

fQm,n,q ¼ tan1

IðMQm,n,q Þ

!

RðMQm,n,q Þ

Q

, fm,n,q A ½0,2pÞ:

ð27Þ

Step 3: Find qa, P

ð21Þ

and if P and Q are dissimilar images, then P RðM QC m,n,q Þ a RðM m,n,q Þ

respectively, then the following steps are used to compute the distance between two images.

ð19Þ ð20Þ

259

Q

qa ¼ ðfm,n,q fm,n,q Þ, qa A ½0,2pÞ:

ð28Þ

Step 4: Derive the phase corrected real and imaginary components C C RðM Qm,n,q Þ and IðM Qm,n,q Þ using Eqs. (19) and (20), respectively. Step 5: Find L1-norm m  max n max q max  X X X C C dC ¼ Þ þ IðM Pm,n,q ÞIðM Qm,n,q Þ : RðM Pm,n,q ÞRðM Qm,n,q m¼0n¼0q¼0

ð29Þ The overall algorithm is depicted graphically in Fig. 1. The WMs of the database (training) images M Qm,n,q are computed offline and saved. The features of the test (query) image MPm,n,q are computed online. The phase corrected angle qa is obtained from the phase angles of the database image and the test image using Eq. (28). C The phase corrected moments M Qm,n,q is obtained from Eqs. (19) and (20). If the test and training images are the same then the real C and imaginary components of MPm,n,q and M Qm,n,q must be identical. However, due to discretization error, there can be same difference in their values. This difference is measured using L1-norm and it is represented by di in the figure for the ith database image. If the two images are different then the magnitude of di will be large. Therefore, the database image for which di is the minimum ðdmin Þ will be the image similar to the test image as recognized by the proposed system. The possibility of recognizing an incorrect image from the database is reduced by specifying a parameter dmax which acts as an upper limit for dmin so that if dmin 4dmax , then no database image similar to the test image will be identified.

3.2. Fast computation of wavelet moments One of the major issues in face recognition problem is the computational complexity of the method [20]. Most of the prominent methods including the subspace based method and Gabor based methods suffer from heavy computational load. Fortunately, the wavelet based methods are very efficient in time computation. However, in real time applications fast computation of WMs is required. The computation complexity of WMs is O(N2L) which is still very high. Here L is the total number of WMs. This order is required because the moments are to be computed at N2 locations of image pixels at m scales and for each scale the spatial positions are n ¼0, 1, 2,y 2m þ 1. We can achieve a significant improvement in speed by exploring the eight-way symmetry of the radial kernel function cm,n(r) and eight-way

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Fig. 1. Block diagram of the proposed method.

symmetry/anti-symmetry of the angular function e  jqy, as shown by Singh and Kaur [49], for polar harmonic transforms. The procedure given in [49] is also applicable to WMs which provides significant improvement in speed as the radial kernel cm,n(r) is required to be evaluated only at N(Nþ2)/8 locations instead of N2 locations. The angular functions e  jqy are also required to be evaluated at N(Nþ2)/ 8 locations with fast recursive algorithms applicable for the trigonometric functions. It is observed that the fast method reduces feature extraction time by a factor of 8 approximately. Later, in the experimental section we provide the execution time required for feature extraction for training and testing.

4. Databases used for experiments The performance of the proposed method is evaluated on four different types of face databases that are discussed below: a) Japanese Female Facial Expression (JAFFE) face database: Contains 213 images of seven different types of facial expression such as surprise, fear, disgust, anger, happiness, sadness and neutral, for

ten Japanese female models. Each female has two to four examples for each facial expression. The size of each image is 256  256 pixels. b) Facial Recognition Technology (FERET) face database: Contains 14051 eight-bit gray scale 256  384 pixel images from 1196 individuals. Each subject has images with facial expression, illumination, and pose variations. FERET evaluation protocol divides database into four probe sets, namely, fafb, fafc, duplicate I, and duplicate II. The images in fafb set are with facial expression variation, fafc set contains images with illumination variations, and the images in dupI and dupII sets represent aging effects. c) UMIST face database: Consists of 564 frontal and profile images for twenty individuals. The size of each image is 220  220 pixels. The poses of each individual start from right profile to frontal, i.e.  901 to 01. d) Olivetti Research Laboratory (ORL) face database: It consists of 400 images of 40 human subjects, and each subject has 10 different facial view representations. The size of each image is 92  112 pixels with 256 Gy levels. The image of each human subject varies in facial expression, position, pose, illumination, detail, and scale.

C. Singh, A.M. Sahan / Optics & Laser Technology 47 (2013) 256–267

The images in above databases are of different sizes. In order to facilitate the experimentation, we convert all images to the size 64  64pixels. This also reduces the computation time for carrying out the experiments. A few images from above databases are shown in Fig. 2.

5. Experimental results The performance of the proposed system is compared with WMs magnitude based approach. In addition, the performance of the proposed system is also compared with the state-of-the-art

261

approaches for face recognition [46,47,50–52]. We implement two algorithms, viz WMs magnitude (MWMs), and CWMs. These algorithms are referred to as Algorithm A and Algorithm B, respectively. These algorithms are implemented in Microsoft’s Visual Cþþ 6.0 under Windows environment on a PC with 3.0 GHZ CPU and 2 GB RAM. Before we present the results for the recognition performance of the proposed system and compare the results with other methods, we demonstrate the rotation invariance property of the system. A total of 136 WMs, which are normally used in pattern recognition problems [26], are selected for all experiments with m¼0, 1, 2, 3, n ¼0, 1,..., 2m þ 1, and q¼0, 1, 2, 3. The

Fig. 2. A few face images from different databases: First and second rows (UMIST), third and fourth rows (ORL), fifth and sixth rows (JAFFE), seventh and eighth rows (FERET).

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proposed CWMs use 238 features as each moment consists of two parts except for the moment with q¼0.

the class of the test image. The second database image belongs to a different class. The computed WMs for the test and the database images, before and after phase correction, are shown in Figs. 10–13, respectively. The distance dC between the test image and the

5.1. Invariance property of the proposed system In order to demonstrate the invariance property of the proposed system, we carry out two sets of experiments. The first set of experiments consists of a face image (test image) and its five versions (database images) obtained by rotating the test image by 151, 331, 451, 671, and 801 as shown in Fig. 3. The WMs are computed for the test image and the database images and the WMs of the database images are corrected according to Eqs. (19) and (20). Figs. 4–7 show values of the real and imaginary components of twenty WMs before and after phase correction, respectively. These twenty moments are: WM0,0,1, WM0,0,2, WM0,0,3, WM0,1,1, WM0,1,2, WM0,1,3, WM0,2,1, WM0,2,2, WM0,2,3, WM1,0,1, WM1,0,2, WM1,0,3, WM1,1,1, WM1,1,2, WM1,1,3, WM1,2,1,WM1,2,2, WM1,2,3, WM1,3,1, and WM1,3,2 which are numbered from 1 to 20 and denoted by the letter L. The L1-norm distance dC between the test image and database images, before and after correcting the phase components for all 238 coefficients, are shown in Fig. 8. It is observed from this figure that the proposed method provides very small values of dC for images belonging to the same class after correcting the phase components. The second set of the experiments comprises a test image given in Fig. 9(a) and two database images shown in Fig. 9(b) which are rotated version of their unrotated counterparts by 331. Out of the two database images, the first image belongs to

Fig. 5. Imaginary components of WMs of the test image and database images before phase correction.

0°

15°

33°

45°

67°

80°

Fig. 3. (a) Test image, and (b) five database images which are rotated versions of the test image.

Fig. 4. Real components of WMs of the test and database images before phase correction.

Fig. 6. Real components of WMs for the test image and database images after phase correction.

Fig. 7. Imaginary components of WMs for the test image and database images after phase correction.

C. Singh, A.M. Sahan / Optics & Laser Technology 47 (2013) 256–267

263

Fig. 11. Imaginary components of WMs for the test and two database images before phase correction. Fig. 8. L1-norm distance between test and database images before and after phase correction (all database images belong to the same class of test image).

0°

33°

33° Fig. 12. Real components of WMs for the test and two database images after phase correction.

Fig. 9. (a) Test image, and (b) two database images. The first database image is rotated versions of the test image. The second database image does not belong to the class of test image.

Fig. 13. Imaginary components of WMs for the test and two database images after phase correction.

Fig. 10. Real components of WMs for the test and two database images before phase correction.

database images are shown in Fig. 14. It is observed that the real and imaginary components of WMs of the test image and the database image belonging to the class of the test image become very close after making phase correction. On the other hand, the WMs of the test image and the database image which belongs to a different class, are significantly different. This fact is further elaborated when we compute L1-norm between the test image and the database images which are shown in Fig. 14. This analysis shows that the proposed method of combining the magnitude and the phase angle of WMs is very effective in comparing face images. It is also seen

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Table 2 Recognition rates using Algorithm B, GWþ LBP and LG þPCA þLDA on JAFFE database.

Fig. 14. L1-norm distance values between the test and two database images before and after phase correction.

Table 1 Recognition rates and time taken by Algorithm A and Algorithm B on JAFFE database. Method

Recognition rate (%)

Feature extraction Feature extraction time (in s) for training time (in s) for testing stage stage

MWMs (Algorithm A) CWMs (Algorithm B, proposed method)

98.6

16.4

33.3

99.9

2.1

4.4

that the magnitude and phase of WMs can be considered as single descriptor instead of taking them separately and then using two different distance measures for them separately. 5.2. Performance evaluation of proposed approach under facial expression variation Experiments on face images with different facial expressions are conducted on JAFFE face database to evaluate the performance of both Algorithm A and Algorithm B under the condition of facial expression variation. In these experiments, we have randomly selected one face image from each of basic seven expression groups (anger, disgust, happiness, neutral, fear, sadness, surprise) of each subject for training and remaining all for testing i.e. the total number of training face images is 70 while it is 143 for testing out of a total of 213 images. The results of recognition performance along with the time taken for feature extraction are presented in Table 1. In moment based face recognition approach, the major time taken is during the computation of WMs, therefore, here we mention the time taken for feature extraction only. The time taken for the comparison of features using L1-norm is very small, which is why it is ignored here. It is observed that the average recognition rate of Algorithm B is 99.9% while for Algorithm A it is 98.6%. Algorithm A uses the traditional method of computing WMs, while Algorithm B uses the fast computation of WMs as explained in Section 3.2. The overall time taken by Algorithm B is approximately 1/8th of the time taken by Algorithm A. Since Gabor wavelet is one of the most effective methods in facial expression recognition, we further compare the performance of the proposed method with the methods in [50,51] on JAFFE database.

Method

Recognition rate (%)

CWMs (Algorithm B) GWþ LBP [50] LGþ PCAþ LDA [51]

99.9 96.2 97.3

The method in [50] uses ensemble of Gabor wavelets and LBP features which is referred to GWþLBP. The method in [51] uses a combination of local Gabor filter and principle component analysis (PCA) and linear discriminant analysis (LDA). This method is referred to LGþPCAþ LDA. As mentioned in Table 2, the recognition rates achieved by GaborþLBP and LGþPCAþ LDA are 96.2% and 97.3%, respectively, while the recognition rate achieved using Algorithm B is 99.9%. It is observed from the table that the performance of the proposed method is better than the combined approaches based on Gabor and LBP on JAFFE face database. In order to test the performance of the proposed method in facial expression variation using large face database, we conduct experiments on FERET database. The set fa consisting of 1196 frontal face images is used for training and the set fb consisting of 1195 images, which represents facial expression variation is used for testing. Table 3 shows the recognition rates for Algorithm A, Algorithm B, LBP [47], histogram of Gabor phase patterns (HGPP) [47], and Gaborþ LBP [52]. It is observed that the recognition rate of the proposed method is less than LBP and Gabor wavelet based methods on FERET fb dataset. One of the reasons for achieving high recognition rates by these methods is due to very effective classifiers adopted by them. On the other hand, the classifier used in the proposed method is based on L1-norm distance which is very simple to implement. Nonetheless, it shows the efficacy of the proposed system on a large database such as the FERET fb set which represents diverse variations in face images. Moreover, it has advantage of being rotation invariant over the two methods. Further, the proposed method is comparable to LBP in time complexity, while the Gabor methods are very time consuming. Again, Algorithm B provides 3% improvement in recognition rate compared to Algorithm A. The CPU elapse time for feature extraction for training and testing are also mentioned in the table. The proposed fast computation of WMs takes only 0.03 s on average for feature extraction of one image. 5.3. Performance evaluation under pose variation In this section, we compare the performance of Algorithm A and Algorithm B for recognizing face images under the condition of pose variation by using different sets of training and test face images selected randomly from UMIST and FERET face databases. Comparison with the method of complex Zernike moments (CZMs) [46] is also made on FERET datasets. We conduct three experiments on UMIST. In the first experiment, we randomly select 9 face images from each class for training and the remaining 384 images for testing. In the second and third experiments, we randomly select 10 and 11 face images from each class, respectively, for training and the remaining 364 and 344 images for testing. For experiments on FERET datasets, we randomly select 100 subjects with seven different poses: 03 , 7 22:53 , 7 67:53 , 7 903 . The results of the experiments conducted on different sets of UMIST and FERET database are presented in Tables 4 and 5, respectively. It is observed that Algorithm B outperforms Algorithm A in all experiments which are conducted on different sets of face images with pose variation. This trend is also reflected when the experiments are performed on FERET database. This shows that the inclusion of phase angles in the WMs features is an effective way to enhance the face recognition rate

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Table 3 Comparison of recognition rates on FERET database fb using the proposed and other methods. Method

Recognition rate (%)

Feature extraction time (in s) for training stage

Feature extraction time (in s) for test stage

MWMs (Algorithm A) CWMs (Algorithm B, proposed method) LBP [47] HGPP [47] LBP þGabor [52]

88.0 91.0 93.0 97.0 98.0

279.27 36.48 Not available, but low Not available, but very high Very high

290.03 36.45 Not available, but low Not available, but very high Very high

Table 4 Recognition rates using Algorithm A and Algorithm B on UMIST face database. No. of images per person for training (randomly selected) 9 10 11

Method Total size of training/ test set

Recognition rate (%)

180/384 Algorithm A Algorithm B 200/364 Algorithm A Algorithm B 220/344 Algorithm A Algorithm B

91 94 92 94.5 96.2 97.6

Feature extraction time (in s) for training stage

Feature extraction time (in s) for test stage

41.5 5.5 46.7 6.1 51.2 6.81

88.9 11.8 85.7 11.2 80.4 10.6

Table 6 Comparison of recognition rates between Algorithm A, Algorithm B and CZMs method [46] on ORL database. Number of training face images per person

First three (1–3) First four (1–4) First five (1–5) First six (1–6) Even numbered (2, 4, 6, 8, 10) Random five Random one

Recognition rates (%) CZMs [46]

Algorithm A (WMs)

Algorithm B (CWMs)

88.5 89.7 92.0 96.2 97.0 96.5 70.5

85.0 88.0 90.0 91.8 92.0 93.5 69.7

86.7 91.2 93.5 96.2 93.0 96.0 73.3

Table 5 Comparison of recognition rates between Algorithm A, Algorithm B and CZMs method [46] on FERET database. Number of training/test images per person along with pose variation

1ð03 Þ=6 ð7 22:53 , 7 67:53 , 7 903 Þ 1ð03 Þ=4 ð7 22:53 , 7 67:53 Þ 1ð03 Þ=2 ð 7 67:53 Þ 1ð03 Þ=2 ð 7 22:53 Þ

Recognition rates (%) CZMs [46]

Algorithm A (WMs)

Algorithm B (CWMs)

55.6 69.7 43.0 100

51.5 63.7 40.5 92.5

54.3 68.0 43.0 97.5

Fig. 15. (a) Five face images from ORL database, (b) their rotated versions at 451.

even in the presence of pose, facial expression and illumination variation. A comparison of recognition rates of CWMs on FERET dataset with that obtained by CZMs [46] reveals that the recognition rates are almost the same. It must, however, be noted that CWMs are computationally very fast compared to CZMs. Therefore, comparative recognition rates are achieved by CWMs at low computational cost.

magnitude of WMs is very beneficial in representing the local variations in the image. The recognition rates of CZMs and CWMs are almost the same. Therefore, CWMs achieves the same recognition rate with much less computation complexity than CZMs.

5.4. Comparative performance analysis on ORL database

5.5. Performance evaluation under in-plane rotation

The methodology of the proposed system is similar to our recent work on face recognition using CZMs [46]. It is shown in [46] that the CZMs outperform many similar techniques when global descriptors are used as features. Therefore, we compare the recognition rate of the proposed method with CZMs on ORL database. In this experiment, we consider first-three/four/five/six images, even numbered images, random five images and random one image per person in training and the corresponding remaining images in test set. We use random number generator of Cþþ to choose an image from a set of 10 images. In the sixth set which selects five images randomly, the first five distinct random numbers are considered. In the seventh set only the first random number is used. The results on these experiments using CZMs [46], Algorithm A and Algorithm B are shown in Table 6. It is observed that the recognition rates of Algorithm B are much better than that obtained by Algorithm A. The phase angle along with the

In order to asses and analyze the performance of the proposed method under in-plane rotation, we conduct experiments on ORL database. Again we use the first five distinct random numbers to choose five training images and rests are used for test images for each subject in ORL database. Thus, there are 200 face images for training and 200 face images for testing, out of a total of 400 face images. In these experiments, we rotate each test face images by 331, 451, 901, and 1801 thus using a total of 1000 images for testing. Fig. 15 shows some of the face images and their rotated versions at 451. The recognition rates for the unrotated and rotated images are presented in Table 7 for Algorithm A and Algorithm B. It is observed that the in-plane rotation of images does not affect the recognition rate. The maximum effect is observed at 451 rotation where the recognition rates have dropped from 93.5% to 92.7% for Algorithm B and from 92.02%

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Table 7 Recognition rates using Algorithm A and Algorithm B on in-plane rotated images of ORL face database. Method

Recognition rate (%) under in-plane rotation Unrotated image

Algorithm A 93.0 Algorithm B 95.2

331 rotation

451 rotation

901 rotation

1801 rotation

92.2 94.7

91.8 94.4

92.6 95.0

93.0 95.2

represents variations in facial expression, position, pose, illumination, detail and scale also exhibits a similar trend in recognition rates as provided for other databases implying thereby that the proposed system is much better than the magnitude only WMs based approach. Therefore, the proposed system can be used where good recognition rate is required in real time environment as the feature extraction time on a PC with 3.0 GHz CPU is only 0.03 s for an image of size 64  64 pixels.

Acknowledgments

to 90.5% for Algorithm A. Therefore, the CWMs provide very good recognition rate even under image rotation.

The authors are thankful to the useful comments and suggestions of the anonymous reviewers for raising the standard of the paper. Thanks are also due to Indian Council for Cultural Relations, New Delhi, Govt. of India, for sponsoring and providing financial support to the second author.

6. Conclusion In this paper, we develop a technique based on complex wavelet moments (CWMs) for face recognition. Face images contain many variations such as facial expression, pose, illumination, and aging. Moreover, the images can have different orientations and scales. WMs are capable of representing such variations because they provide both space and frequency localization. The magnitude of WMs is rotation invariant and the phases of rotated images have well defined relationship. WMs are computed in unit disk, therefore, they are expected to be scale invariant. These properties of WMs are exploited to present an effective face recognition system. The proposed system uses both real and imaginary components of the moments thus provide twice the number of features to that of the magnitude only features of wavelet moments (MWMs). Rotation invariance is achieved after correcting the real and imaginary parts of CWMs by exploiting the relationship of phase angles of wavelet moments of the nonrotated and rotated images. Detail experiments for face recognition are carried out on JAFFE, FERET, UMIST and ORL databases. The recognition rates are compared with several techniques based on moments, Gabor wavelets and LBP. It is observed that CWMs provide approximately 3% improvement in recognition rates over the magnitude based wavelet moments (MWMs) in almost all experiments. This improvement is achieved because of the phase inclusion in the features of WMs. A comparison of results with a closely related method, namely, the complex Zernike moments (CZMs) reveals that the proposed method have comparative recognition rates with that obtained by CZMs. It has a major advantage of having low time complexity compared to CZMs. The proposed method has an excellent performance on JAFFE database. It achieves a recognition rate of 99.9% as compared to GWþLBP and LG þPCAþLDA which achieve 96.2% and 97.3% recognition rates, respectively. However, on the FERET database, its performance is not as good as on JAFFE. The proposed technique achieves 91.0% recognition rate compared to 93.0%, 97.0% and 98.0% recognition rates achieved by LBP, HGPP and LBPþGabor, respectively. One of the main reasons for high recognition rates achieved by these methods is the use of very effective classifiers which are not as simple to implement as the L1-norm based classifier adopted in this paper. Moreover, the Gabor based methods are computationally very slow. Nonetheless, the proposed method exhibits its efficacy in providing high recognition rates for face expression variation. In addition, it is rotation invariant unlike the Gabor and LBP based methods. The performance evaluation test carried on UMIST and FERET databases, which represent pose variations also, provides a similar trend on recognition rates, although CZMs provide a slightly better recognition rate. The results on the ORL database which

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