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International Journal of Image and Graphics Vol. 9, No. 3 (2009) 355–367 c World Scientific Publishing Company
A FACE RECOGNITION SCHEME BASED ON EMBEDDED HIDDEN MARKOV MODEL AND SELECTIVE ENSEMBLE STRATEGY
XINBO GAO∗ , JINXIU LI and BING XIAO School of Electronic Engineering, Xidian University P. O. Box 133, No. 2 South Taibai Road, Xi’an 710071, P. R. China ∗
[email protected] Received 26 December 2007 Revised 24 November 2008 Accepted 2 April 2009 As an effective method, the embedded hidden Markov model (E-HMM) has been widely used in pattern recognition. On applying the E-HMM to face recognition, the performance heavily depends on the selection of model parameters. Aiming at the problem of model selection, a selective ensemble of multi E-HMMs based face recognition algorithm is proposed. Experimental results illustrate that compared with the traditional E-HMM based face recognition algorithm the proposed method cannot only obtain better and more stable recognition performance, but also achieve higher generalization ability. Keywords: Face recognition; embedded hidden Markov model (E-HMM); model selection; selective ensemble; generalization ability.
1. Introduction With the rapid development of IT industry, information security has received substantial attention from both researcher communities and the market. Therefore expeditious and effective automatic identity authentication technique is demanded urgently. Such physiological and behavior characteristics as face, fingerprint, iris, gait and handwriting are utilized as features of identity distinguishing, because they have self-stability and individual differences. Among the existing biological identification techniques, face recognition has become the most popular method because of its friendly interface and understanding ability.1 Research on face recognition began in 1960s.2 There are two main methods in early period,3 one is based on geometrical local feature1,4 and another based on holistic template.5 The comparison study of the two methods by R. Brunelli5 indicates that the first method is fast and small memory required with a lower recognition rate, while the second one is slow and large memory required with a higher recognition rate. In recent years a lot of new methods are presented, for example, the K-L transform based method,6 the elastic bunch graph matching 355
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based method,7 neural network based method,8 Hausdorff distance based method9 and the hidden Markov model (HMM)10 based method, among which the HMM attracts more and more attention because of its effectiveness for face recognition and facial expression recognition.11–15 The basic theory of HMM is founded by Baum at the end of 1960s.16–18 After 1980s, the HMM is well known and applied in speech and printing recognition successfully. The earliest HMM of face is built by F. Samaria in 1994.19 It is a onedimensional model using pixel-intensity as the observation vectors. Later, a kind of HMM with two-dimensional discrete cosine transform (2D-DCT) coefficients as observation vectors are proposed by Nefian,20 which can be used more effectively in scale invariant systems and offer a more flexible framework for face recognition. However, the image is a two-dimensional (2D) array so HMM may lose a lot of spatial information. 2D-HMM is proposed for face recognition21 as an enhanced version of HMM. But its application is limited due to high computational complexity and memory requirement. Then the embedded HMM (E-HMM) is introduced for face recognition by Nefian.22 The E-HMM not only can extract main information of the 2D images, but is also robust for pose and environment variation with a receivable complexity. However, the E-HMM with different parameters will generate different information expression and recognition performance, so reasonable selection of model parameters turns into an urgent problem. Aiming at this, a new face recognition algorithm is proposed based on E-HMM and selective ensemble strategy. By selecting many accurate and diverse models, the sensitivity of recognition performance to E-HMM is depressed and the generalization ability of the face recognition algorithm is improved. 2. E-HMM Based Face Modeling and Recognizing 2.1. E-HMM based face modeling E-HMM is composed of a series of super states in vertical and embedded states in horizontal direction. These states are non-observable and we can only obtain observation vectors, O = {ox,y }, generated by them, where ox,y represents the observation vector at the xth row and yth column (1 ≤ x ≤ X; 1 ≤ y ≤ Y ), X and Y are the number of observations in vertical and horizontal direction respectively. The model is denoted as λ = (Π, A, Λ) and parameters are described as: • Π is the initial super state distribution Π = {Πi , 1 ≤ i ≤ Ns }, where Ns is the number of super states in vertical; • A is the super transition probability matrix; • Λ denotes super states, and the ith super state, consisting of several embedded states, is defined as Λ = {Πi , Ai , Bi , 1 ≤ i ≤ Ns }, where Πi = {πik , 1 ≤ k ≤ N i } is the initial distribution of embedded states, N i is the number of states embedded in the ith super state; Ai is the transition probability matrix of the embedded
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states; Bi is state probability matrix of the ith super state and Bi = {bik (ox,y )}, where bik is distribution of observation vectors in the kth embedded state and the ith super state. In this paper, Bi is a finite mixture of the form: bik (ox,y ) =
K
i Ckj N (ox,y , µikj , Σikj ),
1 ≤ k ≤ N i,
(1)
j=1
where K is the number of mixture components, each of which is described by the Gaussian probability density functions (pdf) N (ox,y , µikj , Σikj ) with mean vector i for the jth mixture in µikj , covariance matrix Σikj and the mixture coefficient Ckj the kth embedded state and ith super state. The traditional E-HMM for face image is shown in Fig. 1.19 There are five super states in vertical direction: forehead, eyes, nose, mouth and chin, which are used to express the global features. The embedded states in each super state are used to describe the local features. Each face is modeled by an E-HMM, and the difference of faces is just depicted by different model parameters. For example, the diversification of face shapes can be described by different state transformation and the variety of gray can be expressed by various mean vectors of Gaussian mixture model. Thereby, with different values of Ns , N i and K, one can develop various models. So the HMM can be denoted as λ = (Π, A, Λ|Ns , N i , K), and if the E-HMM is constructed, Ns , N i and K should be specified firstly. When it comes to observation vectors, they are generated according to Fig. 2. A window with size of P × L moves from left to forehead eyes nose mouth chin
Fig. 1.
The traditional E-HMM of face image.
O i , j Oi +∆x , j Oi, j +∆ y Oi+∆x , j+∆ y
Fig. 2.
The observation extraction procedure for E-HMM of face image.
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right and top to bottom. The overlap between adjacent windows is ∆x in vertical direction and ∆y in horizontal direction.19 The lower frequency coefficients of each window’s 2D-DCT serve as observation vectors and they are determined by the parameters P × L, ∆x × ∆y , N2D−DCT . Hereby, the observation vectors can be denoted as: O = (o1 , o2 , . . . , oT |P × L, ∆x × ∆y , N2D−DCT ). 2.2. The E-HMM based face recognition According to the given parameters: P × L, ∆x × ∆y , N2D−DCT , Ns , N i and K, the E-HMMs are trained as follows23 : • The observation vector sequence O is partitioned to initialize the parameters of the E-HMM. First the overall sequence is segmented into Ns super states from top to down, and then each super state is uniformly segmented into N i sub-states from left to right; • During the iterative model training procedure, the uniform segmentation is replaced by the partition of a doubly embedded Viterbi algorithm. The super state probability together with the super state transition probabilities and the initial super state probability are used to calculate P (O |λ ) with Forward-Backward algorithm; • The model parameters are estimated by a 2D extended segmental K-means algorithm, and the model parameters are obtained by the following equations. aikj =
number of transitions from πik to πij , number of transitions from πik
µik = mean of samples in the kth state of the ith super state,
(2) (3)
Σik = covariance of samples matrix of the kth state in the ith super state, (4) aij =
number of transitions from Πi to Πj . number of transitions from Πi
(5)
• When the output likelihood value of the doubly embedded Viterbi algorithm is less than a pre-specified threshold, the iteration will be stopped and the model is obtained. The E-HMMs for training images are acquired according to the above procedure and we make use of them to perform the recognition of probe images. After extracting an observation sequence for a probe face image, the probability of the observation sequence with each trained E-HMM is computed via the doubly embedded Viterbi algorithm. The model with the highest likelihood is selected and this model reveals the identity of the probe face, which is shown as Eq. (6). O ∈ λt ,
if P (O|λt ) = max P (O|λr ). r
(6)
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3. The Proposed Face Recognition Algorithm Based on E-HMM and Selective Ensemble A good machine learning or pattern classification system should have a strong generalization ability, which means the ability to recognize or process the unknown things using the obtained knowledge and techniques. Therefore, generalization ability is always the ultimate problem concerned about in machine learning. Ensemble learning is a new machine learning technique developed in last decades, where results of many algorithms are jointly used to solve a problem. The ensemble learning cannot only improve the classification or recognition accuracy, but also obviously improve the generalization ability of the learning system. So it is regarded as one of the fourth fundamental research topics in recent years.24 3.1. Selective ensemble It is well known that ensemble learning of multiple classifiers can achieve stronger generalization ability than the single classifier. Hereby, is it better with more individual classifier? The answer is negative. The more classifiers lead to larger complexity and storage; on the other hand, when the number of classifiers is increased, the difference between them will be hard to get. Aiming at this problem, the concept of “selective ensemble” is proposed by Zhi-Hua Zhou.25 Later research26–28 proves that ensemble constructed with partial higher accurate and diverse classifiers is better. This means that good performance can be achieved by middle or small scale selective ensemble. Here we discuss the selective ensemble of the E-HMMs to improve the generalization ability. Usually, different models constructed with different parameters describe the different characteristics of the face. For example, the smaller sampling windows emphasize the local information, while the larger ones pay attention to the global information. Based on the idea of “Many could be better than all”,25 for the model ensemble, it is the more the better, but need to select diverse models with higher accuracy to ensemble. Therefore, a novel face recognition algorithm is proposed based on E-HMM and selective ensemble, and the scheme is shown in Fig. 3. The algorithm is divided into two parts: the first part is training module, which trains n models and selects m divers models with higher accuracy for selective ensemble; the second section is the ensemble module, which is used to ensemble the m selected models for face recognition. In Fig. 3, M1 , M2 , . . . , Mn are models of faces with different parameters, denoted as M = (O; λ), where O = (o1 , o2 , . . . , oT |P × L, ∆x × ∆y , N2D−DCT ) is the feature information of the model; λ = (Π, A, Λ|Ns , N i , K) is the structure information of the model. Therefore, model M is determined by the above six groups of parameters.
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Recognition Training Training samples
...
Model selection
... Mn
M2
Mm
Ensemble recognition
M1
M1 M2
Testing samples
Result
Fig. 3. The diagram of the proposed face recognition algorithm based on E-HMM and selective ensemble.
3.2. The selective ensemble algorithm of E-HMMs A selective ensemble of E-HMMs is proposed in this section. Given a database with L face images, each person has l images, which consists of l1 gallery images and l2 probe images. The detailed algorithm is given as follows: • Suppose n models {M1 , M2 , . . . , Mn } are trained by the gallery images, they are used to recognize all the probe images and the corresponding recognition rates are ri (i = 1, 2, . . . , n); • Sort the n models Mi (i = 1, 2, . . . , n) according to descending order of ri as: {M1 , M2 , . . . , Mn }. Let S be the set of selected models and initialized as S = {M1 }, and Z = {M1 , M2 , . . . , Mn } − S, m − 1 models are selected by performing the following steps: (a) εt is the number of faces wrongly recognized by the models in S; (b) For each model Mi ∈ Z, calculate the number of the probe faces that are recognized correctly by Mi and wrongly by at least one of the models in S. The number is denoted as ςi which reflects the error correction ability of Mi . The model Mk rectifying most images is selected. Actually, there may be several models having the same ability of error correction; therefore, recognition rate of each model should also be referred to and then model Mk is selected based on the following rule: εt k = arg max w1 ri + w2 , (7) Mi ∈Z ςi where w1 + w2 = 1, and w1 is the weight of face recognition rate, w2 is the weight of the rectifying rate; (c) S ← S ∪ Mk , Z ← Z − Mk ; (d) If t < m, let t = t + 1, then go to (a), else stop and m models {M 1 , M 2 , . . . , M m } are selected.
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3.3. The ensemble of E-HMM based face recognition algorithms Using the m models {M 1 , M 2 , . . . , M m } to recognize faces in the following method. Suppose there are H person’s images in database containing one image per person, when the probe image is input, the m selected models are used to calculate the likelihood of it belonging to each person and a likelihood matrix is resulted: P (O1 |λ12 ) · · · P (O1 |λ1H ) P (O1 |λ11 ) P (O2 |λ21 ) P (O2 |λ22 ) · · · P (O2 |λ2H ) , (8) P = ··· ··· ··· ··· m m m m P (Om |λm 1 ) P (O |λ2 ) · · · P (O |λH ) m×H where the observation vector sequence of the probe image according to the model M i is Oi (i = 1, 2, . . . , m), the E-HMM of the model M i is λij (i = 1, 2, . . . , m; j = 1, 2, . . . , H), and P (Oi |λij )(i = 1, 2, . . . , m; j = 1, 2, . . . , H) is the likelihood of the probe image corresponding to the jth person based on the ith model M i . The weights of its m models for each face are wi (i = 1, 2, . . . , m) and i wi = 1. There are many ways to set weight wi , such as, average weighting, namely wj = 1/m; or setting weight according to the recognition rate: ri w i = m
j=1 rj
,
(9)
where ri is the recognition rate of the ith model. In order to determine the identity of a given image, the likelihood matrix P is transformed into binary matrix Pd : 1 if P (Oi |λij ) = max{P (Oi |λik )} i i k . (10) Pd (O |λj ) = 0 otherwise Then, the decision is made according to the following equation: m i i i D = arg max w · Pd (O |λj ) . j
(11)
i=1
4. Experimental Results and Analysis Experiments are conducted to demonstrate the effectiveness of the proposed method on the ORL (Olivetti Research Ltd) database,29 which consists of 400 gray images composed of 40 people’s face, and 10 images for each person. The images are at the resolution of 92 × 112 pixels, 8-bit gray levels. For each subject, 5 images were selected randomly as gallery images in training, the left ones are used as probe images, so sample set A is gained. Then swap the gallery and probe images, sample set B is obtained. Both A and B are utilized to determine E-HMMs of faces for ensemble. The sample sets C, D, and E are selected from ORL database, 5 images were selected randomly as gallery images for each subject, the left 5 images are probe images. C, D and E are different from A and B.
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In experiment, the number of people is L = 40, the number of images for each person is l = 10, and number of gallery images is l1 = 5, the number of probe images is l2 = 5. The model set is Ω = {M1 , M2 , . . . , M2000 }, the range of parameters is set as follows: sampling window size: 2 × 2 ≤ P × L ≤ 31 × 31, sampling step: 1 × 1 ≤ ∆x × ∆y ≤ 26 × 26, 2D-DCT coefficients: 4 ≤ N2D−DCT ≤ 24, number of pdfs: 2 ≤ Ns ≤ 7, number of state: 1 ≤ N i ≤ 9. In model selection module, the weight of face recognition rate is w1 = 0.05, and the weight of rectifying rate is w2 = 0.95. 4.1. Experiment of face recognition based on single model In this subsection, the N models of Ω are used to recognize the sample set C, D and E, and the model recognizing each sample set optimally is denoted as MC , MD and ME . Model MW was randomly selected from Ω. The widely used model in 19, 22, 23 is denoted as MT , and it is used as a reference model. Parameters of the above models are shown in Table 1. For the given ORL database, the recognition rates of above five models are shown in Table 2, and the result indicates that: • For a sample set, the performance of different models is various and may be greatly different, for example, in the sample set D, discrepancy between the recognition rate of model MD and model MW actually reaches to 54%. This is because different models can express a type of feature information in varying degrees, which leads to different recognition rate. • The performance of each model, such as MC , MD and ME , is optimal only for some certain dataset. This means that each model specializes in expressing a type of feature information rather than all features and the generalization ability of single model is not strong enough. Table 1.
The models and their parameters.
Models
P ×L
∆x × ∆y
N2D−DCT
Ns
N i , i = 1, 2, . . . , Ns
K
MC MD ME MW MT
8×8 18 × 18 12 × 12 31 × 31 10 × 8
3×3 4×4 2×2 24 × 24 2×2
12 10 6 6 24
7 4 7 2 5
(3, 3, 3, 3, 3, 3, 3) (9, 9, 9, 9) (2, 2, 2, 2, 2, 2, 2) (3, 3) (3, 6, 6, 6, 3)
6 6 3 2 3
Table 2. Models MC MD ME MT MW
The recognition rates of five models on three test samples (%). Sample set C
Sample set D
Sample set E
98.5 98.0 95.5 95.5 55.5
96.5 99.5 98.0 98.5 45.5
96.0 97.0 98.5 94.0 62.0
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4.2. Experiment of the two different ensemble As previously stated, weights for ensemble can be set averagely or according to the recognition rate of each component model. A set of experiments are performed in order to examine the performance of E-HMM ensemble based on these two weighting methods respectively. Model sets MA and MB are selected from Ω using the method introduced in Sec. 3.2, and then, the models in each set are equally weighted to constitute MAe and MBe , while MAu and MBu are formed by unequally weighting the models. Sample sets C, D and E are recognized by these four models. The result is shown in Table 3. From the experiment results of Table 3, some facts can be found: • With average weighting in both model sets MA and MB , it cannot reach the optimal performance of single models, like MC , MD and ME in Table 2. It is difficult to achieve expecting results by integrating E-HMMs based on average weighting; • No matter in MA or MB , result of unequal weighting method is obviously better than that of average weighting method and single models. Therefore, E-HMM ensemble based on unequal weighting method is able to express the face information more effectively and achieve better recognition results. 4.3. Comparison experiment of face recognition algorithms To verify the stability and generalization ability of the proposed algorithm, the selective ensemble of model sets MA and MB with unequal weighting is tested respectively on dataset C, D and E. The single model MC , MD , ME and MT are employed as benchmarks. The recognition results are presented in Table 4. Several interesting conclusions can be achieved from Table 4: Table 3. Models
Recognition results of MA and MB on three sample sets (%). Sample set C
Sample set D
Sample set E
95.0 98.5 95.5 98.0
98.5 100 97.5 99.0
97.5 99.0 94.5 98.0
e MA u MA e MB u MB
Table 4. Model (set) u MA u MB MC
MD ME MT
The results of six face recognition algorithms (%).
Sample set C
Sample set D
Sample set E
Average
Variance
98.5 98.0 98.5 98.0 95.5 95.5
100 99.0 96.5 99.5 98.0 98.5
99.0 98.0 96.0 97.0 98.5 94.0
99.17 98.33 97.00 98.17 97.33 96.0
0.39 0.22 1.17 1.06 1.72 3.50
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X. Gao, J. Li & B. Xiao Table 5. Model (set) Recognition rate
The results of five face recognition algorithms (%).
u MA
u MB
Eigenfaces
Fisherfaces
Laplacianfaces
CNN
99.17
98.33
85.9
92.3
93.2
96.2
• For all the sample sets, the recognition rate of the proposed algorithm in this paper is higher than that of the traditional algorithms based on E-HMM. It is obvious that the E-HMM common used is not universally applicable. On the other hand, although the method using single E-HMM leads to recognition rate equal to or reducing by no less than 0.5% of that resulting from the proposed algorithm, we could not forecast which model’s generalization ability is better in actual application, so it is necessary to integrate single models rather than selecting a model among these ones; • The model ensemble method obtains higher recognition rate than single models, with lower variance, which shows that the proposed method leads to better and more stable recognition performance, that is to say, it can deal with new data with higher accuracy, and has strong generalization ability. This means that the proposed algorithm makes good use of recognition and error correction ability of each single model, and these component models are complemented with each other so as to improve recognition results. Except for methods based on E-HMM, there are many popular approaches for face recognition. To further evaluate the proposed algorithm, it is compared with Eigenface,30 Fisherface,31 Laplacianfaces32 and convolutional neural network (CNN),33 whose best results are listed in Table 5. It is obvious that average recognition rate of our methods is superior to that of others.
5. Conclusion Based on the idea of selective ensemble, a multiple E-HMMs based face recognition algorithm is proposed in this paper, which solves the model selection problem in E-HMM to some extent. The experimental result shows that this algorithm achieves higher recognition rate and stronger generalization ability. That is to say, this algorithm has a stronger ability to deal with new data. Of course, the ensemble of multiple E-HMMs will lead to high computational complexity. Fortunately, the new algorithm is parallel virtually, which can be used to improve the efficiency by parallel computing.
Acknowledgments We want to thank the helpful comments and suggestions from the anonymous reviewers. This research was supported by National Science Foundation of China (60771068, 60702061, 60832005), the Open-End Fund of National Laboratory of
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Pattern Recognition in China and National Laboratory of Automatic Target Recognition, Shenzhen University, China, and the Program for Changjiang Scholars and innovative Research Team in University of China (IRT0645).
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19. F. Samaria, Face Recognition Using Hidden Markov Models, PhD Thesis, Univ. of Cambridge, Cambridge (1994). 20. A. V. Nefian and M. H. Hayes III, “Hidden Markov models for face recognition,” Proc. IEEE Int’l. Conf. Acoust. Speech and Sig. Proc. 5, 2721–2724 (1998). 21. H. Othman and T. Aboulnasr, “A separable low complexity 2D HMM with application to face recognition,” IEEE Trans. Pattern Anal. Mach. Intell. 25(10), 1229–1238 (2003). 22. V. N. Ara and H. H. Monson, “Face recognition using an embedded HMM,” Proc. IEEE Int’l Conf. Audio Video-based Biometric Person Authentication, pp. 19–24 (1999). 23. V. N. Ara, A Hidden Markov Model-Based Approach for Face Detection and Recognition, PhD Thesis, Georgia Institute of Technology, Atlanta (1999). 24. T. G. Dietterich, “Machine learning research: Four current directions,” AI Magazine 18(4), 97–136 (1997). 25. Z.-H. Zhou, J. Wu and W. Tang, “Ensemble neural networks: Many could be better than all,” Artif. Intell. 137(12), 239–263 (2002). 26. J. Wang, Z. H. Zhou and A. Y. Zhou, Machine Learning and Application (Tsinghua University Press, Beijing, 2006), pp. 170–188. 27. X. Geng and Z. H. Zhou, “Image region selection and ensemble for face recognition,” J. Comput. Sci. & Tech. 21(1), 116–125 (2006). 28. J. J. Zhong, X. B. Gao and C. N. Tian, “Face sketch synthesis using E-HMM and selective ensemble,” Proc. IEEE Int’l. Conf. Acoust. Speech and Sig. Proc., I-485-I-488 (2007). 29. ORL face database, http://www.cam-orl.co.uk/facedatabase.html. (2006). 30. M. Turk and A. Pentland, “Eigenfaces for recognition,” J. Cogn. Neurosci. 3(1), 71–86 (1991). 31. K. Etemad and R. Chellappa, “Discriminant analysis for recognition of human face images,” J. Opt. Soc. of America A 14(8), 1724–1733 (1997). 32. X. He, S. Yan, Y. Hu, P. Niyogi and H. J. Zhang, “Face recognition using laplacianfaces,” IEEE Trans. Pattern Anal. Mach. Intell. 27(3), 1–13 (2005). 33. S. Lawrence, C. L. Giles, A. C. Tsoi and A. D. Back, “Face recognition: A convolutional neural network approach,” IEEE Trans. Neural Netw. 8(1), 98–113 (1997).
Xinbo Gao received his BS in electronic engineering, his MS and his PhD degrees both in signal and information processing from Xidian University, Xi’an, China, in 1994, 1997, and 1999, respectively. From 1997 to 1999, he was with the Computer Games Research Institute of Shizuoka University as a research fellow. From 2000 to 2001, he also worked at Multimedia Lab of the Chinese University of Hong Kong as a research Associate. He is currently a Professor in the School of Electronic Engineering, Xidian University, China. His research interests include video processing, pattern recognition, and artificial intelligence.
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Jinxiu Li received her BS in electronic engineering from Xidian University, Xi’an, China, in 2005. From August 2005 to September 2007, she was at the Xidian University as a Candidate for Master of Signal and Information Processing. She is currently in the School of Electronic Engineering. Her research interests include pattern recognition and computer vision.
Bing Xiao received her BS in Computer Science and Technology and her M.Eng. in Computer Software and Theory from Shaanxi Normal University, Xi’an, China, in 2003 and 2006, respectively. Since August 2006, she has been working towards her PhD degree in Intelligent Information Processing at Xidian University, Xi’an, China. Her research interests include pattern recognition and computer vision.
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