Face based Biometric Identification using Multi-Resolution Trace Transform and Fuzzy ART Combination

R. Fooprateepsiri

May 7, 2011

Faculty of Information Science and Technology

Mahanakorn University of Technology

140, Cheumsampan Road, Nongchok

Bangkok, Thailand 10530

Abstract

Face recognition research still challenge in some specific domains such as pose, illumination and Expression (PIE). This paper proposes a highly robust method for face recognition with variant pose, illumination, scaling, rotation, blur, reflection and difference expression (smiling, angry and screaming). Techniques introduced in this work are composed of two parts. The first one is the detection of facial features by using the concept of multi-resolution Trace transform. Then, in the second part, the supervised fuzzy ART is employed to measure and determine of similarity between the models and tested images. Finally, our method is evaluated with experiments on the XM2VTS and FERET face databases and compared with other related works (e.g. Eigen face, Enhance-EBGH, Hausdorff ARTMAP and Trace-Hamming). The extensive experimental results show that the average of accuracy rate of face recognition with variant pose, illumination, scaling, rotation, blur, reflection and difference expression is very high and it was found that our proposed method performed better than the other related works in all cases.

Keywords: Biometric, Face Recognition, Multi-resolution Trace Transform, Fuzzy ART.

Table of Contents

Abstract / 2
Table of Contents / 2
1. Introduction / 4
2. Features Extraction / 4
2.1 Pre-processing / 4
2.2 The Trace Transform / 5
2.2.1 Invariant Functional / 6
2.3 Multi-Resolution Trace Transform / 6
2.4 Facial Image Identifier Extraction Algorithm / 7
3. Similarity Measure and Learning Algorithm / 10
3.1 The Fuzzy ART Network / 10
3.1.2 The Modified Fuzzy ART / 12
4. Experimental Results / 12
5. Conclusions / 14
References / 14

.

1. Introduction

Biometric identification [1] system makes use of either physiological characteristics [2, 3, 4] (such as a fingerprint, iris pattern, or face) or behavior patterns [5, 6, 7] (such as hand-writing, voice, or key-stroke pattern) to identify a person. Because of human inherent protectiveness of his/her eyes, some people are reluctant to use eye identification systems. Face recognition has the benefit of being a passive, non-intrusive system to verify personal identity in a “natural” and friendly way. In general, there are two approaches to face recognition systems: 1) Brightness-based, which make use of the pixel brightness directly or features in low dimensionality manifolds without shape information, such as PCA-based approaches, and 2) Feature-based, which involve the use of geometric features such as positions of facial features. The proposed method combines elements from both approaches. We compare its results with several traditional methods in typical experiments and demonstrate the superiority of the face representations proposed. The well-known approaches used for face recognition is based on the use of eigenfaces [8, 9, 10, 11, 12, 13], elastic matching [14, 15, 16, 17, 18, 19], neural networks [20, 21], waveletfaces [22], fisherfaces [23, 24], hausdorff ARTMAP [25] and trace transform [26, 27, 28]. The organization of this paper is as follows. An introduction to the multi-resolution Trace transform, its properties and how it can be used to extract invariant features is given and the extraction of the string identifier from a facial image in Section 2. We describe a modified fuzzy ART network with supervise training algorithm in section 3. We present our experimental results in section 4. Finally, we conclude in section 5.

2. Features Extraction

In this paper, we use a trace transform with multi-resolution technique for extracting features from clustered segments. The multi-resolution trace transform method able to produce feature values of an input image, invariant to translation, rotation and even reflection of an input image. Accordingly, it is suitable to extract feature values from various shapes of facial segments, even if deformed by translation, rotation, or reflection.

2.1 Pre-processing

The pre-processing phase that helps to improve the robustness of features extraction by removing possible artifacts due to resampling when trace transform is computed. Following [29], we represent each extracted face inside an ellipse. Therefore, all faces have a shape that is not intrinsic to the face. So, we describe the algorithm for face detection. This algorithm will search only the human skin areas, not the entire image. The whole algorithm can be described as shown in table 1.

Table 1 The face detection algorithm [29].

Algorithm-I
Step 1: / RGB to HSV Color Model Conversion.
Step 2: / Human Skin Detection.
Step 3: / The Region of Human Skin.
Step 4: / RGB to Gray scale Conversion.
Step 5: / Edge Detection.
Step 6: / Face Region Searching and Snipping by using an Elliptical Model.

2.2 The Trace Transform

The Trace transform [30] projects all lines over an image and applies functional over these lines. A further functional, known as the diametrical functional, is applied to the Trace transform to obtain a one-dimension function known as the circus function. A facial image identifier is developed using the trace and diametrical functionals. A line is parameterized in a co-ordinate system by, as show in figure 1.

(a) (b)

Figure 1(a) The Trace transforms projects line over the facial image. The lines are parameterized by the angle  and distance d. (b) The trace transform of facial image of (a) using functional IF1.

Where the angle of the normal to the line is, is the distance between the origin and line and is the distance along the line. The values of the image function along a particular line are. And then, the Trace transform T applies some functional over the image function that results in the diametrical function. The diametrical functional D operates on the diametrical function to give the circus function.

. (1)

2.2.1 Invariant Functional

Shift invariance means that the value of the functional does not change if the function shifts. Examples are the integral, the median value, the maximal value of a function, etc. One might say that an invariant functional chooses an ordinate independently of the shift. A functional is called shift invariant if for any admissible function is invariant if for all (Property). The invariant functionals can have two further properties for all (Property ), and for all (Property). It can be shown [30] that and , where the constants and are called homogeneity constants of functional . Some invariant functionals and their properties are shown in table 2.

2.3 Multi-Resolution Trace Transform

Multi-resolution representations are popular technique for their powerful ability to describe signals at varying levels of detail from coarse gain to fine gain. Here a multi-resolution Trace transform is introduced that is quickly and efficiently generated from the original Trace transform. A Trace transform T with a specific functional provides one representation of an image. From this one abstraction a multi-resolution representation of the image can be generated which captures information at different scales. The Trace transform multi-resolution decomposition is performed by sub-sampling the original Trace transform of the image in either of its two dimensions, d or , or in both dimensions.

(a) / (b)

Figure 2.The multi-resolution Trace transform (a) with difference d (b) with difference 

This corresponds to projecting strips of width d over the image during the Trace transform, as shown in figure 2(a). Sub-sampling also takes place by integrating over intervals in the θ parameter as shown in figure 2(b).

Table 2 Invariant functionals and their properties.

No / Functional / /
IF1 / / -1 / 1
IF2 / / -r / qr
IF3 / / 0 / 1
IF4 / / -3 / 1
IF5 / / -2 / 0
IF6 / / 0 / 1
IF7 / / 0 / 1

** We used IF1, IF3and IF6 for this work.

2.4 Facial Image Identifier Extraction Algorithm

An imagecan be viewed from two different co-ordinate systems C1 and C2.The coordinate system, C2, is obtained from the C1 by a rotation of angle -, scaling the axis by parameter v and by translating with the vector . The image viewed from C2 can be seen as the image having undergone rotation by , scaling by v-1and shifting by. These linear transformations a line in f1will still be a line in f2; the transformations are line preserving. The parameters of an image line in co-ordinate system C1 in terms of the parameters of the line in C2 are and .From equation (1); it can be seen that the relationship of the circus function of an image in co-ordinate system C2 to the image in coordinate system C1 is given as

(2)

The Trace functional T is chosen to obey I1 and i1

. (3)

Furthermore, the diametrical functional T can be chosen to obey I1, i1 and i2 such that , we obtain , and it can then be define as

, (4)

where . From equation (4) it can be seen that the one-dimension circus function in C2 is a scaled and shifted version of the circus function in C1. From equation (4) we taking the Fourier transform gives, then exploiting the linearity identity and translation property of the Fourier Transform gives. Taking the magnitude of F() gives

. (5)

By the properties of the circus function and the magnitude of the Fourier transform an identifier can be extracted from an image. An algorithm to extract the binary identifier is given in table 3. The identifier is robust under similarity transform, which is scaling, rotation and translation.

The multi-resolution Trace transform provides more identifiers. One-dimension decomposition over the distance (d) parameter is performed. The extraction process shown in table 2, steps 2 to 5, are used for each level of the multi-resolution Trace transform. Significant performance improvements are obtained by extracting multiple identifiers from each image. Firstly different identifiers are extracted by making different choices for the diametrical functionals in steps 1 and 2 of Algorithm-II (see in table 3).

Table 3 The binary identifier extraction algorithm.

Algorithm-II
Step 1: / Take the Trace transform of the image using the functional i.e., integrating over all lines in the image.
Step 2: / Find the first two circus functions by applying the following diametrical functionals to the columns of the two dimensions matrix resulting from step 1, where ' is the gradient.
Step 3: / Get the magnitude of two circus functions by taking the Fourier transform.
Step 4: / Obtain the binary strings from each circus function that comes from taking the difference of neighboring coefficients
, (6)
where is defined by .
Step 5: / The first bit i1 corresponding to the different-combinations component is discarded and the identifier is made up of the subsequent N bits, I={i1,i2,…,in}.
Step 6: / For each diametrical functional perform steps (2) to step (5).
Step 7: / Concatenate each of the identifiers to obtain the complete identifier.

3. Similarity Measure and Learning Algorithm

3.1 The Fuzzy ART Network

The fuzzy ART network [32] is an unsupervised neural network. It proposes to a categorization with class in hyper right-angled. Each one represents a prototype (weight of the neuron). It is composed of three layers:

  • A layer F0 (layer where the data are prepared) receiving the bodies of the vectors a (fuzzy input). It has a double number of nodes according to the size of the vector a, and its complement. Thus we generate the vector I=(a, ac).
  • A layer F1 for comparison, having the same number of nodes than F0. Each node of F1 is related to the same order of F0’s node by a weight equal to one.
  • A layer F2 for competition entirely inter-connected with F1. Each node j of F2 is connected with all nodes of F1. The adaptive weight associated to the vector is noted Wj. The vector T expresses the activation of F2.

Figure 3 Architecture of Neural Network of Fuzzy ART.

The dynamics of the fuzzy ART network depends [33, 34] on the choice of the  parameter (a > 0 used at the time of the competition between neurons in F2), the training parameter fixing the speed of training, and the vigilance parameter of defining the size of the right-angled hyper.

Table 4 The Fuzzy ART Algorithm.

Algorithm-III
Step 1: / To initialize the weights Wij with one, and  > 0.
Step 2: / For each example, to generate the inputI, I=(a, ac).
Step 3: / To calculate the Tj activity of each neuron of F2 by:
, (7)
where  , is the fuzzy intersection given by (pq)=min(piqi) and the norm by .
Step 4: / The neuron J having the highest activation Tj is selected like the winner neuron.
Step 5: / Test of vigilance is carried out by checking:
. (8)
If the test is respected then the neuron J is updated (next step). If not, this neuron is desactived and another competition (previous step) takes place until a winning neuron respects the test of vigilance, or there are not active neurons.
Step 6: / The winner neuron is updated; these new weights are calculated by :
. (9)
And activate again all neurons.

3.1.2 The Modified Fuzzy ART

The fuzzy ART network is an unsupervised training network. The choice of vigilance parameters and training are strongly influence the result. To control the outputs so as to make them comparable with the desired outputs (to return it supervised), this paper proposes to find in the field of possible values of these parameters, those giving the network which gave the best results. The idea consist to vary ,  and  between 0 and 1 with a step , to carry out the training of fuzzy ART for each triplet, to calculate the mean square error (MSE) between the outputs obtained by the network and desired output of the training base, and to retain the triplet (, , ) giving the smallest MSE, if this one is considered to be acceptable, if not to decrease the variation of step  and to remake the training.

Table 5 The Modified Fuzzy ART Algorithm.

Algorithm-IV
Step 1: / To fix the variation of step .
Step 2: / For  going from 0 to 1 with a variation of step , carry out step 2.1
Step 2.1: / For  going from 0 to 1 with a variation of , carry out step 2.2
Step 2.2: / For  going from 0 to 1 with a variation of 
(a) Carry out the training of fuzzy ART
(b) Calculate MSE between the outputs obtained and the outputs of the training
base.
(c) Retain the best MSE and the associated parameters (, , ).
Step 3: / If MSE obtained is not satisfactory, to decrease  and to remake starting from first step.

The fuzzy ART network with fixed architecture has three layers. The first layer (F0) is the input layer, which consists of IM nodes (where IM is length of binary identifier string from section 2). Each node represents a pixel in the input pattern. The second layer (F1) is the cluster layer. The nodes in this second layer are constructed during the training phase. The third layer (F2) is the output layer. To be able to determine the values of the best network, we proceed as proposed in this section. A study of the parameters according to the step value λ was carried out. Table 6 includes the minimal mean square error (MSE) in training and control phase as well as the associated parameters. It is obvious that the mean square errors at training and control are proportional to the λ step. The minimal error is obtained for a value of λ equal to 0.01. The corresponding parameters are α = 0.69, β = 0.11 and ρ = 0.93 of the fuzzy ART network offering the best classification. In control phase, the mean square error is 0.0699.

4. Experimental Results

In this section, we describe a face database we used and then present a face authentication result under variant pose, illumination, scaling, rotation, blur and different expression (smiling, angry, and screaming). Our proposed method was implemented on the XM2VTS [34] and AR [35] face databases. The XM2VTS database is a multi-modal database consisting of face images, video sequences and speech recordings taken of 295 subjects at one month intervals. This database is available at the cost of distribution from the University of Surrey. The database is primarily intended for research and development of personal identity verification systems where it is reasonable to assume that the client will be cooperative. Since the data acquisition was distributed over a long period of time, significant variability of appearance of clients, e.g. changes of hair style, facial hair, shape and presence or absence of glasses, is present in this work. And, the AR database has contained color images corresponding to 126 people (70 men and 56 women). The pictures were taken at the CVC under strictly controlled conditions. No restrictions on wear (clothes, glasses, etc.), make-up, hair style, etc., were imposed on participants. Each person participated in two sessions, separated by 2 weeks’ time. The same pictures were taken in both sessions. Some sample examples of face images used in the training procedure are shown in Figure 4.

Figure 4. Some sample examples of face images used in this work.

Table 6 The evaluation of the modified fuzzy ART according to λ.

λ / Parameters / Learning MSE / Control MSE
α / β / ρ
0.01 / 0.69 / 0.11 / 0.93 / 0.1038 / 0.0699
0.05 / 0.70 / 0.15 / 0.90 / 0.0793 / 0.1038
0.10 / 0.70 / 0.90 / 0.80 / 0.1011 / 0.0992
0.20 / 0.80 / 0.80 / 0.80 / 0.1329 / 0.1313
0.50 / 0.00 / 1.00 / 0.00 / 0.3710 / 0.3456

Our proposed method has been compared with other approaches using the same database and test protocol presented in [27]. The success rates corresponding to evaluation and test sets are summarized in table 7.

5. Conclusions

We have introduced a novel face feature representation using shapes derived from the masked Trace transform. Our primary contribution in this work is the general framework for constructing robust features from the multi-resolution Trace transform. More practically, the shape Trace transform captures the key characteristics of face images by suppressing variation of recognition face, while maintaining discriminability. A robust measure, the fuzzy ART with supervised learning is used to search the optimal parameters of the algorithm. Extensive experimental results demonstrate that the average of accuracy rate of face recognition with variant pose, illumination, scaling, rotation, blur, reflection and difference expression is very high and it was found that our proposed method performed better than the other related works in all cases.

Table 7. Performance of the propose method (the results with * are from [27])

Reference

  1. J. R. Bhatnagar, B. Lall, and R. K. Patney, “Performance issues in biometric authentication based on information theoretic concepts: A review,” IETE Technical Review, vol. 27, pp. 273-285, July 2010.
  2. D. Lee, K. Choi, H. Choi and J. Kim, “Recognizable-Image Selection for Fingerprint Recognition With a Mobile-Device Camera,” IEEE Trans. on Systems Man and Cybernetics, vol. 38. no. 1. February 2008.
  3. J. Thornton, M. Savvides and V. Kumar, “A Bayesian Approach to Deformed Pattern Matching of Iris Images,” IEEE Tran. on Pattern Analysis and Machine Intelligence, Vol. 29 , no. 4, pp. 596- 606, April 2007.
  4. L. Zhang and D. Samaras, “Face Recognition from a Single Training Image under Arbitrary Unknown Lighting Using Spherical Harmonics,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 28, no. 3, pp.351 - 363, March 2006.
  5. M. R. Moradian ,A. Esmkhani , and F. M. Jafarlou , “Recognition of Persian handwritten digits using Characterization Loci and Mixture of Experts ,” International Journal of Digital Content Technology and its Applications, vol. 3, no. 3, pp. 42 - 46, September 2009.
  6. I. Mporas, T. Ganchev, O. Kocsis and N. Fakotakis, “Speech Enhancement for Robust Speech Recognition in Motocrycle Environment,” International Journal on Artificial Intelligence Tools, vol. 19, no. 2, pp.159-173, April 2010.
  7. A. Guven and I. Sogukpinar, “Understanding users' keystroke patterns for computer access security,” Computers & Security, vol. 22, no. 8, pp. 695-706, December 2003.
  8. A. M. Martinez and A. C. Kak, “PCA versus LDA,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 23, no. 2, pp. 228-233, February 2001.
  9. B. Moghaddam, “Principal Manifolds and Probabilistic Subspaces for Visual Recognition,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 6, pp. 780-788, June 2002.
  10. I. Craw, N. Costen, T. Kato and S. Akamatsu, “How Should We Represent Faces for Automatic Recognition?,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 8, pp. 725-736, August 1999.
  11. J. Zhang, Y. Yan and M. Lades, “Face Recognition: Eigenface, Elastic Matching, and Neural Nets,” Proc. of IEEE, vol. 85, no. 9, pp. 1423-1435, September 1997.
  12. M. Turk and A. Pentland, “Eigenfaces for Recognition”, Journal of Cognitive Neuroscience, Vol. 3, No. 1, pp. 71-86, Winter 1991.
  13. P. N. Belhumeur, J. P. Hespanha and D. J. Kriegman, “Eigenfaces vs. Fisherfaces: Recognition using Class Specific Linear Projection”, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 7, pp. 711-720, July 1997.
  14. A. Tefas, C. Kotropoulos and I. Pitas, “Using Support Vector Machines to Enhance the Performance of Elastic Graph Matching for Frontal Face Authentication," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 23, no. 7, pp. 735-746, July 2001.
  15. B. Duc, S. Fischer and J. Bigun, “Face Authentication with Gabor Information on Deformable Graphs,” IEEE Trans. Image Processing, vol. 8, no. 4, pp. 504-516, April 1999.
  16. C. L. Kotropoulos, A. Tefas and I. Pitas, “Frontal Face Authentication using Discriminating Grids with Morphological Feature Vectors,” IEEE Trans. Multimedia, vol. 2, no. 1, pp. 14-26, March 2000.
  17. J. Zhang, Y. Yan and M. Lades, “Face Recognition: Eigenface, Elastic Matching, and Neural Nets,” Proc. of IEEE, Vol. 85, No. 9, pp. 1423-1435, September 1997.
  18. L. Wiskott, J.-M. Fellous, N. Kruger and C. v.d. Malsburg, “Face Recognition by Elastic Bunch Graph Matching,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 7, pp. 775-779, July 1997.
  19. M. Lades, J. C. Vorbruggen, J. Buhmann, J. Lange, C. v.d. Malsburg, R. P.Wurtz and W. Konen, “Distortion Invariant Object Recognition in the Dynamic Link Architecture,” IEEE Trans. Computers, vol. 42, no. 3, pp. 300-311, March 1993.
  20. S. H. Lin, S. Y. Kung and L. J. Lin, “Face Recognition/Detection by Probabilistic Decision-Based Neural Network,” IEEE Trans. Neural Networks, vol. 8, no. 1, pp. 114-132, January 1997.
  21. S. Lawrence, C. L. Giles, A. C. Tsoi and A. D. Back, “Face Recognition: A Convolutional Neural-Network Approach,” IEEE Trans. Neural Networks, vol. 8, no. 1, pp. 98-113, January 1997.
  22. J. T. Chien and C. C. Wu, “DiscriminantWaveletfaces and Nearest Feature Classifiers for Face Recognition,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 12, pp. 1644-1649, December 2002.
  23. C. Liu and H.Wechsler, “A Shape- and Texture-Based Enhanced Fisher Classifier for Face Recognition,” IEEE Trans. Image Processing, vol. 10, no. 4, pp. 598-608, Apr. 2001.
  24. P. N. Belhumeur, J. P. Hespanha and D. J. Kriegman, “Eigenfaces vs. Fisherfaces: Recognition using Class Specific Linear Projection”, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 7, pp. 711-720, July 1997.
  25. A. Thammano and C. Rungruang, “Hausdorff ARTMAP for Human Face Recognition,” WSEAS Trans. Computers, vol. 3, no. 3, pp. 667-72. July 2004.
  26. S. Srisuk, M. Petruu, M. Petrou, R. Fooprateepsiri, K. Sunat, W. Kurutach, and P. Chopaka, “A Combination of Shape and Texture Classifiers for a Face Verification System,” Lecture Note on Computer Science, vol. 3072 pp. 44-51, July 2004.
  27. R. Fooprateepsiri and W. Kurutach, “A Fast and Accurate Face Authentication Method Using Hamming-Trace Transform Combination,” IETE Technical Review vol. 27, no. 5, pp. 365-370, September 2010.
  28. R. Fooprateepsiri, and W. Kurutach, “Facial Recognition using Hausdorff -Shape -Radon Transform," International Journal of Digital Content Technology and its Applications, vol. 3, no. 2, pp. 67-74, June 2009.
  29. S. Srisuk, W. Kurutach and K. Limpitikeat, “A Novel Approach for Robust, Fast and Accurate Face Detection,” International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol. 9, no. 6, pp. 769-779, December 2001.
  30. A. Kadyrov and M. Petrou, “The Trace Transform and Its Applications,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 23, no. 8, pp. 811-828, August 2001.
  31. G. A Carpenter, S. Grossberg and D. B. Rosen, “Fuzzy ART: An Adaptive Resonance Algorithm for Rapid, stable classification of Analog Patterns”, in International Joint Conference of Neural Networks, Seattle, Nov. 1991, pp. 411-416.
  32. G. A. Carpenter, S. Grossberg, N. Markuzon, J. H. Reynolds and D. B. Rosen, “Fuzzy ARTMAP: A Neural Network Architecture for Incremental Supervised Learning of Analog Multidimensional Maps”, IEEE Trans. Neural Networks, vol. 3 no. 5, September 1992.
  33. G. A. Carpenter, S. Grossberg, N. Markuzon and J. H. Reynolds, “A Fuzzy ARTMAP Nonparametric Probability Estimator for Nonstationary Pattern Recognition Problems”, IEEE Trans. Neural Networks, vol. 6, no. 6, November 1995.
  34. The XM2VTS database, Available:
  35. The AR Database, Available:

1