Modular Neural Networks with Type-2 Fuzzy Integration for Pattern ...
Modular Neural Networks with Type-2 Fuzzy Integration for Pattern Recognition of Iris Biometric Measure Fernando Gaxiola, Patricia Melin, Fevrier Valdez, and Oscar Castillo Tijuana Institute of Technology, Tijuana México [email protected], {pmelin,fevrier,ocastillo}@tectijuana.mx
Abstract. This paper presents a new modular neural network architecture that is used to build a system for pattern recognition based on the iris biometric measurement of persons. In this system, the properties of the person iris database are enhanced with image processing methods, and the coordinates of the center and radius of the iris are obtained to make a cut of the area of interest by removing the noise around the iris. The inputs to the modular neural network are the processed iris images and the output is the number of the identified person. The integration of the modules was done with a type-2 fuzzy integrator at the level of the sub modules, and with a gating network at the level of the modules. Keywords: Type-2 Fuzzy Logic, Modular Neural Network, Iris Biometric, Pattern Recognition.
1
Introduction
This paper is focused on the area of modular neural networks for pattern recognition based on biometric measures, specifically in the recognition by the human iris biometric measurement. At present, biometric measurements are being widely used for person recognition systems. A lot has been said about the use of such measures, particularly for the signature, fingerprint, face and voice. As more research was done in this area further biometric measures were discovered, among which the human iris by its peculiarity of not losing over the years its universality and authenticity. In order to get a good identification, we propose a modular neural network divided into three modules, each module’s input is a part of the database of human iris, and some methods or techniques are used for pre-processing the images such as normalization, resizing, cut, edge detection, among several others. Each module was divided into two sub modules with different neural networks. The rest of the paper is organized as follows: Section 2 contains a brief explanation from previous research with human iris for recognition and basic concepts relevant to the area, section 3 defines the method proposed for this research and the description of problem addressed in this paper, section 4 presents the results achieved in this work and Section 5 draws conclusions and future work. I. Batyrshin and G. Sidorov (Eds.): MICAI 2011, Part II, LNAI 7095, pp. 363–373, 2011. © Springer-Verlag Berlin Heidelberg 2011
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Background and Basic Concepts
2.1
Modular Neural Network
An artificial neural network (ANN) is a distributed computing scheme based on the structure of the nervous system of humans. The architecture of a neural network is formed by connecting multiple elementary processors, this being an adaptive system that has an algorithm to adjust their weights (free parameters) to achieve the performance requirements of the problem based on representative samples [1][2]. The most important property of artificial neural networks is their ability to learn from a training set of patterns, i.e. able to find a model that fits the data [3][4][5]. The modular neural networks are composed of simpler networks that behave as functional blocks and these are the neural modules. A modular neural network works similarly to a classical neural network, as it is composed of sigmoidal activation neurons or linear, discrete and trains with common learning algorithms (gradient descent with adaptive learning algorithm, backpropagation, gradient descent scaling , etc.). What distinguishes it from other neural models is that it develops based functional modules and each module runs a neural network with the same characteristics or different (input layer, hidden layers, output layer, depending activation, learning algorithm, number of neurons per layer, etc.). In this model the modules work independently and in the end a form commonly called integrator performs the function of deciding between the different modules to determine which of them has the best solution (including gating networks, fuzzy integrator, etc.). [6]. Figure 1 shows a modular neural network scheme:
Fig. 1. Schematic of an modular artificial neural network
2.2
Fuzzy Logic
Fuzzy logic is an area of soft computing that enables a computer system to reason with uncertainty [7]. A fuzzy inference system consists of a set of if-then rules
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defined over fuzzy sets. Fuzzy sets generalize the concept of a traditional set by allowing the membership degree to be any value between 0 and 1 [8]. This corresponds, in the real world, to many situations where it is difficult to decide in an unambiguous manner if something belongs or not to a specific class [9]. The basic structure of a fuzzy inference system consists of three conceptual components: a rule base, which contains a selection of fuzzy rules, a database (or dictionary) which defines the membership functions used in the rules, and a reasoning mechanism that performs the inference procedure [10][11][12]. 2.3
Type-2 Fuzzy Logic
The concept of a type-2 fuzzy set, was introduced by Zadeh (1975) as an extension of the concept of an ordinary fuzzy set (henceforth called a “type-1 fuzzy set”). A type-2 fuzzy set is characterized by a fuzzy membership function, i.e., the membership grade for each element of this set is a fuzzy set in [0,1], unlike a type-1 set where the membership grade is a crisp number in [0,1]. Such sets can be used in situations where there is uncertainty about the membership grades themselves, e.g., uncertainty in the shape of the membership function or in some of its parameters. Consider the transition from ordinary sets to fuzzy sets. When we cannot determine the membership of an element in a set as 0 or 1, we use fuzzy sets of type-1. Similarly, when the situation is so fuzzy that we have trouble determining the membership grade even as a crisp number in [0,1], we use fuzzy sets of type-2 [13][14][15][16][17][18]. 2.4
Historical Development
The first use of the iris was presented in Paris, where criminals were classified according to the color of their eyes following a proposal by the French ophthalmologist Bertillon (1880) [19]. Research in visual identification technology began in 1935. During that year an article appeared in the ‘New York State Journal of Medicine’, which suggested that "the pattern of arteries and veins of the retina could be used for unique identification of an individual" [20]. After researching and documenting the potential use of the iris as a tool to identify people, ophthalmologists Flom and Safir patented their idea in 1987 [21]; and later, in 1989, they patented algorithms developed with the mathematician Daugman. Thereafter, other authors developed similar approaches [20]. In 2001, Daugman also presented a new algorithm for the recognition of people using the biometric measurement of Iris [22]. In 2005, Roy proposes an iris recognition system for the identification of persons using support vector machine [23]. In 2006, Cho and Kim presented a new method to determine the winner in LVQ neural network [24].
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In 2009, Sarhan used the discrete cosine transform for feature extraction and artificial neural network for recognition [25]; Abiyev and Altunkaya presented the iris recognition system using neural network [26]. The literature has well documented the uniqueness of visual identification. The iris is so unique that there are no two irises alike, even twins, in all humanity. The probability of two irises producing the same code is 1 in 1078, becoming known that the earth's population is estimated at approximately 1010 million [27], it is almost impossible to occur.
3
Proposed Method and Problem Description
This work focuses primarily on the identification of individuals. This problem is well known by the scientific community, as innumerable investigations have been developed in this area, considering various measures to achieve it with biometrics (fingerprint, voice, palm of hand, signature) and various methods of identification (with particular emphasis on neural networks). The specific problem considered in this work is: "Obtain a good percentage of person identification based on the biometric measurement of the human iris, using modular neural networks”. We used a database of human Iris from the Institute of Automation of the Chinese Academy of Sciences (CASIA) (see Figure 2). It consists of 14 images (7 right eye - 7 left eye) per person, for a total of 99 individuals, giving a total of 1386 images. The image dimensions are 320 x 280, JPEG format [28][29][30].
Fig. 2. Examples of the human iris images from the CASIA database
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Proposed Modular Neural Network
The work was focused on the recognition of persons using a modular neural network with type-2 fuzzy integration, and image preprocessing methods to obtain the interest region of the iris.
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Iris Image Pre-processing
The pre-processing that has been applied to the images before they are introduced to the modular neural network is as follows: • • • • • 4.2
Obtain the coordinates and radius of the iris and pupil using the method developed by Masek and Kovesi [31]. Making the cut in the Iris. Resize the cut of the Iris to 21-21 Convert images from vector to matrix Normalize the images. Modular Neural Network with Type-2 Fuzzy Logic Integration
The proposed modular neural network consist of three modules, in each module the inputs are the preprocessed iris images, of which the first 33 persons are the input in the first module, the next 33 persons in the second module and the last 33 persons in the third module, given a total of 99 persons (792 for training – 594 for test in total and 264 for training – 198 for test in each module). All the modules consist of a neural network with an input layer (the preprocessed image iris), two hidden layers and one output layer (see Figure 3). Each module has two sub modules with different architecture and learning algorithm.
Fig. 3. Proposed modular neural network architecture
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In the first module, the first sub module has 70 neurons in the first hidden layer and 67 neurons in the second hidden layer, and uses the gradient descent with learning rate algorithm for training; the second sub module has 70 neurons in first hidden layer and 41 neurons in the second layer, and uses the scaled gradient conjugate algorithm for training. In the second module, the first sub module has 70 neurons in the first hidden layer and 67 neurons in the second hidden layer, and uses the gradient descent with learning rate algorithm for training; the second sub module has 70 neurons in first hidden layer and 100 neurons in the second layer, and uses the scaled gradient conjugate algorithm for training. In the third module, the first sub module has 70 neurons in the first hidden layer and 100 neurons in the second hidden layer, and uses he scaled gradient conjugate algorithm for training; the second sub module has 70 neurons in first hidden layer and 100 neurons in the second layer, and uses gradient descent with momentum and learning rate algorithm for training. The integration of the two sub modules in each module are realized with type-2 fuzzy integration, which has two inputs, the output of the first and second sub module (see Figure 4); the input has three membership functions, two of generalized bell type and one of trapezoid type; the output are the recognition person with two membership functions (see Figure 5 (a) and 5 (b)), one of trapezoid type and one of generalized bell type (see Figure 5 (c)); and work with nine rules (see Figure 6). The integration of the modules is realized with gating network integration.
Fig. 4. Type-2 fuzzy integration system
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(c) Fig. 5. (a) Membership functions of first input. (b) Membership functions of second input. (c) Membership functions of output.
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Fig. 6. Rules of the type-2 fuzzy integrator
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Simulation Results
10 tests were performed with the proposed modular neural network under the same conditions and the same database of the iris; in Table 1 we show the obtained results: Table 1. Table of results from the experiments
No.
Epoch
Error
Total Rec.
T1
8000
0.000001
T2
8000
0.000001
T3
8000
0.000001
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8000
0.000001
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0.000001
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8000
0.000001
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8000
0.000001
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8000
0.000001
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8000
0.000001
T10
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0.000001
97.98 (582/594) 96.29 (572/594) 96.96 (576/594) 96.13 (571/594) 96.80 (575/594) 96.29 (572/594) 96.13 (571/594) 95.95 (570/594) 96.29 (/572594) 95.95 (570/594)
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The best result is a total recognition of 582 out of 594 images of iris of 99 persons; giving a recognition rate of 97.98 %. The average of the 10 tests is 96.47 percent of recognition. In Table 2, we present a comparison of results with those of other researchers obtained for iris recognition of persons, realized with different or similar methods. Table 2. Table of comparison of results
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Method.
Percentage of recognition
Proposed Method
97.98 %
Gaxiola [32]
97.13 %
Sanchez-Avila [33]
97.89 %
Ma [28]
98.00 %
Tisse [18]
89.37 %
Daugman [21]
99.90 %
Sarhan [24]
96.00 %
Conclusions
In this paper we presented a modular neural network architecture with type-2 fuzzy integration, which has as input the database of human iris images, three modules with two sub modules for each module for training. In this work, several methods were used to make the elimination of noise that the original pictures had until the coordinates of the center and radius were obtained, and then make a cut around the iris. The type-2 fuzzy integration provides optimal results for integration of a modular neural network, because the results obtained are on average of 96.47 percent of recognition and a best result of 97.98 percent of recognition. The type-2 fuzzy integration manages uncertainty that allows to work with more complex pattern, which allows obtaining better results.
References [1] Cazorla, M., Escolano, F.: Two Bayesian Methods for Junction Detection. IEEE Transaction on Image Processing 12(3), 317–327 (2003) [2] Martinez, G., Melin, P., Bravo, D., Gonzalez, F., Gonzalez, M.: Modular Neural Networks and Fuzzy Sugeno Integral for Face and Fingerprint Recognition. Advances in Soft computing 34, 603–618 (2006)
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[3] De Wilde, P.: The Magnitude of the Diagonal Elements in Neural Networks. Neural Networks 10(3), 499–504 (1997) [4] Salazar, P.A., Melin, P., Castillo, O.: A New Biometric Recognition Technique Based on Hand Geometry and Voice Using Neural Networks and Fuzzy Logic. Soft Computing for Hybrid Intelligent Systems, 171–186 (2008) [5] Phansalkar, V.V., Sastrq, P.S.: Analysis of the Back-Propagation Algorithm with Momentum. IEEE Transactions on Neural Networks 5(3), 505–506 (1994) [6] Morcego, B., Cembrano, G., Fuertes, J.: MIGA, A Software Tool for Nonlinear System Modelling with Modular Neural Networks. Applied Intelligence. Kluwer Academic Publishers (2004) [7] Castillo, O., Melin, P.: Soft Computing for Control of Non-Linear Dynamical Systems. Springer, Heidelberg (2001) [8] Zadeh, L.A.: Fuzzy Sets. Journal of Information and Control 8, 338–353 (1965) [9] Melin, P., Castillo, O.: Hybrid Intelligent Systems for Pattern Recognition Using Soft Computing, pp. 2–3. Springer, Heidelberg (2005) [10] Okamura, M., Kikuchi, H., Yager, R., Nakanishi, S.: Character diagnosis of fuzzy systems by genetic algorithm and fuzzy inference. In: Proceedings of the Vietnam-Japan Bilateral Symposium on Fuzzy Systems and Applications, Halong Bay, Vietnam, pp. 468–473 (1998) [11] Wang, W., Bridges, S.: Genetic Algorithm Optimization of Membership Functions for Mining Fuzzy Association Rules, Department of Computer Science Mississippi State University (March 2, 2000) [12] Jang, J., Sun, C., Mizutani, E.: Neuro-Fuzzy and Soft Computing. Prentice Hall, New Jersey (1997) [13] Castillo, O., Melin, P.: Type-2 Fuzzy Logic Theory and Applications, pp. 29–43. Springer, Berlin (2008) [14] Castro, J.R., Castillo, O., Melin, P.: An Interval Type-2 Fuzzy Logic Toolbox for Control Applications. FUZZ-IEEE, 1–6 (2007) [15] Castro, J.R., Castillo, O., Melin, P., Rodriguez-Diaz, A.: Building Fuzzy Inference Systems with a New Interval Type-2 Fuzzy Logic Toolbox. Transactions on Computational Science 1, 104–114 (2008) [16] Hidalgo, D., Castillo, O., Melin, P.: Type-1 and Type-2 Fuzzy Inference Systems as Integration Methods in Modular Neural Networks for Multimodal Biometry and Its Optimization with Genetic Algorithms. Soft Computing for Hybrid Intelligent Systems, 89–114 (2008) [17] Sanchez, D., Melin, P.: Optimization of modular neural networks and type-2 fuzzy integrators using hierarchical genetic algorithms for human recognition. In: IFSA 2011, OS-414, Surabaya-Bali, Indonesia (2011) [18] Sepúlveda, R., Castillo, O., Melin, P., Rodriguez, A., Montiel, O.: Experimental study of intelligent controllers under uncertainty using type-1 and type-2 fuzzy logic. Information Sciences 177(11), 2023–2048 (2007) [19] Tisse, C., Martin, L., Torres, L., Robert, M.: Person identification technique using human iris recognition. Universite de Montepellier (2000) [20] López, J., González, J.: State of the Art: Automatic Recognition of Human Iris. Politécnico Colombiano, and National University of Colombia, Scientia et Technica Año XI (29), 77–81 (2005) [21] Khaw, P.: Iris recognition technology for improved authentication, Sala de Lectura de Seguridad de la Información, SANS Institute, pp. 1–17 (2002)
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[22] Daugman, J.: Statistical Richness of Visual Phase Information: Update on Recognizing Persons by Iris Patterns. International Journal of Computer Vision 45(1), 25–38 (2001) [23] Roy, K., Bhattacharya, P.: Iris Recognition with Support Vector Machines. In: Zhang, D., Jain, A.K. (eds.) ICB 2005. LNCS, vol. 3832, pp. 486–492. Springer, Heidelberg (2005) [24] Cho, S., Kim, J.: Iris Recognition Using LVQ Neural Network. In: Wang, J., Yi, Z., Żurada, J.M., Lu, B.-L., Yin, H. (eds.) ISNN 2006. LNCS, vol. 3972, pp. 26–33. Springer, Heidelberg (2006) [25] Sarhan, A.: Iris Recognition using Discrete Cosine Transform and Artificial Neural Networks. Journal of Computer Science 5, 369–373 (2009) [26] Abiyev, R., Altunkaya, K.: Neural Network based Biometric Personal Identification with fast iris segmentation. International Journal of Control, Automation and Systems 7(1), 17–23 (2009) [27] Sánchez, O., González, J.: Access Control Based on Iris Recognition, Technological University Corporation of Bolívar, Faculty of Electrical Engineering, Electronics and Mechatronics, Cartagena of Indias, Monography, pp. 1–137 (November 2003) [28] Muron, A., Pospisil, J.: The human iris structure and its usages, Czech Republic, Physica, pp. 89–95 (2000) [29] Ma, L., Wang, Y., Tan, T.: Iris recognition based on multichannel Gabor filtering. In: 5th Asian Conference on Computer Vision, ACCV 2002, Melbourne, Australia, vol. 1, pp. 279–283 (2002) [30] Database of Human Iris. Institute of Automation of Chinese Academy of Sciences (CASIA). Found on the Web page, http://www.cbsr.ia.ac.cn/english/IrisDatabase.asp [31] Masek, L., Kovesi, P.: MATLAB Source Code for a Biometric Identification System Based on Iris Patterns. The School of Computer Science and Software Engineering, The University of Western Australia (2003) [32] Gaxiola, F., Melin, P., López, M.: Modular Neural Networks for Person Recognition Using the Contour Segmentation of the Human Iris Biometric Measurement. In: Melin, P., Kacprzyk, J., Pedrycz, W. (eds.) Soft Computing for Recognition Based on Biometrics. SCI, vol. 312, pp. 137–153. Springer, Heidelberg (2010) [33] Sanchez-Avila, C., Sanchez-Reillo, R., de Martin-Roche, D.: Iris Recognition for Biometric Identification using Dyadic Wavelet Transform Zero-Crossing. In: Proceedings of the IEEE 35th International, Camahan Conference on Security Technology, pp. 272–277 (2001)
Abstract. This paper presents a new modular neural network architecture that is used to build a system for pattern recognition based on the iris biometric measurement of persons. In this system, the properties of the person iris database are enhanced with image processing methods, and the coordinates of the center and radius of the iris are obtained to make a cut of the area of interest by removing the noise around the iris. The inputs to the modular neural network are the processed iris images and the output is the number of the identified person. The integration of the modules was done with a type-2 fuzzy integrator at the level of the sub modules, and with a gating network at the level of the modules. Keywords: Type-2 Fuzzy Logic, Modular Neural Network, Iris Biometric, Pattern Recognition.
1
Introduction
This paper is focused on the area of modular neural networks for pattern recognition based on biometric measures, specifically in the recognition by the human iris biometric measurement. At present, biometric measurements are being widely used for person recognition systems. A lot has been said about the use of such measures, particularly for the signature, fingerprint, face and voice. As more research was done in this area further biometric measures were discovered, among which the human iris by its peculiarity of not losing over the years its universality and authenticity. In order to get a good identification, we propose a modular neural network divided into three modules, each module’s input is a part of the database of human iris, and some methods or techniques are used for pre-processing the images such as normalization, resizing, cut, edge detection, among several others. Each module was divided into two sub modules with different neural networks. The rest of the paper is organized as follows: Section 2 contains a brief explanation from previous research with human iris for recognition and basic concepts relevant to the area, section 3 defines the method proposed for this research and the description of problem addressed in this paper, section 4 presents the results achieved in this work and Section 5 draws conclusions and future work. I. Batyrshin and G. Sidorov (Eds.): MICAI 2011, Part II, LNAI 7095, pp. 363–373, 2011. © Springer-Verlag Berlin Heidelberg 2011
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Background and Basic Concepts
2.1
Modular Neural Network
An artificial neural network (ANN) is a distributed computing scheme based on the structure of the nervous system of humans. The architecture of a neural network is formed by connecting multiple elementary processors, this being an adaptive system that has an algorithm to adjust their weights (free parameters) to achieve the performance requirements of the problem based on representative samples [1][2]. The most important property of artificial neural networks is their ability to learn from a training set of patterns, i.e. able to find a model that fits the data [3][4][5]. The modular neural networks are composed of simpler networks that behave as functional blocks and these are the neural modules. A modular neural network works similarly to a classical neural network, as it is composed of sigmoidal activation neurons or linear, discrete and trains with common learning algorithms (gradient descent with adaptive learning algorithm, backpropagation, gradient descent scaling , etc.). What distinguishes it from other neural models is that it develops based functional modules and each module runs a neural network with the same characteristics or different (input layer, hidden layers, output layer, depending activation, learning algorithm, number of neurons per layer, etc.). In this model the modules work independently and in the end a form commonly called integrator performs the function of deciding between the different modules to determine which of them has the best solution (including gating networks, fuzzy integrator, etc.). [6]. Figure 1 shows a modular neural network scheme:
Fig. 1. Schematic of an modular artificial neural network
2.2
Fuzzy Logic
Fuzzy logic is an area of soft computing that enables a computer system to reason with uncertainty [7]. A fuzzy inference system consists of a set of if-then rules
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defined over fuzzy sets. Fuzzy sets generalize the concept of a traditional set by allowing the membership degree to be any value between 0 and 1 [8]. This corresponds, in the real world, to many situations where it is difficult to decide in an unambiguous manner if something belongs or not to a specific class [9]. The basic structure of a fuzzy inference system consists of three conceptual components: a rule base, which contains a selection of fuzzy rules, a database (or dictionary) which defines the membership functions used in the rules, and a reasoning mechanism that performs the inference procedure [10][11][12]. 2.3
Type-2 Fuzzy Logic
The concept of a type-2 fuzzy set, was introduced by Zadeh (1975) as an extension of the concept of an ordinary fuzzy set (henceforth called a “type-1 fuzzy set”). A type-2 fuzzy set is characterized by a fuzzy membership function, i.e., the membership grade for each element of this set is a fuzzy set in [0,1], unlike a type-1 set where the membership grade is a crisp number in [0,1]. Such sets can be used in situations where there is uncertainty about the membership grades themselves, e.g., uncertainty in the shape of the membership function or in some of its parameters. Consider the transition from ordinary sets to fuzzy sets. When we cannot determine the membership of an element in a set as 0 or 1, we use fuzzy sets of type-1. Similarly, when the situation is so fuzzy that we have trouble determining the membership grade even as a crisp number in [0,1], we use fuzzy sets of type-2 [13][14][15][16][17][18]. 2.4
Historical Development
The first use of the iris was presented in Paris, where criminals were classified according to the color of their eyes following a proposal by the French ophthalmologist Bertillon (1880) [19]. Research in visual identification technology began in 1935. During that year an article appeared in the ‘New York State Journal of Medicine’, which suggested that "the pattern of arteries and veins of the retina could be used for unique identification of an individual" [20]. After researching and documenting the potential use of the iris as a tool to identify people, ophthalmologists Flom and Safir patented their idea in 1987 [21]; and later, in 1989, they patented algorithms developed with the mathematician Daugman. Thereafter, other authors developed similar approaches [20]. In 2001, Daugman also presented a new algorithm for the recognition of people using the biometric measurement of Iris [22]. In 2005, Roy proposes an iris recognition system for the identification of persons using support vector machine [23]. In 2006, Cho and Kim presented a new method to determine the winner in LVQ neural network [24].
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In 2009, Sarhan used the discrete cosine transform for feature extraction and artificial neural network for recognition [25]; Abiyev and Altunkaya presented the iris recognition system using neural network [26]. The literature has well documented the uniqueness of visual identification. The iris is so unique that there are no two irises alike, even twins, in all humanity. The probability of two irises producing the same code is 1 in 1078, becoming known that the earth's population is estimated at approximately 1010 million [27], it is almost impossible to occur.
3
Proposed Method and Problem Description
This work focuses primarily on the identification of individuals. This problem is well known by the scientific community, as innumerable investigations have been developed in this area, considering various measures to achieve it with biometrics (fingerprint, voice, palm of hand, signature) and various methods of identification (with particular emphasis on neural networks). The specific problem considered in this work is: "Obtain a good percentage of person identification based on the biometric measurement of the human iris, using modular neural networks”. We used a database of human Iris from the Institute of Automation of the Chinese Academy of Sciences (CASIA) (see Figure 2). It consists of 14 images (7 right eye - 7 left eye) per person, for a total of 99 individuals, giving a total of 1386 images. The image dimensions are 320 x 280, JPEG format [28][29][30].
Fig. 2. Examples of the human iris images from the CASIA database
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Proposed Modular Neural Network
The work was focused on the recognition of persons using a modular neural network with type-2 fuzzy integration, and image preprocessing methods to obtain the interest region of the iris.
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Iris Image Pre-processing
The pre-processing that has been applied to the images before they are introduced to the modular neural network is as follows: • • • • • 4.2
Obtain the coordinates and radius of the iris and pupil using the method developed by Masek and Kovesi [31]. Making the cut in the Iris. Resize the cut of the Iris to 21-21 Convert images from vector to matrix Normalize the images. Modular Neural Network with Type-2 Fuzzy Logic Integration
The proposed modular neural network consist of three modules, in each module the inputs are the preprocessed iris images, of which the first 33 persons are the input in the first module, the next 33 persons in the second module and the last 33 persons in the third module, given a total of 99 persons (792 for training – 594 for test in total and 264 for training – 198 for test in each module). All the modules consist of a neural network with an input layer (the preprocessed image iris), two hidden layers and one output layer (see Figure 3). Each module has two sub modules with different architecture and learning algorithm.
Fig. 3. Proposed modular neural network architecture
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In the first module, the first sub module has 70 neurons in the first hidden layer and 67 neurons in the second hidden layer, and uses the gradient descent with learning rate algorithm for training; the second sub module has 70 neurons in first hidden layer and 41 neurons in the second layer, and uses the scaled gradient conjugate algorithm for training. In the second module, the first sub module has 70 neurons in the first hidden layer and 67 neurons in the second hidden layer, and uses the gradient descent with learning rate algorithm for training; the second sub module has 70 neurons in first hidden layer and 100 neurons in the second layer, and uses the scaled gradient conjugate algorithm for training. In the third module, the first sub module has 70 neurons in the first hidden layer and 100 neurons in the second hidden layer, and uses he scaled gradient conjugate algorithm for training; the second sub module has 70 neurons in first hidden layer and 100 neurons in the second layer, and uses gradient descent with momentum and learning rate algorithm for training. The integration of the two sub modules in each module are realized with type-2 fuzzy integration, which has two inputs, the output of the first and second sub module (see Figure 4); the input has three membership functions, two of generalized bell type and one of trapezoid type; the output are the recognition person with two membership functions (see Figure 5 (a) and 5 (b)), one of trapezoid type and one of generalized bell type (see Figure 5 (c)); and work with nine rules (see Figure 6). The integration of the modules is realized with gating network integration.
Fig. 4. Type-2 fuzzy integration system
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(c) Fig. 5. (a) Membership functions of first input. (b) Membership functions of second input. (c) Membership functions of output.
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Fig. 6. Rules of the type-2 fuzzy integrator
5
Simulation Results
10 tests were performed with the proposed modular neural network under the same conditions and the same database of the iris; in Table 1 we show the obtained results: Table 1. Table of results from the experiments
No.
Epoch
Error
Total Rec.
T1
8000
0.000001
T2
8000
0.000001
T3
8000
0.000001
T4
8000
0.000001
T5
8000
0.000001
T6
8000
0.000001
T7
8000
0.000001
T8
8000
0.000001
T9
8000
0.000001
T10
8000
0.000001
97.98 (582/594) 96.29 (572/594) 96.96 (576/594) 96.13 (571/594) 96.80 (575/594) 96.29 (572/594) 96.13 (571/594) 95.95 (570/594) 96.29 (/572594) 95.95 (570/594)
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The best result is a total recognition of 582 out of 594 images of iris of 99 persons; giving a recognition rate of 97.98 %. The average of the 10 tests is 96.47 percent of recognition. In Table 2, we present a comparison of results with those of other researchers obtained for iris recognition of persons, realized with different or similar methods. Table 2. Table of comparison of results
6
Method.
Percentage of recognition
Proposed Method
97.98 %
Gaxiola [32]
97.13 %
Sanchez-Avila [33]
97.89 %
Ma [28]
98.00 %
Tisse [18]
89.37 %
Daugman [21]
99.90 %
Sarhan [24]
96.00 %
Conclusions
In this paper we presented a modular neural network architecture with type-2 fuzzy integration, which has as input the database of human iris images, three modules with two sub modules for each module for training. In this work, several methods were used to make the elimination of noise that the original pictures had until the coordinates of the center and radius were obtained, and then make a cut around the iris. The type-2 fuzzy integration provides optimal results for integration of a modular neural network, because the results obtained are on average of 96.47 percent of recognition and a best result of 97.98 percent of recognition. The type-2 fuzzy integration manages uncertainty that allows to work with more complex pattern, which allows obtaining better results.
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