Combining Bayesian Conditioning with Distributed Neural Networks

Combining Bayesian Conditioning with Distributed Neural Networks Vallesi Germano Dragoni Aldo Franco Montesanto Anna Univ. Politecnica delle Marche Via Brecce Bianche 1 Cap: 60131 Ancona 0390712204390 Univ. Politecnica delle Marche Via Brecce Bianche 1 Cap: 60131 Ancona 0390712204390 Univ. Politecnica delle Marche Via Brecce Bianche 1 Cap: 60131 Ancona 0390712204449 g.vallesi@univpm.it a.f.dragoni@univpm.it a.montesanto@univpm.it ABSTRACT There are many methods to perform iris biometric identification systems, but all of them have a problem: the presence of noises in the image of the eye (eyelid, eyelashes, etc…). To remove it many authors apply appropriate preprocessing to the image, but unfortunately this yields losses of information. Our work aims at correctly recognizing the subject also in presence of high rates of noise. The basic idea is that of partitioning the image of iris into 8 not-interleaved segments of the same size. Each segment is given to a Neural Network (LVQ network) which generates prototypes with a high resistance to noise. Notwithstanding this, the 8 LVQ nets may still disagree in identifying the subject. In this paper we apply a method developed by the “belief revision” community to identify conflicts and rearrange the degrees of reliability of each expert (the LVQ nets) through a Bayesian algorithm. This estimated ranking of reliability is useful to take the final decision. Our work has produced an interesting 91.67 % of positive identification on Test set. Categories and Subject Descriptors I.2.6 [Artificial Intelligence]: Learning – connectionism and neural nets. General Terms Reliability. Keywords Biometry Identification, Iris Detection, Hybrid Systems, Artificial Neural Networks, LVQ, Bayesian Conditioning. 1.INTRODUCTION Biometrics automated personal identification has recently received considerable attention with increasing emphasis on access control. Among biometric technologies, iris recognition is Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Conference’04, Month 1–2, 2004, City, State, Country. Copyright 2004 ACM 1-58113-000-0/00/0004…$5.00. distinguish for its high reliability and is currently a subject great interest in academia and industry [1], [ 2]. Irises are particularly advantageous for use in biometric recognition systems since they have been shown to be especially stable throughout a person’s life. Patterns in human iris remain constant from the age of one year. The procedure is very quick and non-invasive, requiring only that a photograph be taken. Iris and retina have been shown to have higher degrees of distinctiveness than hand or finger geometry. The actual pattern within the iris is not determined by genetics and is so random that an individual’s left and right irises are as different from each other as from the irises of an other person. Even monozygotic twins have completely different iris patterns. One iris contains more data than in a person’s finger, face and a hand combined. This data-richness means that it is possible to gain an accurate pattern match even if the eye is partially obscured by eyelashes or eyelids. Much work has been done on coding the human iris. According to the various iris features utilized, these works can be grouped into three main categories: Zero-crossing representation [3]; Phasebased method [4], [5]; Texture analysis [2], [6]. In general, a typical iris recognition system involves four steps: iris imaging, iris detection, iris image quality assessment and iris recognition. Our paper wants to work into the last two steps, working directly on the image of the iris with a pattern recognition technique obtained from the union of neural networks (LVQ) [7] and Bayesian conditioning [8], [9], and [10]. The iris database used for the training of the neural networks and to the test is the CASIA [11] database. 2.CLASSIC APPROACHES TO IRIS RECOGNITION The French ophthalmologist Alphonse Bertillon was the first one who proposed the use of iris pattern as a basis for personal identification [12], but most works are done in the last decade. Daugman [1], [4] used multiscale quadrature wavelets to extract texture phase structure information of the iris to generate a 2048bit iris code and he compared the difference between a pair of iris representation by computing their Hamming distance. He showed that for identification, it is enough to have a lower than 0.34 Hamming distance with any of the iris template in database. Wildes et al. [2], [13] represented the iris pattern using a fourlevel Laplacian pyramid and the quality of matching was determined by the normalized correlation results between the acquired iris image and the stored template. Boles and Boashash [14] used zero-crossing of 1D wavelet at various resolution levels to distinguish the texture of iris. Sanchez-Reillo and SanchezAvila in [15] provided a partial implementation of the algorithm by Daugman. Also their other work on developing the method of Boles and Boashash by using different distance measures (such as Hamming and Euclidean distances) for matching was reported in [3]. Lim et al. [6] used 2D Haar wavelet and quantized the 4 thlevel high-frequency information to form an 87-binary code length as feature vector and applied an LVQ neural network for classification. Tisse et al. [5] constructed the analytic image (a combination of the original image and its Hilbert transform) to demodulate the iris texture. Ma et al. [16], [17] adopted a wellknown texture analysis method to capture both global and local details in iris. Bae et al. [18] projected the iris signal onto a bank of basis vectors derived by independent component analysis and quantized the resulting projection coefficients as features. Nam et al [19] exploited a scale-space filtering to extract unique features that use the direction of concavity of an image from an iris image. Using sharp variations points in iris was represented by Ma et al. [20]. They constructed one-dimensional intensity signal and used a particular class of wavelets with vector of position sequence of local sharp variation point as features. 3.LVQ NEURAL NETWORKS Learning vector quantization (LVQ) originally was introduced by Linde et al. [21] and Gray [22] as a tool for image data compression. Later it was adapted by Kohonen [7] for pattern recognition, because it is a special case of SOM, where LVQ is a supervised Neural Network that uses class information to move the weight vector slightly, so as to improve the quality of the classifier decision regions. Learning is performed in a supervised, decision-controlled teaching process. This method is basically a nearest-neighbour method, as the smallest distance of the unknown vector from a set of reference vectors is sought. In our system we used the LVQ1; it consists of two layers, input and output. The dimension of the input layer is the same of the input vector (iris images). Each node in the output layer represents one output class. The activation of each output node depends on Euclidean distance between the input vector and the input weight vector. During the training the weight vector is adjusted according to the output class and the target class. The target class is the desirable target. Let wc be the input weight vector of the output class node, x is the target class. The weights are adjusted according to the following equations: wc ( n  1)  wc ( n )   ( n ) s ( n )[ x ( n )  wc ( n )] (1) 0   ( n )  1, s(n)  1 if the calssification is correct, (2) 1 if the classification is wrong, where  ( n ) is the learning rate at the nth epoch. It is desirable that it decreases monotonically with the number of iterations n . The input weights of other nodes remain unchanged. Using this algorithm, the input weight vector will get closer to the input vector as time progresses. The LVQ algorithms are sensitive to the starting point, i.e. to the initial values of prototype vectors, which can affect both the speed of convergence and the final recognition error. Considering the high speed of the k-means algorithm, it is recommended that the k-means algorithm be implemented at the beginning of the LVQ training algorithm, and that the resultant cluster centres be assigned as the initial prototype vectors. This initializing approach could be extremely valuable for databases with a huge number of samples or with a slow rate of convergence. The performance of LVQ algorithms depends to the size of network, database, training algorithm and initial point. 4.BELIEF REVISION MECHANISM In this scenario we have a collective activity of a set of interacting agents, LVQ Neural Networks, in which each component contributes with its local beliefs that is their outputs. Belief Revision is an emergent discipline from Artificial Intelligence that studies how the new information changes the previously held knowledge base. The ability to revise opinions and beliefs is imperative for intelligent systems exchanging information in a dynamic word. Let S = {S1, … , Sn} be the set of the information sources, and T = {<S1 ; R1>, … , <Sn ; Rn>} the “reliability set”, where Ri (a real in [0,1]) is the degree of reliability of Si, interpreted as the a-priori probability that Si is reliable. After all the sources have given their information, it is possible to estimate their a-posteriori degree of reliability from the crossexamination of their outputs. Dragoni et al. [8], [9], [10] adopted the Bayesian conditioning in a decision aid for judicial proceedings to help assess witness deception. Since our sources are independent, the probability that only the sources belonged to a subset  S of this hypothesis is: R ( )  �R ��(1  R ) i S i � i S i � (3) this combined reliability can be calculated for any Φ holding that: ￥R ()  1  2 S (4) If the sources belonging to a certain Φ give incompatible information then R(Φ) must be set at zero. So what we do is: • • • finding all the minimal subsets of contradictory sources finding all their supersets summing up into RContradictory the reliability of all these sets • putting at zero all their reliabilities • dividing the reliability of each non-contradictory set of sources by 1- RContradictory The last step assures that the constrain (4) is still satisfied and it is well known as “Bayesian Conditioning”. The new degree of reliability of each Φ is called “revised reliability” and we label it NR(Φ). The revised reliability NRi of each source Si is defined as the sum of the revised reliability of any Φ containing Si. An important feature of this way to recalculate the sources’ reliability is that if Si is involved in contradictions, then NRi ≤ Ri, otherwise NRi = Ri. 5.IMPLEMENTATION This work is an iris recognition system based on neural networks, but unlike previous works [6] the input of networks are the images of irises and not their transformation (2D Haar wavelet transform, 2D Gabor filter, etc. ...). We used the CASIA database [11], form which we take randomly 12 subjects (from the 411 of the database) to form the core group on which to work. Daugman [1], [4] suggested a normal Cartesian to Polar transform that remaps each pixel in iris area into a pair of polar coordinates (r, θ) where r and θ is on interval [0; 1] and [0; 2π] respectively. The remapping of the iris image I(x,y) from raw coordinates (x,y) to the dimensionless non-concentric polar coordinate system (r, θ) can be represented as: These images have 512 64 pixels dimension and to value witch part of this image are most significative the iris image was cut into 8 equal parts of 64 ﾴ64 pixels. Each of the 8 networks is associated with one of this parts and it is trained to became expert of that part. This means that probably they will reach different degrees of expertise since the different parts of ribbon have different levels of noise. Bayesian conditions will be apply just for try to detect their final degrees of expertise. where x(r, θ) and y(r, θ) are defined as linear combinations of both the set of pupillary boundary points (xp(θ), yp(θ)), and the set of limbus boundary points along the outer perimeter of the iris (xs(θ), ys(θ)): x ( r ,  )  (1  r ) x p ( )  rxs ( ) (6) The scheme of the work proposed in this paper consists of three levels: y ( r ,  )  (1  r ) y p ( )  ry s ( ) (7) I ( x ( r ,  ), y ( r ,  )) I (r ,  ) (5) The normalized iris image can be displayed as a rectangular image, with the radial coordinate (r) on the vertical axis, and the angular coordinate (θ) on the horizontal axis. In such representation, the pupillary boundary may be on the top of the image, and the limbic boundary on the bottom. A. Iris recognition and cut B. Training of the neural networks LVQi C. Bayesian conditioning Detailed description of these steps is given below. Our system work whit a ribbon of 512 ﾴ64 pixel (512 pixel along θ and 64 pixels along r), as in Figure 2. 5.1Iris Recognition The first action of preprocessing is to determine iris edge includes inner (with pupil) and outer (with sclera) edges Figure 1(c). Both the inner boundary and the outer boundary of a typical iris can approximately be taken as circles but these two circles are usually not concentric. Figure 2. Iris Polar Transformation Edge Detection This image are now cut in 8 square ( 64 ﾴ64 pixel) as showed in Figure 3, and with these new images we training the respectively 8 LVQ neural networks. (a) (b) (c) Figure 1. Edge Detection The Canny method [23] was applied to these images for edge detection. The edge image was then thresholded. This operation may produce on edge image broken points, spurious edges, and various thicknesses. This image was cleaned using some morphological operation, like clean random dots, remove small edge lines and the broken lines are connected via the “close” procedure of binary morphology. Figure 1(b) is the edge image after these procedures. There is a clear circle in the edge image that represents the outer edge of the pupil (the inner boundary of the iris). The edge above and below the circle are the edges of the eyelids and eyelashes. Then the Hough circle transform [24] was applied to find the best circle and to estimate the circle parameters (centre (x0, y0) and radius r0) for the pupillary and iris boundary, as depicted in Figure 1(c). When the iris region is successfully segmented, the next stage is to find a transformation which can project the iris region into a fixed two dimensional areas in order to be arranged for comparison process. The normalization process projects iris region into a constant dimensional ribbon so that two images of the same iris under different conditions have characteristic features at the same spatial location. Figure 3. Iris Ribbon Cut 5.2Neural Network Training LVQ is a supervised neural network that uses class information to move the weight vector slightly, so as to improve the quality of the classifier decision regions. The input neurons are as many as the input iris image pixel 64 ﾴ64 of the training pattern. Experimental evidence show that it is sufficient to fix the definitions of each class to the first neighbourhood so we have nine nodes for each class: one centroid and eight neighbours. In conclusion, the output layer is made of 108 nodes. The Training set is composed of 12 images (left eye, taken from CASIA database), one from each subject to classified. The learning phase, based on Eq. 1,2, evolves until a maximum of 150.000 epochs using a learning rate calculated with the following equation:  (t )   e ( t) (8) where  (t ) decreases monotonically with the number of iterations t (   0, 35 and   0, 0000009 , values obtained after a series of tests to optimize networks). To test our work, we have taken 5 different images of each subject: whit these 60 images we have built the “Test Set” taken 100 random subjects from this set of images. Table 2. Bayesian Conditioning results Neural Network LVQ1 Reliability Lay1 76,28 % Reliability Lay1-2 88,45 % Reliability Lay1-2-3 89,93 % LVQ2 71,35 % 77,32 % 85,42 % LVQ3 73,08 % 79,35 % 86,63 % LVQ4 78,01 % 87,32 % 88,27 % LVQ5 66,35 % 77,17 % 82,71 % LVQ6 53,28 % 62,58 % 72,78 % LVQ7 66,36 % 75,54 % 81,36 % LVQ8 66,65 % 77,49 % 83,57 % The performance obtained from the training set for each network is 100% of true identification. While the performance obtained from the test set are showed in Table 1. 5.3Bayesian Conditioning In this model of ANN, each node is more or less associated (Euclidean distance) to a subject of the Training set. During the test, each node of each network has a distance associated with the input. As a response of the network have taken the 3 nodes closest to the input and with this nodes we have make 3 layers (Lay1, Lay1-2, Lay1-2-3). The LVQ networks always does not agree in their responses, in some cases one or more of them recognize a subject instead of another (presence of noise), to overcome these situations of disagreement between the networks has introduced the Bayesian conditioning [8], [9], [10], that is used to find maximally consistent subsets of statements produced by LVQ networks, eliminating all information with low credibility, selecting only the statements made by the networks with greater reliability (Eq. 3, 4). Table 1. Test set performance of LVQ networks LVQ1 True Identification 88,3 % False Identification 11,7 % LVQ4 86,7 % 13,3 % LVQ3 83,3 % 16,7 % LVQ2 81,7 % 18,3 % LVQ8 81,7 % 18,3 % LVQ5 80 % 20 % LVQ6 76,7 % 23,3 % LVQ7 76,7 % 23,3 % Average value 81,89 % 18,11 % Neural Network Initially all networks have the same reliability, for every conflict the networks that fall into minority lose credibility than most other, in this way with every new images the reliability of networks rebase. The results obtained from the Test set by the application of Bayesian Conditioning are showed in Table 2. 6.EXPERIMENTAL RESULTS From each random subject of our Test set (100 random subject from a set of 60 images), all the LVQ networks produce their statements (3 nodes). Calculated the reliability for each network (as showed in Table 2), the identity of the subject is established through the method of Inclusion based [8]. To evaluate the results obtained from our work, we have applied Daugman’s algorithm on the same Test set. However, this means that we have compared our work with a re-implementation of Daugman’s algorithm as described in his earliest publications. Thus the used algorithm may not be exactly the same of Daugman and may not give the same performance on the same dataset. 6.1Inclusion Based The algorithm of Inclusion based sort and select the elements of the set of conflict generated by networks B (B = {B1, …, Bn }). The Inclusion based method eliminates always the least credible one among conflicting pieces of knowledge. Let B '  B '1 �K �B ' n and B ''  B ''1 �K �B '' n two consistent subsets of B where Bi '  B ' B '' Bi and B ''i  B ''ﾴ Bi , than B ' iff there exists a stratum i such that B 'i any j<i, B ' j B ''i and for  B '' . j 6.2Daugman’s Approach Given an image of the eye, Daugman’s work approximated the pupillary and limbic boundaries of the eye as circles. Thus, a boundary could be described with three parameters: the radius r, and the coordinates of the center of the circle, x0 and y0. He proposed an integro-differential operator for detecting the iris boundary by searching the parameter space [1]. The next step to describe the features of the iris in a way that facilitates comparison of irises is the introduction of Polar transform [1], [4]. After this transformation, Daugman uses convolution with 2-dimensional Gabor filters to extract the texture from the normalized iris image. In his system, the filters are “multiplied by the raw image pixel data and integrated over their domain of support to generate coefficients which describe, extract, and encode image texture information.” [25]. To match the texture of an image against the stored representation of other irises, Daugman chose to quantize each filter’s phase response into a pair of bits in the texture representation. Each complex coefficient was transformed into a two-bit code: the first bit was equal to 1 if the real part of the coefficient was positive, and the second bit was equal to 1 if the imaginary part of the coefficient was positive. Thus after analyzing the texture of the image using the Gabor filters, the information from the iris image was codified in a 256 byte (2048 bit) binary code (Iris code). Daugman to compare the iris codes uses a metric called Hamming distance, which measures the fraction of bits for which two iris codes disagree. The minimum computed normalized Hamming distance is assumed to correspond to the correct alignment of the two images. 6.3Matching the two methods In Table 3 is showed the results obtained form the application of the Bayesian conditioning with Inclusion based and Daugman’s algorithm. Table 3. Results Inclusion Based Lay1 Lay1-2 Lay1-2-3 86,67 % 88,33 % 91,67 % LVQ6 (76,7 %) LVQ5 (66,35 %) LVQ7 (75,54 %) LVQ7 (81,36 %) LVQ7 (76,7 %) LVQ6 (53,28 %) LVQ6 (62,58 %) LVQ6 (72,78 %) The results contained in Table 3, show how the use of multiple levels (Lay1, Lay1-2, Lay1-2-3) allow to achieve better results for recognition. Future developments of this work will be: the optimization of the parameters used by the neural network (LVQ) for the training, a study on other types of neural networks to be used as experts to improve results, and the implementation of a system for recognizing the face of a person. 8.REFERENCES Daugman 93,33 % 7.CONCLUSION From Table 1 we can see that the neural networks are unable to identify 100% of their subjects, because of the presence of noise. In particular, some networks are more subject to noise than others, and then only using neural networks are not able to recognize the subject, even if they have an average recognition rate of 81.89%. This paper shows how in spite of some LVQ networks, which constitute our group of experts, are not always unanimous to the recognizing of subject, the application of a Bayesian conditioning algorithm on this set of neural networks is able to obtain interesting results in the identification of subjects. Comparing the results obtained by neural networks, which is already known the accuracy or not of response (Table 1) with the reliability of networks calculated through Bayesian conditioning, (Table 2). In the latter case, the reliability of these values are totally disconnected from knowledge of the subject (unknown to the Bayesian conditioning) under review and obtained exclusively on the basis of the processing of conflicts. The results of this comparison are shown in Table 4, in which neural networks were ordered on the basis of their percentages, so that the top networks with the highest rates and in the low those with the lowest percentages. From this table we can see how with different percentages, the final order of the networks on the basis of the results is very similar, showing in this way as the networks are less susceptible to noise are also more reliable. Table 4. Comparison results Neural Network LVQ1 (88,3 %) Reliability Lay1 LVQ4 (78,01 %) Reliability Lay1-2 LVQ1 (88,45 %) Reliability Lay1-2-3 LVQ1 (89,93 %) LVQ4 (86,7 %) LVQ1 (76,28 %) LVQ4 (87,32 %) LVQ4 (88,27 %) LVQ3 (83,3 %) LVQ3 (73,08 %) LVQ3 (79,35 %) LVQ3 (86,63 %) LVQ2 (81,7 %) LVQ2 (71,35 %) LVQ8 (77,49 %) LVQ2 (85,42 %) LVQ8 (81,7 %) LVQ8 (66,65 %) LVQ2 (77,32 %) LVQ8 (83,57 %) LVQ5 (80,0 %) LVQ7 (66,36 %) LVQ5 (77,17 %) LVQ5 (82,71 %) [1] Daugman, J.G. High confidence visual recognition of persons by a test of statistical independence, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 11, 1993, pp. 1148–1161. [2] Wildes, R.P. Asmuth, J. C. Green, G. 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