Considering the increasing usage of biometrics as an authentication method by many institutions in order to replace or enhance traditional security systems, it raises a need to create and improve biometric recognition systems. In this work we will discuss about iris recognition systems and implement a novel technique of template protection based on key-binding. It is a scheme that uses neural networks which nodes are fed by the binary representations of the iris. Keys are encoded according to the idea of Trugenberger, i.e. applying the spin glass and the Hop eld neural network. The system is implemented on a database of 86 subjects to show its applicability.
The increasing demand for security, deriving from past and recent events worldwide, has brought to the front the necessity to use techniques for the identi cation of individuals. Modern societies tend to attribute this increasing importance to systems that provide this type of service by o ering safety and protection towards information. For this reason, the use of biometric systems has been encouraged by many public and private institutions in order to replace or enhance traditional security systems. In essence, the objective is to establish the identity of a subject based on what he is (face, ngerprints, voice, etc), not on what he has (smartcards), or what he knows (passwords).
A biometric recognition system is used to identify a person through the measurement of physiological or behavioral characteristics and the comparison with other previously validated and stored references within a database. These characteristics can be behavioral, such as voice, handwriting or typing style, or physiological such as iris, ngerprint, hand, face, etc. Considering that the recognition performance of a biometric system is achieved, one challenge is to protect our characteristics in the database where they reside, or when they pass through communication channels. To this aim, di erent protection mechanisms have been designed to protect the biometric template, the digital representation of our biometric characteristics. In this work we will discuss about iris recognition systems and a novel technique of template protection based on key-binding. It is a scheme that uses neural networks which nodes are fed by the binary representations of the iris. For the key it is used the theory of spin-glasses where it was tested on a small scale database. 2
When designing a system for user authentication we have to take into consideration three main factors: the level of security, the convenience and the cost of authenticators. An authenticator [Ogo03] can be a password (knowledge-based authenticators), a token (object-based authenticators), and biometric (IDbased authenticators). The third type of authenticator, biometrics, is di erent from the other two since they depend on the human body traits and features. Biometric Systems nowadays use di erent biometric characteristic types in order to identify individuals. The biometric signal that is obtained from the capturing device can be stable over time such as our ngerprints or alterable when it depends on human behaviors such as the voice [Ogo03]. The former are called physiological, and the later behavioral biometrics. Klosterman et al. explain that biometric traits are not secrets and cannot be used in the same way as passwords or tokens are. They present in [Klo00] six di erences between them which are listed below: 1. Biometrics is not secrets. 2. Biometrics is not completely accurate. 3. Biometrics can be continuously monitored. 4. Biometrics is expensive to compute. 5. Biometrics is unique per-individual measures. 6. Biometrics is not universally desirable. In any algorithm extracts the region of interest [Mal03]. (y0 cos#0
x0 sin#0)2 = a (x0 cos#0 + y0 sin#0) (1) where y' and x' indicate the peak coordinates and #' is the rotation angle relative to the horizontal axis.
Daugman method
It requires the use of an integro-di erential operator constructed to locate the circular regions of iris and pupil, and arches that de ne the contours of the eyelids. If they have circular shape, the operator is de ned as: maxr;x0;y0 jG (r)
I r r;x0;y0
I(x; y) 2 r ds case it is necessary to emphasize that there is no system clearly better than the other, the choice therefore appears to be a compromise between the qualities of the properties associated with the selected characteristic and production costs. These properties include [Rath11]: universality, uniqueness, permanence, performance, acceptability, collectability, circumvention.
One of the robust biometric characteristics widely used are irises. The pigmentation and the radial arrangement of the bers of the iris are unique characteristics to each individual (the iris has 266 unique features, while the ngerprint has only 90) [Kal13], [Kha13] and it is also proved that the irises of twins homozygotes are completely di erent from one another (unlike the DNA that is very similar). Even in the same individual the iris of the right eye is di erent from the iris of the left eye [Dau14]. In light of all these considerations, the choice of the iris as a characteristic of a biometric system implies an e cient system.
Recognition systems based on iris have been used with success in distinct sectors, such as the border check-in, or control of refugees. The iris recognition technique consists of ve steps: acquisition, segmentation, normalization, feature extraction and the comparing step [Dau14].
(1) Acquisition
During this process the "captured" image of the subject must serve as input to the recognition system. The aspects to be kept in mind at this stage regard the type of acquisition device.
(2) Segmentation
The region of the iris can be approximated by two circles, one for the outlined iris / sclera and another, internal to the rst, for the contour of the iris / pupil. Eyelashes and eyelids can sometimes occlude the upper and lower parts of this region and for this reason, in addition to locating the region of interest, are used techniques to exclude these parts [Mal03]. Two techniques used to implement iris segmentation are Hough transform and Daugman method.
Hough transform
It is an algorithm commonly used in image processing to determine the parameters of geometric gures within a simple picture [Illi88]. In the context of iris recognition this algorithm can be used to derive radii and centers contours corresponding to the iris and the pupil. The Hough transform can be seen as a transformation of a point from the plane (x, y) of the image to the space of the parameters, in base of the geometric gure to identify [Mal03].To identify better the circles that represent the contour between iris and sclera the (2) (3) (4) (5) (6) (7) where I is the intensity value of the image at the point of coordinates (x, y), r is the radius, s is the track and G is a Gaussian lter de ned as [Dau14]:
G(f ) = e 2((lloogg((fff00))))22 G (r) = p (3) Normalization
Inconsistencies between di erent dimensional images are mainly due to expansion or contraction of the iris, caused by contraction or expansion of the pupil in variable lighting conditions [Mal03]. Rubber Sheet Model of Daugman This normalization model, represents every point extracted from the iris in a space dened from the coordinates (r; #), where r is included in [0, 1] and # is the angle in the interval [0; 2 ]. The normalization of points from the Cartesian plane to polar coordinates is modelled as:
I(x(r; #); y(r; #))
! I(r; #) x(r; #) = (1 y(r; #) = (1 r) xp(#) + r xi(#) r) yp(#) + r yi(#) where, xp and yp indicate the coordinates of the points on the pupil contour for a certain angle # [Mal03].
(4) Feature Extraction
To provide an overview of the procedures required for the extraction and encoding of the biometric feature, we describe one of the methods discussed in the literature. This algorithm explained in [Kah10] works as follows: (1) The normalized template is divided in rows where every row represents the intensity values inside of a circular track. (2) The frequency response of the mono-dimensional Log-Gabor lter is calculated by means of the formula: where f0 is the central frequency.
(3) For every extracted intensity function is calculated the FFT (Fast Fourier Transform) which is then multiplied with the frequency response of the Gabor lter. (4) After calculating the Inverse FFT of the ltered data, it is then quantized in phase by using four levels. Phase quantization is obtained by valuing the complex amplitude values by means of two binary masks, one for the real part and one for the imaginary part. The mask relative to the real part will contain 1 if the real part of the ltered data is greater than zero, and so the mask associated to the imaginary part. (5) The binary codi cation of the iris After being segmented and normalized, it is obtained by placing in columns the two binary masks. This template is called the Iris Code.
In Fig. 1 are presented the noise detection of an iris and the segmentation process. The normalization following it, will provide a binary template, as presented in Fig. 2 One of the major contributions to the study of articial neural networks has been given by the work of Hop eld (from 1982 to 1985 with a series of papers) who studied a network whose units resemble the perceptron. The Hop eld network consists of a certain number of nodes totally connected between them but without auto-connections. The value of output of each node can be 0 or 1 (using the 'step'), or 1 or -1 (using the "sign" function: the output of the unit is 1 if the activation is positive and -1 if the activation is negative). The Hop eld network does not have a layer of input and an output, since each node acts both as input and output [Flo93]. One of the merits of the original work of Hop eld was to describe the dynamics of the network in terms of energy. Each state of the network represents a certain value of global energy. The central property of an energy function is that it always decreases (or remains constant) when a system evolves according to its dynamic rule.
The energy landscape of Hop eld networks presents a hilly view and the rule of adaptation of synaptic weights associates each pattern with an energy minimum. In the test phase the network starts from a state energy high enough which corresponds to a new pattern and slopes down towards the most similar vault. However, energy presents many minima many which do not correspond to any of the stored patterns: the most simple of them is a combination of three original patterns, while a more complex situation can be seen if a local minimum is not correlated to any pattern. These are called spin-glasses state, in correlation to the property of spin glasses in statistical mechanics. Basically, if we consider N-units (or neurons) indexed 1..N, the neuron i can be considered connected to the neuron j with a synaptic weight of W (i; j), where W (i; i) = 0 and W (i; j) = W (j; i). In every instant of time t, the neuron possess a potential of X(t; i) which can have one of the two values: 1 or 1. A certain potential distribution is called state of the system. Considering that time is discrete, at instant t + 1 the neuron assumes a potential that depends on the weighed sum of all the other neurons [Ami85].
X(t + 1; i) = f (X(W (i; j)X(t; j)) j (8) where f is the sign function mentioned above. Taking an initial state X(0; i), the system evolves in a deterministic way, passing from one state to another showing a very particular discrete dynamic system. Such system, in a nite number of steps arrives in a xed point. The xed point can be one of the minima points P and Hop eld proofed that these xed points correspond to the energy function introduced by him: H(X) =
X(W (i; j)X(i)X(j)) (9) i;j His idea was to model the surface of the energy in such a way that its minima should correspond to the states that the machine must acquire. If there are m-con gurations to store/memorize it is su cient to calculate:
W (i; j) =
X(M (t; i)M (t; j)
t
(
The surface of the energy can be imagined made of holes (the local minima) with di erent depths and surrounded of a vault, called the attraction vault. The initial status is represented by a certain position on this surface and it must "fall into" one of these holes. Probably this will happen with a well-determined hole, but if there are holes less deep and narrower vaults, then it would be enough to "shake" a little bit the surface and the point would fall into another vault whose depth is deeper. But what does it mean to "shake" the surface? How is it possible to change the energetic values of the points? At this point we can see an interesting connection between Hop eld Neural Networks and magnetism. 4
There exists an isomorphism between the model of Hop eld and the Ising model of the magnetism at 0 degrees. The Ising model describes a system made of atoms which can be considered as tiny magnets that interact with each other until they reach equilibrium [Mez86]. These are scattered randomly and the function that describes the model of Ising has the same form of the model of Hop eld [Ami85]. In physics 'disorder' may indicate imperfect structures or impurities in a material. It is the counterpart of order since su cient amount of randomness, of imperfections and inconsistencies may destroy the symmetries that dramatically simplify certain physical descriptions [Mez86]. For most the history of 'disorder' was pushed into a corner and scientists have been dedicated for decades to the study of ordered systems [Pen98]. One of the most successful attempts to understand the disordered systems is the study of the so-called 'spinglass'. The composition of this material is a mixture of iron and copper atoms, but its magnetic properties are very complex and are unpredictable.
The 'spin' is the mechanical quantum which originates the magnetic properties and the 'glass' indicates the presence of disorder in the orientation of the spin [Men98]. The spin-glass is an excellent disordered system, applied in complex problems and in a plethora of subjects. Their characteristics, their dynamics and their complexity are as result of the magnetic interactions between the atoms that compound them. If a block of this alloy which certain atoms act as magnets is exposed to an outer magnetic eld, the momenta inside of it tend to align in a particular direction [Mez86]. Sometimes it can be seen the same reaction as a consequence of strong internal e ects [Men98]. As a result of this, the e ect is named ferromagnetism and can be seen even in other materials (nickel, cobalt, etc.). A spin glass can have a lot of states of low energy, which are not separable easily in the same way that energy is stored in the surface of the Hop eld network. To obtain a state of low energy the temperature of the spin glass is raised and the direction of the spin is easily invertible. As a result the probability is higher to come out of holes that are not so deep. The temperature is introduced by means of a probabilistic technique. As in [Tru11] the formula that guides the evolution of the system is P (X(t + 1); i) = 1) = '(Pj (W (i; j)X(t; j)), where P (x) is the probability that at time t + 1 the i-neuron takes the value of 1. The function ' is not the sign function any more, but: '(z) =
1
1 + e Tz
(
In his paper Trugenberger gives the idea of applying the spin glass and the Hop eld NN to encode keys as a local minimum con guration. The key is used to protect ngerprints in a similar way as the fuzzy vault technique does [Jue02]. This process passes through some steps. The rst one is quantization where the ngerprint is represented as a set of M (xi; yi) minutiae coordinates which create a con guration of the Hopeld NN. But, since in the Hop eld model we need a binary representation of data, Trugenberger creates this input by taking into consideration N-squares of pixels from the ngerprint image and to each of them is associated one neuron. If inside the square there is at least one minutiae, the state of the neuron is 1, and if there are no minutiae, then the state of the neuron is 1. Before passing to the second step let's suppose that every column of the iris code, which is a vector of binary values, is represented by one neuron. If the total number of bits '1 ' is more than or equal two the number of bits '0 ' than the neuron will take status 1, otherwise the neuron will take status 0. This is a con guration and we call it iris. As in the ngerprint case, the enrolled iris becomes one particular state con guration: iiris.
The next step is the key generation. This key that will be bounded is created by modifying a certain amount k of columns of the iris con guration. Let's call it ikey. The two con gurations iiris and ikey are considered that belong to the same subject if their Hamming distance is equal to k. 5
During veri cation, the correct iris will evolve toward one xed point, which is the key and if it is not, then the evolution will emerge a completely di erent key. According to Trugenberger the number k of patterns for ngerprints is chosen as = k=N with values between 0:051 and 0:138. We will use in our case = 0:1.
Practically, we generated 86 7 iris codes and each one of them is made of 20 rows and 480 columns. We divided it into blocks of 20 20 having as a result 24 blocks. These blocks will let us create e Hop eld NN made of 24 nodes. If we feed the genuine con guration it always converges to it, otherwise it converges to the nearest one in terms of Hamming distance. The recognition performance based on the Equal Error Rate of the system is 5.3%. 6
In this work we discussed about iris recognition systems and a novel technique of template protection that uses neural networks. It is a scheme in which nodes are fed by the binary representations of the iris. For the key it is used the theory of spin-glasses where it was tested on a small scale database. As future work, it still needs a deeper veri cation of the Neural Network with di erent number of nodes. For a more accurate recognition performance a database with a larger number of subjects needs to be tested.
The authors want to thank the Norwegian Biometrics Laboratory at NTNU, Norway, and the reviewers of RTA-CSIT'16 for their helpful comments.