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This paper develops an approach to measure the information content in a biometric feature representation of iris images. In this context, the biometric feature information is calculated using the relative entropy between the intraclass and interclass feature distributions. The collected data is regularized using a Gaussian model of the feature covariances in order to practically measure the biometric information with limited data samples. An example of this method is shown for iris templates processed using Principal-Component Analysis- (PCA-) and Independent-Component Analysis- (ICA-) based feature decomposition schemes. From this, the biometric feature information is calculated to be approximately 278 bits for PCA and 288 bits for ICA iris features using Masek's iris recognition scheme. This value approximately matches previous estimates of iris information content.

Biometric systems allow identification of human persons based on physiological or behavioral characteristics, such as voice, handprint, iris, or facial characteristics. Iris recognition offers great benefits with respect to other authentication techniques since it has one of the lowest error rates among biometric technologies in terms of identification and verification of individuals. However, one question that remains unclear is “how much information is there in an iris image?” This question is related to many issues in biometric technology from the point of view of uniqueness, identifiability, and discriminating information. Additionally, such a measure is relevant to biometric cryptosystems and privacy measures. Several authors have presented approaches relevant to this question. For example, Wayman [

Such an analysis is intrinsically tied to a choice of biometric features. Based on this definition, this paper develops a mathematical framework to measure biometric feature information for iris images processed using the Daugman’s algorithm implemented by Masek in [

In this section we develop an algorithm to calculate biometric information based on a set of iris features, using the relative entropy measure [

iris region normalization and feature extraction using Log-Gabor filters,

PCA/ICA iris feature decomposition,

distribution modeling of iris biometric features,

biometric information calculation using the relative entropy measure.

Iris recognition is a highly studied and evolved technology in biometrics. The iris is known to contain a rich texture which means that unique information can be extracted from the iris to identify users. Iris features have been used to obtain high recognition accuracy for security applications [

An example of an iris recognition system is shown in Figure

Different stages in an iris recognition system.

This section describes the iris normalization, also known as the “Daugman Rubber Sheet Model” and the feature extraction process prior to iris encoding [

Unwrapping of the iris using Daugman’s Rubber Sheet Model.

After data normalization, feature extraction becomes an essential part in any iris recognition system since good identification rates are directly related to the uniqueness and variability of the extracted features used to distinguish between different biometric templates. In this paper, we use a Log-Gabor filter [

To encode iris information when working with an unwrapped iris matrix representation, each row of pixel intensities corresponds to a ring of pixels centered at the pupil center. In order to extract the phase feature templates, the Log-Gabor filter is applied to the 1D image vectors. Since the normalization process involves unwrapping the iris region from the circular shape to a rectangular matrix (i.e., from the Cartesian coordinates to the normalized polar coordinates), the spatial relationship along the concentric sampling rings and the radius becomes independent.

In this section we develop an algorithm to calculate biometric information based on a set of features, using Masek’s iris recognition system, and the relative entropy measure

This expression calculates the relative entropy in bits for Gaussian distributions

If the intraclass feature distribution matches the interclass feature distribution:

As feature measurements improve, the covariance values,

If a biometric template has a feature distribution far from the population mean,

Combinations of uncorrelated feature vectors yield the sum of the individual

Addition of features uncorrelated to iris features (i.e., iris noise) will not change

In order to guard against numerical instability in our measures, we wish to extract a mutually independent set of

The expression developed in the previous section solves the problem of ill-posedness of

Estimates of feature variances are valid

Estimates of feature covariances

We thus consider this regularization strategy to generate a lower bound on the biometric feature information. The selection of

The previous section has developed a measure of biometric feature information content of a biometric feature representation of a single iris template with respect to the feature distribution of the entire set. As discussed, the biometric feature information will vary between different iris samples; those with feature values further from the mean have larger biometric feature information. In order to use this approach to measure the biometric feature information content of a biometric system, we calculate the average biometric feature information for each iris in group of irises. This is a measure of the system biometric information (SBI) which can be calculated by averaging the iris template BI over the entire set of irises

In this section, we explore the effect of image degradation and the resulting decrease in biometric quality on the relative entropy measure. Intuitively, it is expected that image degradation changes the intra- and interclass distribution of the iris features resulting in a loss of biometric information. In general, image degradation is a nonlinear process; however, in this paper we use a linear degradation model to explore its effect. Different degradation processes are applied to the iris images in order to generate the degraded features. Different levels of speckle, white Gaussian, and salt and pepper noise are applied to the original iris image as well as Gaussian blur, which maps the original high-quality images

Here

Information in a feature representation of an iris is calculated using our described method for different irises. In order to test our algorithm, it is necessary to have multiple images of the same iris. For this reason, we used the CASIA database [

Biometric eigeniris feature information computed for 327 iris features. The

Biometric ICA iris feature information computed for 327 iris features where features are extracted using the Log-Gabor filter from the iris region at a

Biometric ICA iris feature information computed for 327 iris features where features are extracted using the Log-Gabor filter from the iris region at a

In order to investigate the angular variations in iris information density, a plot of the biometric information as a function of the angle is shown in Figure

Biometric iris feature information as a function of iris angle (in

Biometric iris feature information as a function of radius. It is seen that the BI is slightly larger at a small radius (i.e., close to the pupil boundary) which signifies that the iris contains richer information within the collarette area. A 4th-order polynomial curve fit is shown over the BI graph in order to demonstrate the curve trend.

Using the image degradation process described in Section

Fractional BI loss as a function of degradation level for 10 different (a) Gaussian blur levels, (b) white Gaussian noise variances, (c) salt and Pepper noise densities, (d) speckle noise variances where the (

This work describes an approach to measure biometric feature information for iris images. Examples of its application were shown for two different feature decomposition algorithms based on PCA and ICA where features are extracted using the Masek and Daugman’s iris recognition systems [

The result of biometric feature information calculations (approximately 278 bits for PCA and 288 bits for ICA iris features) is compatible with previous analyses of iris recognition accuracy. For example, Daugman states that the combinatorial complexity of the phase information of the iris across different persons spans about 249 degrees of freedom [

A plot of the biometric information as a function of the angle (Figure

In a general biometric system, the following issues associated with biometric features must be considered.

Feature distributions vary. In this work, all features are modeled as Gaussian which may be considered to estimate an upper bound for the entropy.

Feature dimensionality may not be constant. For example, the number of available minutiae points varies. The method presented in this work does not address this issue, since the dimensions of

While we have introduced a measure in the context of iris recognition, we anticipate that such a measure may help address many questions in biometrics technology, such as the following.

Uniqueness of biometric features. A common question is “are biometric features really unique?”. While Pankanti et al. [

Performance limits of biometric matchers. While some algorithms outperform others, it is clear that there are ultimate limits to error rates, based on the information available in the biometric features. In this application, the biometric feature information is related to the discrimination entropy [

Biometric fusion. Systems which combine biometric features are well understood to offer increased performance [

This work describes an approach to measure biometric feature information for iris images processed using Daugman and Masek’s methods [