**2.5. Comparison of iris codes**

The comparison is made by calculating the Hamming distance between the two 256 dwelling codes. The Hamming distance between iris codes *A* and *B* is given as the sum of exclusive totals (XOR) between bits:

**Figure 5.** Examples of localized lids.

**Figure 6.** Implementation of Daugman's algorithm coordinate system.

statistical estimation methods to optimally correspond to each eyelid boundary. An exam-

Daugman's gross alignment model maps each point within the iris to the polar coordinates

The model compensates the pupil enlargement and dilatation due to the representation in the polar coordinate system, invariant to size and translation. However, the model does not compensate for rotational inconsistency, which is solved by shifting the iris template in the direction of the *θ* at the comparison stage until both templates reach a match. The introduction

> ) *e* <sup>−</sup> (*r*−*r*<sup>0</sup> )2 \_\_\_\_\_\_ *<sup>α</sup>*<sup>2</sup> *e* <sup>−</sup> *j*(*θ*−*θ*<sup>0</sup> )2 \_\_\_\_\_\_

where (*r*, *θ*) indicates the position in the image, (*α*, *β*) determine the effective height and length, and *ω* is the frequency of the filter. Demodulation and phase quantification are expressed as

*I*(*ρ*, *φ*) *ej*(*θ*<sup>0</sup>

complex plane corresponding to the sign of the real and imaginary part of the filter response.

The iris code contains 2048 bits (256 bytes). The size of the input image is 64 × 256 bytes, the iris code size is 8 × 32 bytes, and the Gabor filter size is 8 × 8. An example of the iris code is

The comparison is made by calculating the Hamming distance between the two 256 dwelling codes. The Hamming distance between iris codes *A* and *B* is given as the sum of exclusive

<sup>−</sup>*φ*) *e* <sup>−</sup> (*r*0 −*ρ*) 2 \_\_\_\_\_\_ *<sup>α</sup>*<sup>2</sup> *e* <sup>−</sup> (*θ*0 −*φ*)<sup>2</sup> \_\_\_\_\_\_

where *I*(*r*, ) is the rough iris image in the polar coordinate system, and *g*{*Re*,*Im*}

*<sup>β</sup>*<sup>2</sup> (2)

*<sup>β</sup>*<sup>2</sup> *dd* (3)

is a bit in the

(*r*, *θ*) where *r* is from the interval 〈0, 1〉 and *θ* is the angle from the interval 〈0, 2*n*〉.

ple of localized lids is shown in **Figure 5**.

**2.3. Daugman's gross alignment model**

of the coordinate system is shown in **Figure 6**.

*G*(*r*, *θ* ) = *ej<sup>ω</sup>*(*θ*−*θ*<sup>0</sup>

*g*{Re,Im} = sgn{Re,Im} ∬

**Figure 7** shows the coding process of the iris.

Gabor filtering in the polar coordinate system is defined as

**2.4. Iris features encoding**

12 Machine Learning and Biometrics

shown in **Figure 8**.

**2.5. Comparison of iris codes**

totals (XOR) between bits:

**Figure 5.** Examples of localized lids.

$$HD = \frac{1}{N} \sum\_{j=1}^{N} A\_j \bigotimes B\_j \tag{4}$$

where *N* = 2048 (8 × 256), unless the iris is shaded by the lid. Otherwise, only valid areas are used to calculate the Hamming distance.

If both samples are obtained from the same iris, the Hamming distance between them is equal to or close to zero (due to the high correlation of both samples). To ensure rotational consistency, one pattern is shifted to the right/left and the corresponding Hamming distance is always calculated. The lowest value of the Hamming distance is then taken as the resultant comparison score. An example of how to compare iris codes using shifts is shown in **Figure 9**.

#### **2.6. The advantages and disadvantages of the iris for biometric identification**

Some *advantages* of using an iris for biometric identification systems are the following:


The *disadvantages* of using the iris for recognition are as follows:

**Figure 9.** Example of the comparison of iris codes using shifts.

the eye.

**Figure 8.** Example of an iris code.

include them among the disadvantages:

• The lack of a system to counter against a photograph of an iris (spoofing) or contact lenses. • Obstruction may also be the prejudice of users who believe that the scanner may damage

Recognition of Eye Characteristics

15

http://dx.doi.org/10.5772/intechopen.76026

The following list summarizes the limitations of iris recognition. In a way, it is possible to

• The acquisition of an iris image requires user collaboration; the user must stand at a predetermined distance and position in front of the camera. Some systems already allow a

**Figure 7.** Illustration of the encoding process.

**Figure 8.** Example of an iris code.

• The size of the template is small.

14 Machine Learning and Biometrics

**Figure 7.** Illustration of the encoding process.

• The iris is an internal organ that is relatively well protected against external influences. • The iris has a high level of biometric entropy information, much larger than fingerprints.

**Figure 9.** Example of the comparison of iris codes using shifts.

The *disadvantages* of using the iris for recognition are as follows:


The following list summarizes the limitations of iris recognition. In a way, it is possible to include them among the disadvantages:

• The acquisition of an iris image requires user collaboration; the user must stand at a predetermined distance and position in front of the camera. Some systems already allow a semi-automatic scanning to automatic, but the error rate of these systems is still relatively high.

