**2.4. Iris features encoding**

Gabor filtering in the polar coordinate system is defined as

$$G(r, \Theta\_{\cdot}) = e^{\mu(\theta - \theta\_{\cdot})} e^{-\frac{(r - r\_{\phi})^{\mu}}{a^{\mu}}} e^{-\frac{j(\theta - \theta\_{\phi})^{\mu}}{\bar{\beta}^{\mu}}} \tag{2}$$

*HD* = \_\_1

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

• The iris is stable during an individual's life. • Snapshots are noninvasive and user-friendly.

to calculate the Hamming distance.

*<sup>N</sup>* ∑ *j*=1 *N Aj*

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

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:

⨂*Bj* (4)

Recognition of Eye Characteristics

13

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

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

$$\mathcal{g}\_{\text{(Ra,Im)}} = \text{sgn}\_{\text{(Ra,Im)}} \iint\_{\Phi} \mathcal{I}(\rho, \phi) \, e^{i\omega(\theta, \varphi)} \, e^{-\frac{(\theta, \varphi)^{\flat}}{\alpha^{\flat}}} \, e^{-\frac{(\theta, \varphi)^{\flat}}{\beta^{\flat}}} \, \rho d\rho d\phi \tag{3}$$

where *I*(*r*, ) is the rough iris image in the polar coordinate system, and *g*{*Re*,*Im*} is a bit in the complex plane corresponding to the sign of the real and imaginary part of the filter response. **Figure 7** shows the coding process of the iris.

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 shown in **Figure 8**.
