**2.2. Gabor's demodulation (Daugman's algorithm)**

The first step of Gabor's demodulation, or Daugman's algorithm, is to locate the iris in the acquired image. The iris must be properly scanned so that it can be mapped into phase diagrams that carry information about the position, orientation, and number of specific identification features. After extraction, the database is searched for the template. Daugman's algorithm is shown in **Figure 3**.

**Figure 2.** Structure of the iris—features [3].

First, an *iris* (curve boundary) is *located* in the image of the eye. The iris is located with the following operator:

$$\max\_{(r,y,y\_0)} \left| G\_{\boldsymbol{\phi}}(\boldsymbol{r}) \* \frac{\partial}{\partial r}\_{r,t} \oint\_{\nu y\_0} \frac{l(\boldsymbol{x}, \boldsymbol{y})}{2\pi r} \, d\boldsymbol{s} \right| \tag{1}$$

where *G<sup>σ</sup>* (*r*) is the Gaussian smoothing function according to *σ*, *I*(*x*,*y*) is the raw input image, and the operator searches for the maximum in the blurred partial derivative of the image with respect to the radius *r* and the center coordinates (*x*<sup>0</sup> , *<sup>y</sup>*0). The operator is essentially a circular edge detector and returns the maximum if the candidate circle shares the pupil center and the radius. Examples of localized irises are shown in **Figure 4**.

The next step is *locating* the *lid*. The position of the lower and upper eyelids is determined by the same procedure as the iris itself. The part of the previous formula (Eq. (1)) used to detect the contour is replaced by a circular arc, the parameters being set according to standard

**Figure 3.** Identification process of Daugman's algorithm.

**Figure 4.** Examples of localized irises.

• 400–1400 nm: passes through the lens on the retina. For visible light in the range of 400–

• More than 1400nm: it absorbs the cornea, causing strong tearing and increasing temperature.

Under the visible light, we can observe the visible layers, especially on the iris. It reveals less

By contrast, infrared (IR) light melanin predominantly reflects and is preferred for iris recognition because it is more user-friendly; it does not irritate and does not cause the unpleasant

• *Gabor demodulation*: each single pattern on the iris is demodulated to obtain phase informa-

• *Analysis of independent components*: independent component analysis factors [8] are used as

• *Local keys variation*: representations of important information by the set of intensities of onedimensional signals, using wavelet transformation for the extraction of features [9].

The first step of Gabor's demodulation, or Daugman's algorithm, is to locate the iris in the acquired image. The iris must be properly scanned so that it can be mapped into phase diagrams that carry information about the position, orientation, and number of specific identification features. After extraction, the database is searched for the template. Daugman's algorithm is

textural information than infrared (IR) light; melanin usually absorbs visible light.

• *Wavelet features*: extract the vector of features using wavelet transform [7].

700 nm, the eye reacts within 0.25 s.

10 Machine Learning and Biometrics

feelings associated with eye illumination.

tion for the extraction of features [6].

a vector of features.

shown in **Figure 3**.

**Figure 2.** Structure of the iris—features [3].

There are four basic schemes for iris recognition:

**2.2. Gabor's demodulation (Daugman's algorithm)**

statistical estimation methods to optimally correspond to each eyelid boundary. An example of localized lids is shown in **Figure 5**.
