( ) ( ) ( ) *2 2 2x dx d x Wsf x f s       Eq. (2)  ( * )( ) 2 2 2f x dx d  s  s Eq. (3) 
Where, 
$$\theta_{s}=(1/s)\theta(x/s)$$
Ws*f(x)* is proportional to the second derivative of *f(x)* smoothed by өs (x) and the zero crossings 
of the transform correspond to points of inflection in f* θs *(x)* [14]. The motivation for this 
technique is that zero-Crossings correspond to significant features with the iris region [15], [16], 
[17]. A correlation detection operator is defined as 
$$\mathrm{Eq.~}(2)$$
$$\mathrm{Eq.~}(3)$$

![0_image_0.png](0_image_0.png)

 G =

![0_image_1.png](0_image_1.png)

This detector is a 2D zero crossing detector. This operator is used for extracting iris feature by calculating convolution G and iris texture as shown in fig. 6.

## 3.2 Eulers No.

Topological features, extracted using the Euler No. provide local information of iris patterns and are invariant to rotation, translation and scaling of the image. For a binary image, the Euler No. is defined as the difference between the No. of connected components and the No. of holes. 

Each pixel of unwrapped iris can be represented as an 8-bit binary vector {b7. b6. b5. b4. b3. b2. b1. 

b0. }. These bits form eight planes with binary values as shown in fig 7. Four planes formed from the four most significant bits (MSBs) represent the structural information of the iris, and the remaining four planes represent the brightness information. The brightness information is random in nature and is not useful for comparing the structural features of two iris images [18]. The advantage here is role played by each individual bit is significant.

For comparing two iris images using the Euler code, a common mask is generated for both the 