3. Vein biometrics: feature extraction from hand dorsal and wrist images

One of the most promising and intensively developed biometric methods is the method using the network of blood vessels. The pattern of blood vessels is unique for every human being and also in the case of twins. It is also stable over time [18]. Biometrics associated with the network of blood vessels has a significant advantage over other biometric methods, namely [1, 4, 18]:


Figure 12 Shows the networks of blood vessels used in biometry.

We will consider images from Figure 12(e) and (f), which can be obtained in one process of acquiring biometric patterns. In the literature on the subject, the analysis of this type of images for biometrics is referred to as dorsal vein biometrics and wrist vein biometrics [27, 28].

#### 3.1. Vein biometrics

Infinite set of moments mpq; <sup>p</sup>; <sup>q</sup> <sup>¼</sup> <sup>0</sup>; <sup>1</sup>; <sup>⋯</sup> � � uniquely specifies f xð Þ ; <sup>y</sup> and vice versa.

ð Þ x � x̅

<sup>η</sup>pq <sup>¼</sup> <sup>μ</sup>pq μγ 00

We usually use the first seven combinations of central moments of order 3 known in the

The basic set of geometrical moments is non-orthogonal which makes selection of features

Zernike's moments are orthogonal and invariant to rotation, translation, and scale change. The

X N

y¼1 Z∗

> ð Þ �<sup>1</sup> <sup>s</sup> ½ � ð Þ <sup>n</sup>�<sup>s</sup> ! <sup>r</sup>n�2<sup>s</sup> <sup>s</sup>! <sup>n</sup>þj j <sup>m</sup> ð Þ <sup>2</sup> �<sup>s</sup> ! <sup>n</sup>�j j <sup>m</sup> ð Þ <sup>2</sup> �<sup>s</sup> !

.

� � (18)

ð Þ n�j j m 2 s¼0

When calculating Zernike's moments, the size of the image determines the disk size, and the disk center is taken as the origin. In the case of considering moments on the order of 7, we get

In the case of biometric data using images of retinal blood vessels and conjunctival blood vessels, one of the stages of creating a vector of features is to determine geometrical features

where 4 denote the four-element neighborhood of the image point, f <sup>k</sup> assumes the value 0 or 1, and S denotes the set of integers [17]. In the case where k ≥ 9, its value is defined as k � 8.

<sup>f</sup> <sup>k</sup> � <sup>f</sup> <sup>k</sup><sup>f</sup> <sup>k</sup>þ<sup>1</sup><sup>f</sup> <sup>k</sup>þ<sup>2</sup>

<sup>c</sup> ¼ 4, f <sup>k</sup>, is the cross point.

X M

x¼1

<sup>p</sup> ð Þ <sup>y</sup> � <sup>y</sup>̅ q

f xð Þ ; y (15)

nmð Þ r; θ f xð Þ ; y (17)

(16)

X y

<sup>μ</sup>pq <sup>¼</sup> <sup>X</sup> x

Central moments are defined by

102 Machine Learning and Biometrics

<sup>m</sup>00, <sup>y</sup> <sup>¼</sup> <sup>m</sup><sup>01</sup> <sup>m</sup><sup>00</sup> .

literature as Hu moments [15].

20 Zernike's moments.

If N<sup>4</sup>

Standardized central moments receiving as

<sup>2</sup> ð Þþ p þ q 1, dla p þ q ¼ 2, 3, ⋯:

complex set of Zernike's moments is determined by [16]

where Znmð Þ¼ <sup>r</sup>; <sup>θ</sup> Rnmð Þ <sup>r</sup> <sup>e</sup>jm<sup>θ</sup> and Rnmð Þ¼ <sup>r</sup> <sup>P</sup>

based on the topological properties of the image [5, 17].

<sup>c</sup> <sup>¼</sup> 3, <sup>f</sup> <sup>k</sup> is the bifurcation point, and if <sup>N</sup><sup>4</sup>

The number of connected points around the point f <sup>0</sup> is determined by

N4 <sup>c</sup> <sup>¼</sup> <sup>X</sup> k∈ S

Anm <sup>¼</sup> <sup>n</sup> <sup>þ</sup> <sup>1</sup> π

where <sup>x</sup> <sup>¼</sup> <sup>m</sup><sup>10</sup>

where <sup>γ</sup> <sup>¼</sup> <sup>1</sup>

difficult.

In the process of identifying people on the basis of dorsal vein images, we use a feature vector constructed from two parts: features calculated on the basis of the co-occurrence matrix and features calculated using Gabor filtration operation [21–23].

We consider the dorsal vein images shown in Figure 13.

We analyze the co-occurrence matrix for <sup>¼</sup> <sup>1</sup>; <sup>0</sup> � ; 1; 45 � ; 1; 90 � ; 1; 135 � . The five features calculated for each value of distance d are shown in Table 3.

As a result, on the basis of the co-occurrence matrix, we obtain 40 features.

Figure 12. The networks of blood vessels: Retina (a), conjunctiva (b), finger (c), palm (d), hand dorsal (e), and wrist (f).

Figure 13. Dorsal vein images.

The second part of the feature vector is obtained by implementing an input image convolution operation with the bank of Gabor filters.

3.2. Reduction of dimension of the feature vector by the PCA method

, 30� , 60� , 90� , 120� , 150� Þ:

Figure 13a Figure 13b

Table 3. Features calculated on the basis of co-occurrence matrix.

IDM Contrast Energy Entropy Corr. IDM Contrast Energy Entropy Corr.

0.210 50.890 3.218E-4 8.368 2.271E-4 0.255 141.318 0.007 7.662 2.926E-4

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0.173 67.564 2.622E-4 8.507 2.289E-4 0.218 198.051 0.006 7.794 2.932E-4

0.244 31.936 3.479E-4 8.218 2.268E-4 0.306 86.913 0.007 7.464 2.934E-4

0.146 80.621 2.375E-4 8.608 2.286E-4 0.214 199.180 0.006 7.803 2.931E-4

0,111 179.516 1.944E-4 8.804 2.265E-4 0.184 378.481 0.005 7.991 2.928E-4

0.102 206.593 1.757E-4 8.861 2.302E-4 0.161 456.028 0.004 8.065 3.010E-4

0.155 88.528 2.386E-4 8.581 2.273E-4 0.226 198.554 0.006 7.772 2.963E-4

0.078 288.156 1.626E-4 8.932 2.286E-4 0.161 459.783 0.004 8.075 3.002E-4

elements per image.

and columns to orientation (0�

d 1; 0 �

d 1; 45 �

d 1; 90 �

d 1; 135 �

d 2; 0 �

d 2; 45 �

d 2; 90 �

d 2; 135 �

In the case of the 128 � 128 image and 3 � 6 of Gabor's filter bank, the feature vector has a dimension of 128 � 128 � 3 � 6 = 294,912. The size of the feature is very correlated with each other; after down-sampling (according to factor 8), we get a vector of 36,864 elements or 2304

Figure 14. Real part of Gabor's filter responses of a hand dorsal image with Figure 13a. Rows correspond to scale (2, 4, 8),

In order to reduce information redundancy, we use the principal component analysis (PCA)

method. In some studies it is also called a Karhunen-Loeve discrete transform [29, 30].

For each of the image, a filtration operation is carried out in accordance with Eq. (13) (Figures 14–16).

In the case of biometric identification of people based on texture features obtained using Gabor filter bank, we must solve the problem of a very large dimension of Gabor vector of traits.

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Table 3. Features calculated on the basis of co-occurrence matrix.

Figure 14. Real part of Gabor's filter responses of a hand dorsal image with Figure 13a. Rows correspond to scale (2, 4, 8), and columns to orientation (0� , 30� , 60� , 90� , 120� , 150� Þ:

#### 3.2. Reduction of dimension of the feature vector by the PCA method

The second part of the feature vector is obtained by implementing an input image convolution

Figure 12. The networks of blood vessels: Retina (a), conjunctiva (b), finger (c), palm (d), hand dorsal (e), and wrist (f).

For each of the image, a filtration operation is carried out in accordance with Eq. (13)

In the case of biometric identification of people based on texture features obtained using Gabor filter bank, we must solve the problem of a very large dimension of Gabor vector of

operation with the bank of Gabor filters.

(Figures 14–16).

Figure 13. Dorsal vein images.

104 Machine Learning and Biometrics

traits.

In the case of the 128 � 128 image and 3 � 6 of Gabor's filter bank, the feature vector has a dimension of 128 � 128 � 3 � 6 = 294,912. The size of the feature is very correlated with each other; after down-sampling (according to factor 8), we get a vector of 36,864 elements or 2304 elements per image.

In order to reduce information redundancy, we use the principal component analysis (PCA) method. In some studies it is also called a Karhunen-Loeve discrete transform [29, 30].

The principal features of the PCA method are represented by eigenvectors. The eigenvectors of the covariance matrix are calculated based on the image training set and represent the princi-

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We use two author's database of images of the blood vessel network, namely, a database of dorsal vein images and a database of wrist vein images containing 42 images created as part of a session with students and 58 images found in the resources of www. Each database had 100 images.

The collection of training images consisted of 50 images (50% of images from the student base

The image Gω,θð Þ x; y has M � N pixels and is converted into a 1 � MN size vector. Images from

T ¼ G1; G2; ⋯; Gq

<sup>Ψ</sup> <sup>¼</sup> <sup>1</sup> q X q

1

Then, we calculate the difference between each image from the training database and the mean

� � (19)

Φ<sup>i</sup> ¼ Gi–Ψ (21)

Gq (20)

<sup>i</sup> <sup>¼</sup> AA<sup>t</sup> (22)

the training set are presented in the form of a T matrix (Figure 17):

We calculate the mean image of all the images from the training database:

<sup>C</sup> <sup>¼</sup> <sup>1</sup> q X q

1

Φ<sup>i</sup> Φ<sup>t</sup>

where q is the number of images in the training set.

pal components of the training image set.

and 50% of images from web sources). The PCA algorithm is made as follows:

• Learning/training phase

The covariance matrix is defined as

Figure 17. Image processing using PCA.

image:

Figure 15. Real part of Gabor's filter responses of a hand dorsal image with Figure 13b. Rows correspond to scale (2, 4, 8), and columns to orientation (0� , 30� , 60� , 90� , 120� , 150� Þ:

Figure 16. Real part of Gabor's filter responses of a wrist image with Figure 12f. Rows correspond to scale (2, 4, 8), and columns to orientation (0� , 30� , 60� , 90� , 120� , 150� Þ:

The principal component analysis (PCA) method reduces the amount of data analyzed by subjecting them to linear transformation to a new coordinate system, resulting in new independent variables called the principal components.

The principal features of the PCA method are represented by eigenvectors. The eigenvectors of the covariance matrix are calculated based on the image training set and represent the principal components of the training image set.

We use two author's database of images of the blood vessel network, namely, a database of dorsal vein images and a database of wrist vein images containing 42 images created as part of a session with students and 58 images found in the resources of www. Each database had 100 images.

The collection of training images consisted of 50 images (50% of images from the student base and 50% of images from web sources).

The PCA algorithm is made as follows:

• Learning/training phase

The image Gω,θð Þ x; y has M � N pixels and is converted into a 1 � MN size vector. Images from the training set are presented in the form of a T matrix (Figure 17):

$$T = \begin{bmatrix} \mathbf{G}\_1, \mathbf{G}\_2, \dots, \mathbf{G}\_{\eta} \end{bmatrix} \tag{19}$$

where q is the number of images in the training set.

We calculate the mean image of all the images from the training database:

$$\Psi = \frac{1}{q} \sum\_{1}^{q} \mathcal{G}\_{q} \tag{20}$$

Then, we calculate the difference between each image from the training database and the mean image:

q

$$
\Psi\_i = G\_i \neg \Psi \tag{21}
$$

The covariance matrix is defined as

Figure 17. Image processing using PCA.

The principal component analysis (PCA) method reduces the amount of data analyzed by subjecting them to linear transformation to a new coordinate system, resulting in new inde-

Figure 16. Real part of Gabor's filter responses of a wrist image with Figure 12f. Rows correspond to scale (2, 4, 8), and

Figure 15. Real part of Gabor's filter responses of a hand dorsal image with Figure 13b. Rows correspond to scale (2, 4, 8),

pendent variables called the principal components.

, 30� , 60� , 90� , 120� , 150� Þ:

and columns to orientation (0�

106 Machine Learning and Biometrics

columns to orientation (0�

, 30� , 60� , 90� , 120� , 150� Þ: where

$$A = \begin{bmatrix} \Phi\_1, & \Phi\_2, & \cdots, & \Phi\_q \end{bmatrix} \tag{23}$$

and matrix A has a dimension of MN � q.

The covariance matrix has a dimension of MN � MN.

Then, we calculate the eigenvalues and eigenvectors of the covariance matrix:

$$\mathbf{C} \ v\_i \ = \lambda\_i \upsilon\_i \qquad \mathbf{i} = 1, \cdots, q \tag{24}$$

Then, we organize our eigenvectors according to their decreasing eigenvalues. We choose k principal components corresponding to k largest eigenvalues.

• Test/recognition phase

The new image is processed to obtain eigenvectors and eigenvalues. k the main components of the G~ image are defined as

$$w = v^t \left(\tilde{G} - \Psi\right) \tag{25}$$

FV1 is Gabor's feature vector

verified.

4. Conclusion

for recognition.

that a person possesses.

FV2 is the co-occurrence feature vector

Figure 18. Variance as a function of the number of eigenvectors.

parameters FRR is 1.16% and FAR is 0.26%.

The quality of biometric systems is measured by two parameters: false acceptance rate (FAR) and false reject rate (FRR). FAR indicates the situation when the biometric input image is incorrectly accepted, and the FRR indicates the rejection of the user who should be correctly

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The size of the FV1 vector has been set to 60 eigenvectors. The featVect size is 100. For these

Recognition of people in biometric systems is based on the physiological or behavioral features

In this chapter, we presented the image preprocessing operations used in static biometric systems (physiological modality). In particular, we discussed operations related to the transformation of the brightness scale of the image, modification of the brightness histogram, median filtering, edge detection, and image segmentation. In the course of these operations, we obtain an image enabling the extraction and measurement of features that serve as the basis

Next, we discuss the feature extraction process, focusing on certain geometrical features and texture features. We present a representation of texture features based on parameters obtained from the co-occurrence matrix and images after Gabor's filtration with various scaling and orientation parameters. In terms of geometric features, we discuss the moment-based features

We provide and discuss the feature extraction process in the images of the blood vessels of the hand dorsal and wrist. We present features calculated on the basis of matrix of co-occurrences

and geometrical features based on the topological properties of the image.

where v ¼ ð Þ v1; v2; ⋯; vk .

Approximated image is calculated as

$$
\overline{G} = \upsilon w + \Psi \tag{26}
$$

We choose the k value according to the dependence:

$$\inf\_{k}(k) = \frac{\sum\_{i}^{k} \lambda\_{i}}{\sum\_{1}^{q} \lambda\_{i}} \tag{27}$$

where k is the predefined number of eigenvectors and q the total number of eigenvectors.

A high value of k means that a large amount of input information will be stored, e.g., infð Þk ≥ 0:99 means that we retain 99% of information.

The variance of the first eigenvector is about 60% of the variance of the data set, the variance of the first 30 eigenvectors is about 85% of the variance of the data set, and 45 or more eigenvectors account for over 90% of the variance of the data set (Figure 18).

By increasing the number of eigenvectors, we increase the recognition efficiency.

We defined the vectors of features as follows:

$$\text{FentVect} = (FV1, FV2) \tag{28}$$

where

Figure 18. Variance as a function of the number of eigenvectors.
