2. Feature extraction

Methods for feature extraction on biometric traits can be categorized into geometrical analysis and textural analysis (Table 2).

The texture image can be seen as an image area containing repetitive pixel intensity patterns arranged in a certain structural manner. The concept of texture has no formal and mathematical definition, but there are a number of methods for extracting texture features that can be roughly divided into model-based (fractal and stochastic method), statistical, and using signal processing algorithms.

Methods using signal processing algorithms (in the frequency domain and/or space-frequency domain) are widely used in transform-based texture analysis, e.g., Fourier transform, Gabor transform, Riesz transform, Radon transform, and wavelet transform.


Table 2. Biometric feature extraction methods.

The segmentation of the image f xð Þ ; y according to the Reg rule is the division

<sup>¼</sup> false <sup>∨</sup> <sup>i</sup> 6¼ <sup>j</sup>:

Seg : f xð Þ! ; y si,j (9a)

si,j ¼ λ<sup>i</sup> for xð Þ ; y ∈Si, i ¼ 1, 2, ⋯, K (9b)

The Reg rule specifies a certain homogeneity criterion and depends on the function of f xð Þ ; y .

where f xð Þ ; y and si,j are functions that define the input image and the segmented image,

(8)

S ¼ f g S1; S2; ⋯; SK corresponding to the conditions as follows:

We consider segmentation as

Figure 8. Canny edge detector.

98 Machine Learning and Biometrics

respectively, while λ<sup>i</sup> is the label (name) of Si area.

a: ⋃ K i¼1

Si ¼ X;

Figure 9. Original image after edge detector operator: Roberts (a), Prewitt (b), Sobel (c), and Canny.

d: Reg Si ∩ Sj

b: Si⋂Sj ¼ 0, ∨ i 6¼ j; c: Reg Sð Þ¼<sup>i</sup> true ∨ i;

One of the popular representations of texture feature is the co-occurrence matrix proposed by Haralick et al. [8–10]. The gray-level co-occurrence matrix (GLCM) Cdð Þ k; l counts the co � occurrence of pixels with gray values k and l at a given distance d and then extracts statistical measures from this matrix. The element of co-occurrence matrix is defined as

$$\begin{aligned} \mathcal{L}c(k,l) &= \sum\_{\mathbf{x}, \mathbf{y} \in \mathcal{D}} \begin{cases} 1 & \text{if } (f(\mathbf{x}, \mathbf{y}) = k \text{ and } f(\mathbf{x} + \Delta \mathbf{x}, \mathbf{y} + \Delta \mathbf{y}) = l \\ 0 & \text{otherwise} \end{cases} \\ &+ \sum\_{\mathbf{x}, \mathbf{y} \in \mathcal{D}} \begin{cases} 1 & \text{if } (f(\mathbf{x}, \mathbf{y}) = l \text{ and } f(\mathbf{x} + \Delta \mathbf{x}, \mathbf{y} + \Delta \mathbf{y}) = k \\ 0 & \text{otherwise} \end{cases} \end{aligned} \tag{10}$$

These features provide information about the texture and are as follows:

$$\begin{aligned} \text{Element difference moment of order p} &: \sum\_{\mathbf{k}} \sum\_{\mathbf{l}} (\mathbf{k} - \mathbf{l})^{\mathbf{P}} \mathbf{C}\_{\mathbf{d}}(\mathbf{k}, \mathbf{l}). \text{ When } \mathbf{p} = 2, \text{it} \\ &\text{is called the contrast}; \\ \text{Entropy.Entropy} &= -\sum\_{\mathbf{k}} \sum\_{\mathbf{l}} \mathbf{C}\_{\mathbf{d}}(\mathbf{k}, \mathbf{l}) \log \mathbf{C}\_{\mathbf{d}}(\mathbf{k}, \mathbf{l}); \\ \text{Energy.Energy} &= \sum\_{\mathbf{k}} \sum\_{\mathbf{l}} \mathbf{C}\_{\mathbf{d}}(\mathbf{k}, \mathbf{l})^{2}; \\ \text{Inverse difference moment.IDM} &= \sum\_{\mathbf{k}} \sum\_{\mathbf{l}} \frac{1}{1 + (\mathbf{k} - \mathbf{l})^{2}} \mathbf{C}\_{\mathbf{d}}(\mathbf{k}, \mathbf{l}). \end{aligned} \tag{11}$$
 
$$\text{Correlation moment.IDM} = \sum\_{\mathbf{k}} \sum\_{\mathbf{l}} (\mathbf{k}, \mathbf{l}) \mathbf{C}\_{\mathbf{d}}(\mathbf{k}, \mathbf{l}) - \mu\_{\mathbf{x}} \mu\_{\mathbf{y}}$$
 
$$\text{Correlation.Corr} = \frac{\sum\_{\mathbf{k}} \sum\_{\mathbf{l}} (\mathbf{k}, \mathbf{l}) \mathbf{C}\_{\mathbf{d}}(\mathbf{k}, \mathbf{l}) - \mu\_{\mathbf{x}} \mu\_{\mathbf{y}}}{\sigma\_{\mathbf{x}} \sigma\_{\mathbf{y}}}.$$

The distance d is most often represented in polar coordinates in the form of a discrete distance and an orientation angle. In practice, we use four angles, namely, 0� , 45� , 90� , 135� (Figure 10).

Mathematically, Gabor filters is defined as [11]

$$\begin{split} \text{Gab}\_{\boldsymbol{w},\boldsymbol{\theta}}(\mathbf{x},\boldsymbol{y}) &= \frac{1}{2\pi\sigma\_{\mathbf{x}}\sigma\_{\mathbf{y}}} \exp\left\{-\left(\frac{(\mathbf{x}\cos\theta+\mathbf{y}\sin\theta)^{2}}{2\sigma\_{\mathbf{x}}^{2}}+\frac{(-\mathbf{x}\sin\theta+\mathbf{y}\cos\theta)^{2}}{2\sigma\_{\mathbf{y}}^{2}}\right)\right\} \\ &\left[\exp\left\{i(\boldsymbol{w}\mathbf{x}\cos\theta+\boldsymbol{w}\boldsymbol{y}\sin\theta)\right\}-\exp\left\{-\frac{\boldsymbol{w}^{2}\sigma^{2}}{2}\right\}\right] \end{split} \tag{12}$$

Typically, Gabor's filter bank was created by varying the frequency parameter, the orientation parameter, and the variance parameter (Figure 11).

Gabor's features are obtained by convolution of the image f (x, y) with the Gabω,θð Þ x; y filter:

$$G\_{\omega,\theta}(\mathbf{x},y) = f(\mathbf{x},y) \* \mathbf{G}ab\_{\omega,\theta}(\mathbf{x},y) \tag{13}$$

Moment-based features can be successfully used as elements of a feature vector in biometrics

X y

where hpqð Þ x; y is a certain polynomial in which x is the degree p, while y is the degree q. If

f xð Þ ; y hpqð Þ x; y (14)

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The geometric moments of order ð Þ p þ q of the image f xð Þ ; y is determined by

hpqð Þ¼ <sup>x</sup>; <sup>y</sup> xpyq, then we consider the geometrical moments of the image ð Þ <sup>x</sup>; <sup>y</sup> .

mpq <sup>¼</sup> <sup>X</sup> x

Figure 11. 2D Gabor's filters in spatial domain: (a) real and (b) imaginary components.

using blood vessel network [13, 14].

Figure 10. The gray-level co-occurrence matrices.

where ∗ is the convolution operator [11–13].

A Survey on Methods of Image Processing and Recognition for Personal Identification http://dx.doi.org/10.5772/intechopen.76116 101

Figure 10. The gray-level co-occurrence matrices.

One of the popular representations of texture feature is the co-occurrence matrix proposed by Haralick et al. [8–10]. The gray-level co-occurrence matrix (GLCM) Cdð Þ k; l counts the co � occurrence of pixels with gray values k and l at a given distance d and then extracts statistical

1 if ðf xð Þ¼ ; y k and f xð þ Δx; y þ ΔyÞ ¼ l

1 if ðf xð Þ¼ ; y l and f xð þ Δx; y þ ΔyÞ ¼ k 0 otherwise

ð Þ <sup>k</sup> � <sup>l</sup> <sup>p</sup>

Cdð Þ <sup>k</sup>; <sup>l</sup> <sup>2</sup> ;

ð Þ k; l Cdð Þ� k; l μxμ<sup>y</sup>

( ) !

2

Gω,θð Þ¼ x; y f xð Þ ; y ∗Gabω,θð Þ x; y (13)

X l

σxσ<sup>y</sup>

Cdð Þ k; l logCdð Þ k; l ;

1

<sup>1</sup> <sup>þ</sup> ð Þ <sup>k</sup> � <sup>l</sup> <sup>2</sup> Cdð Þ <sup>k</sup>; <sup>l</sup> :

:

, 45� , 90� , 135�

<sup>þ</sup> ð Þ � xsin <sup>θ</sup> <sup>þ</sup> ycos <sup>θ</sup> <sup>2</sup> 2σ<sup>2</sup> y

( (10)

Cdð Þ k; l : When p ¼ 2, it

(11)

(Figure 10).

(12)

0 otherwise

X k

> X l

k

X l

The distance d is most often represented in polar coordinates in the form of a discrete distance

exp � ð Þ <sup>x</sup> cos <sup>θ</sup> <sup>þ</sup> <sup>y</sup> sin <sup>θ</sup> <sup>2</sup>

exp i <sup>f</sup> ð Þ <sup>ω</sup><sup>x</sup> cos <sup>θ</sup> <sup>þ</sup> <sup>ω</sup><sup>y</sup> sin <sup>θ</sup> g � exp � <sup>ω</sup><sup>2</sup>σ<sup>2</sup>

� � � �

Typically, Gabor's filter bank was created by varying the frequency parameter, the orientation

Gabor's features are obtained by convolution of the image f (x, y) with the Gabω,θð Þ x; y filter:

2σ<sup>2</sup> x

is called the contrast;

k

X k

X l

X l

k

measures from this matrix. The element of co-occurrence matrix is defined as

(

These features provide information about the texture and are as follows:

Entropy:Entropy ¼ �<sup>X</sup>

Inverse difference moment:IDM <sup>¼</sup> <sup>X</sup>

and an orientation angle. In practice, we use four angles, namely, 0�

Correlation:Corr ¼

Mathematically, Gabor filters is defined as [11]

1 2πσxσ<sup>y</sup>

parameter, and the variance parameter (Figure 11).

where ∗ is the convolution operator [11–13].

Gabω,θð Þ¼ x; y

Energy:Energy <sup>¼</sup> <sup>X</sup>

c kð Þ¼ ; <sup>l</sup> <sup>X</sup>

100 Machine Learning and Biometrics

x, y∈ D ð Þ x þ s; y þ t ∈ D

<sup>þ</sup> <sup>X</sup> x, y ∈ D ð Þ x þ s; y þ t ∈ D

Element difference moment of order p :

Figure 11. 2D Gabor's filters in spatial domain: (a) real and (b) imaginary components.

Moment-based features can be successfully used as elements of a feature vector in biometrics using blood vessel network [13, 14].

The geometric moments of order ð Þ p þ q of the image f xð Þ ; y is determined by

$$m\_{pq} = \sum\_{\mathbf{x}} \sum\_{\mathbf{y}} f(\mathbf{x}, \mathbf{y}) \, h\_{pq}(\mathbf{x}, \mathbf{y}) \tag{14}$$

where hpqð Þ x; y is a certain polynomial in which x is the degree p, while y is the degree q. If hpqð Þ¼ <sup>x</sup>; <sup>y</sup> xpyq, then we consider the geometrical moments of the image ð Þ <sup>x</sup>; <sup>y</sup> .

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.

Central moments are defined by

$$\mu\_{pq} = \sum\_{\mathbf{x}} \sum\_{\mathbf{y}} \left( \mathbf{x} - \overline{\mathbf{x}} \right)^{p} (\mathbf{y} - \overline{\mathbf{y}})^{q} f(\mathbf{x}, \mathbf{y}) \tag{15}$$

where <sup>x</sup> <sup>¼</sup> <sup>m</sup><sup>10</sup> <sup>m</sup>00, <sup>y</sup> <sup>¼</sup> <sup>m</sup><sup>01</sup> <sup>m</sup><sup>00</sup> .

Standardized central moments receiving as

$$
\eta\_{pq} = \frac{\mu\_{pq}}{\mu\_{00}^{\mathcal{V}}} \tag{16}
$$

The feature vector defining the topology of blood vessels is made up of the number of bifurcation points, number of crossing points, coordinates of bifurcation points, and coordi-

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By using the relationship between the characteristic points of the user blood vessel image and

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]: • Allows only identification of living people: the NIR camera records the image only in the case of deoxygenated hemoglobin, and this is possible only in the living organism [19, 26];

• The network of blood vessels is inside the body, and it is practically impossible to repro-

• Usually, we use the network of blood vessels associated with the following parts of the

• Eye. This applies first of all not only to the retinal blood vessels but also to the blood

• Hand. In this case, we are talking about the network of blood vessels of the finger, palm,

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

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

; 1; 45 �

; 1; 90 � ; 1; 135 �

. The five fea-

for biometrics is referred to as dorsal vein biometrics and wrist vein biometrics [27, 28].

blood vessel image of template, we can calculate the matching score results.

duce outside of it, which results in very high level of safety.

nates of crossing points.

body:

3.1. Vein biometrics

vessels of the conjunctiva.

hand dorsal, wrist, and forearm [20, 24, 25].

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

features calculated using Gabor filtration operation [21–23].

tures 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.

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> �

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

We usually use the first seven combinations of central moments of order 3 known in the literature as Hu moments [15].

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

Zernike's moments are orthogonal and invariant to rotation, translation, and scale change. The complex set of Zernike's moments is determined by [16]

$$A\_{nm} = \frac{n+1}{\pi} \sum\_{x=1}^{M} \sum\_{y=1}^{N} Z\_{nm}^\*(\rho, \theta) f(x, y) \tag{17}$$

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> ð Þ n�j j m 2 s¼0 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> ! .

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 20 Zernike's moments.

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

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

$$N\_c^4 = \sum\_{k \in \mathcal{S}} \left( f\_k - f\_k f\_{k+1} f\_{k+2} \right) \tag{18}$$

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.

If N<sup>4</sup> <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> <sup>c</sup> ¼ 4, f <sup>k</sup>, is the cross point. The feature vector defining the topology of blood vessels is made up of the number of bifurcation points, number of crossing points, coordinates of bifurcation points, and coordinates of crossing points.

By using the relationship between the characteristic points of the user blood vessel image and blood vessel image of template, we can calculate the matching score results.
