Application of fingerprint image fuzzy edge recognition algorithm in criminal technology

2.1 Fingerprint identification system

Fingerprint recognition refers to the classification and comparison of the fingerprints of the identified objects. Fingerprint recognition system is a typical pattern recognition system, including fingerprint image acquisition, processing, feature extraction, and comparison modules. With the acceleration of the social information process, the application of fingerprint identification in the criminal field is becoming more and more mature [15]. Figure 1 shows a common fingerprint identification system in criminal work, and its identification process is relatively complicated. Interactive query is an important link between users and fingerprint recognition. On the one hand, the user’s fingerprint should be stored, and on the other hand, the recognition result should be fed back to the user in time. Fingerprint collection is the first step of the whole system. After the fingerprint collector collects the fingerprint from the suspect, it will transmit the fingerprint image to the fingerprint processor. The fingerprint processor needs to perform preprocessing, feature extraction, feature encoding, etc., on the fingerprint. After all these steps are completed, it will send a matching identification request to the fingerprint feature database. After the database successfully matches the fingerprint, the fingerprint identification is officially completed.

Figure 1

Fingerprint identification system.

2.2 Fingerprint image recognition preprocessing algorithm

In the fingerprint recognition algorithm, the fingerprint image preprocessing algorithm is the most important part. In criminal work, fingerprint image collection often has problems of low resolution and insufficient smoothness, and the effect of fingerprint collection will be affected by external and human factors such as the incoherent texture and chapped dry and wet fingerprint, which requires preprocessing of collected fingerprint images. The specific function of preprocessing is to try to eliminate the wrong information caused by these factors and keep only the most original fingerprint lines.

There are many ways to collect fingerprints. The fingerprints collected by the police on criminal detention, administrative detention, suspects of committing crimes, drug-related persons, etc., are collectively referred to as fingerprinting. In the process of collecting fingerprints, some fingerprint collection systems will automatically judge the quality and finger position of the collected fingerprints to ensure that the collected fingerprint images meet the three-element requirements of high quality, no dislocation, and no repetition. The specific acquisition quality control functions include fingerprint wet test, fingerprint image quality judgment, fingerprint image automatic centering, fingerprint image angle automatic correction, fingerprint image automatic background removal, repeated fingerprint judgment, plane and scroll corresponding finger position judgment, triangle and center acquisition incomplete judgment, fingerprint collection area judgment, etc. The fingerprints left by the suspect at the crime scene are called scene fingerprints, and are usually abbreviated as LT in English. On-site fingerprints are finger marks left unintentionally by suspects when committing a crime. Usually, there are uneven marks, blurred textures, and cluttered backgrounds. The preprocessing algorithm can improve the quality of the input fingerprint image, remove the noise in the image, and convert the fingerprint trajectory into a clear scatter plot, so as to extract the correct fingerprint features and improve the accuracy of the comparison results. Figure 2 shows the process of fingerprint preprocessing, including input image, normalization, filter enhancement, binarization, and refinement.

Figure 2

Fingerprint preprocessing process.

3.1 Edge detection algorithm

Edge detection is a relatively common phenomenon in image processing and computer vision, and its main purpose is to identify points in digital images with significant changes in brightness [16]. The so-called edge refers to the set of pixels around which the grayscale of the pixels changes sharply. It is the most basic feature of the image. The edge exists between the target, the background, and the region. Therefore, it is the most important basis for image segmentation. Commonly used operators in edge detection algorithms are Canny operator, Prewitt operator, and Sobel operator. The Sobel edge detection algorithm is the most efficient algorithm in edge detection. The edge detection algorithm usually has directionality, which is divided into horizontal edge and vertical edge detection. Figure 3 is an application example of edge detection. Bidirectional slope coefficients in detection must be determined before detection, i.e., k x = 0 ; k y = 1 ; % horizontal , k x = 1 ; k y = 0 ; % vertical . Next the gradient image is calculated. The edge points are actually the points where the grayscale jumps violently into the image. The brightest part of the gradient image can be regarded as part of a simple edge.

Figure 3

Example of edge detection gradient image.

The Sobel operator usually uses a filter to filter the image to obtain the gradient image. After the filter is defined, the gradient image in the vertical and vertical directions can be obtained by rotating the filter with the image to obtain a gradient image.

3.2 Edge detection algorithm based on fingerprint image

When criminal staff obtain criminal’s fingerprint images, they often use gradient changes to sharpen the image. But this method will enhance the tone and lines at the same time, which brings recognition difficulties. However, the Sobel operator in edge detection does not have such a problem. Due to the introduction of the averaging factor, the Sobel operator can achieve a smoothing effect when processing random noise in the image, and because it has a difference between two rows or two columns, the image elements on both sides of the edge will be enhanced. The edges will appear thicker and brighter. The fingerprint image edge detection process is shown in Figure 4. First, the fingerprint samples of criminal suspects are detected and located, and then the fingerprint image is input for image enhancement, feature extraction, and edge refinement. The subsequent processing is performed by criminal personnel for fingerprint matching.

Figure 4

Fingerprint image edge detection.

3.3 Fuzzy theory

3.3.2 Fuzzy inference system and fuzzy rule table

Taking the fuzzy control rules of the model as an example, assume that the two inputs are M 1 and M 2 , and the fuzzy rules of single output N have the following forms:

if ( M 1 is O 1 ) and ( M 2 is O 2 ) Then N is P , where O i is the label of the input membership function and P is the label of the output membership function, where the label is the language quantity. The overall architecture of the fuzzy inference system is shown in Figure 5. The work of the fuzzy controller is specified by the fuzzy knowledge base, including rules and membership functions. According to the current sampled input signal of the control system, the input is first fuzzified, and the clear value is converted to the fuzzy value, and then the fuzzy approximate reasoning is performed. The reasoning result is converted into the clear value through anti fuzzification and used as the current control output.

Figure 5

Overall architecture of fuzzy reasoning system.

Table 1 is the rule table of the fuzzy controller. The two input signals are, respectively, the error e and error change rate ce of the measured value of the controlled system, one output signal is the variation cu of control output. The labels NB, NM, NS, ZR, PS, PN, and PB, respectively, indicate that the signal is negative large, negative medium, negative small, zero, positive small, positive medium, and positive large. The single point method is commonly used for input fuzzification, that is, to calculate the membership value of the input membership function according to the current input value.

Table 1

Rules of fuzzy controller

	E
	NB	NM	NS	ZR	PS	PM	PR
NB	NB	NB	NB	NB	NM	NS	ZR
NM	NB	NR	NB	NM	NS	ZR	PS
NS	NB	NS	NM	NS	ZR	PS	PM
ZR	NB	NM	NS	ZB	PS	PM	PD
PS	NM	NS	ZR	PS	PM	PB	PB
PM	NS	ZR	PS	PM	PB	PB	PB
PB	ZR	PS	PM	PD	PB	PB	PB

3.4 Examples of applications in criminal technology

In the practice of fingerprint technology application, the use of automatic fingerprint identification technology in the criminal field is to detect cases. The criminal investigators compare the fingerprints left at the crime scene and the fingerprints of the suspects (sample fingerprints) with the files of each archive to obtain a large number of fingerprints with high similarity (alternative fingerprints), and then the suspect is identified through the fingerprint. By judging and investigating one by one, experts determine whether the sample fingerprint is consistent with the candidate fingerprint, and then find the murderer [17]. Figure 6 is an application frame of the police fingerprint identification system based on fingerprint image fuzzy edge identification algorithm. Criminal officers look for fingerprints at the crime scene, input suspicious fingerprints into the fingerprint system, and then process and compare the fingerprint owners through algorithms. On the other hand, criminal officers collect, fuzzy identify, edge detect the fingerprints of suspicious persons, and after investigation, compare the fingerprints with the fingerprint owners found before, and finally implement arrests.

Figure 6

Framework of police fingerprint recognition system based on fuzzy edge recognition algorithm of fingerprint image.

4.1 Mathematical modeling

For a grayscale image of Z = f ( x , y ) , the mathematical modeling process of the fingerprint image is as follows.

4.2 Field-based fingerprint image enhancement algorithm

Using the modeling of the fingerprint field and the visualization model of the Gabor wavelet function mentioned above, the visualization model of the field-based fingerprint image enhancement can be established, and its mathematical model can be obtained at the same time. Finally, the field-based fingerprint image enhancement algorithm can be realized.

The Gabor wavelet function is obtained by repeating the Gaussian activity and the triangular activity. According to the structure of these two functions, the Gabor wavelet function produces periodic oscillations [18]. The field-based fingerprint enhancement mathematical model derived from the Gabor wavelet enhancement physical model is as follows:

The field-based one-dimensional expression is given as follows:

The field-based two-dimensional (2D) expression is given as follows:

and the formula is specified as follows:

Gaussian component

where σ is the Gaussian diffusion factor, the mathematical meaning is the standard deviation; f is the width scale factor, indicating the frequency of the wave; λ is the coordinate axis scale factor, and the mathematical geometric meaning is the ratio of the long and short axes of the ellipse plane at the bottom of the image.

The rotation formula of the coordinate axis is given as follows:

where θ is the rotation factor, the mathematical geometric meaning represents the angle between the direction vector of the point and the positive direction of the x -axis, and the physical meaning is the direction field of the point.

4.3 Fingerprint image frequency domain enhancement

The frequency domain enhancement method is to modify the transformed coefficients in a certain transform domain of the image, such as the coefficients of Fourier transform, DCT transform, etc., to operate the image, and then inverse transform to obtain the processed image. Generally, the frequency domain enhancement algorithm can be divided into several algorithms according to the different switching methods, including the enhancement algorithms based on wavelet transform, enhancement algorithms based on fast Fourier transform (FFT), and enhancement algorithms based on short time Fourier transform (STFT) [19]. In practical applications, the latter two algorithms are the most commonly used.

The FFT-based image enhancement algorithm first performs FFT transformation on the image to obtain a modified frequency image, then filters the frequency image in different ways, and finally performs Fourier transform on the filtered image to obtain an enhanced image. As shown in equations (9) and (10), H ( ρ ) is a bandpass filter with a bandpass center of ρ 0 and a bandwidth of ρ BW . In the algorithm, the convex cosine function is used as the direction filter, and its width and center are ϕ BW and ϕ C .

The algorithm takes into account the curvature characteristics of fingerprint ridges. When a certain point is a singular point, the curvature of the ridge near the point is relatively high, and the change in the direction field at this point is also very sharp. A band pass filter with a fixed orientation angle cannot be used, as false features will be generated. Since then, some people have improved the algorithm, using the linear function of the distance from the ridge to the singular point as a pair filter, which can improve the enhancement effect to a certain extent. However, this algorithm also has some defects. Like the previous algorithm, when the quality of the fingerprint image is low, it is difficult to locate the singular point accurately and quickly.

The implementation method of the STFT method is to truncate the window function in the time domain, perform Fourier transform on the window signal, that is, obtain the Fourier transform at this moment, and constantly move the center of the window. The Fourier transforms at different times can be obtained, and the collection of these Fourier transforms is the short-time Fourier transform. The obtained graph is called a time-frequency graph.

It is found that the effect is better when the fingerprint image is enhanced using the STFT method [20]. For the enhancement of the 2D fingerprint image in the STFT method, the conversion from the spatial domain to the frequency domain is shown in formula (11), among them I ( x , y ) represents the original image, W ( x , y ) represents the 2D window function, and the position of the 2D window W ( x , y ) is represented by τ 1 and τ 2 , and w 1 and w 2 represent the spatial frequency parameters.

4.4 Fingerprint image enhancement based on wavelet transform

Wavelet transform is a local time-frequency analysis algorithm, the time window and frequency window can be changed, but the size of these windows will not change [21]. For a 2D fingerprint image, assuming its size is N × M , which is represented by C 0 ( i , j ) 0 , the standard 2D discrete wavelet transform is decomposed as follows:

In the formula, p is the wavelet decomposition stage, h is the low-pass filter, and g is the high-pass filter. It can be seen from the recurrence from equations (12)–(15) that only the low-pass component is decomposed each time, and the low-pass component CP 0 obtained by the previous-level decomposition is decomposed into four dimensions again in the next level decomposition. The exact same image components continue to be decomposed until the required decomposition level p is reached. C 0 p + 1 represents the double low components of the original fingerprint image, that is, the low frequency components in the horizontal and vertical directions. C 3 p + 1 represents the double high component of the original image, that is, the high-frequency components in the horizontal and vertical directions, while C 1 p + 1 and C 2 p + 1 represent the horizontal low-frequency component, the vertical high-frequency component, and the horizontal high-frequency component, and the vertical-low frequency component, respectively.

Image normalization is the most important part of image augmentation. Image normalization is to adjust the grayscale pixel value and variance value of the real fingerprint image to the expected range [22]. The normalization process is as follows:

where I ( i , j ) is the average value of pixels, N ( i , j ) is the normalized fingerprint image quality average, M is the grayscale average of each pixel in the original image, and σ 2 is the quality variance of each pixel in the original image. M 0 and σ 0 2 are the pre-set image grayscale mean and image variance values.

The locality principle points out [23] that the position of the fingerprint image represents the direction field, and the direction of the fingerprint ridges is basically consistent within a certain range. The Sobel operator is used to calculate the horizontal gradient value ∂ x ( u , v ) and the vertical gradient value ∂ y ( u , v ) of the pixel point ( u , v ) of each fingerprint sub-block, and then the local direction of the sub-block centered on point 5 is calculated by using formulas (17)–(19).

where θ ( i , j ) represents the local ridge line direction of the sub-block whose center point is at ( i , j ) , and w represents the total side length of the sub-block. Because the fingerprint image has a strong gradient feature, this feature can be used to separate the sub-images obtained after wavelet transform decomposition. The method divides each sub-image into w × w sub-blocks first, takes w = 16 , and then uses the formulas (20) and (21) to process.

where ∂ x ( u , v ) and ∂ y ( u , v ) are the gradient values of the sub-block pixels along the x -axis and y -axis, respectively, and V x 2 ( i , j ) and V y 2 ( i , j ) are the results obtained from the operations of formulas (17) and (18). After calculating the R value of all sub-blocks, it is compared with the preset threshold R 0 . When R < R 0 , this sub-block is the background area, and the area mask M ( i , j ) = 0 is marked, otherwise the sub-block is the foreground area, and the area mask M ( i , j ) = 1 is marked.