CN102103692A - Fingerprint image enhancing method - Google Patents

Abstract

The invention discloses a fingerprint image enhancing method, and belongs to the technical field of image processing. The method comprises the following steps of: performing gray shearing and gray stretching on fingerprint foreground region image gray to obtain fingerprint foreground region image gray2; performing Gaussian filtration on the fingerprint foreground region image gray2 by using a Gaussian filter g sigma, and calculating a normalized fingerprint gradient vector; then constructing a structure tensor, and calculating the direction field of fingerprint ridge lines; and finally, constructing two one-dimensional anisotropic filters to perform two-time filtration enhancement on the fingerprint foreground region image gray2 to obtain a final filtration enhanced fingerprint foreground region image. Based on a nonlinear diffusion model and the normalized structure tensor, the method can effectively remove various structural noises, reduce the dynamic change range between the fingerprint ridge lines and the valley lines and connect certain broken fingerprint ridge lines at the same time. The method has good enhancement effect and characteristic of effectively saving the time, and can meet the requirement of on-line fingerprint identification.

Description

A kind of enhancement method of fingerprint image

Technical field

The invention belongs to technical field of image processing, relate generally to the fingerprint image enhancement techniques in the biometrics identification technology.

Background technology

Living things feature recognition is to adopt the digitizing automatic technique to measure a local feature or the individual behavioural characteristic of human body, and the feature of measuring these features and given data library storage is mated, and finishes a solution of authentication.In networking technology and highly developed epoch of informationization technology, biometrics identification technology has obtained important use with people's routine work and life extensive connection in fields such as authentication, information securities.Fingerprint identification technology be in the biometrics identification technology application time also be the widest a kind of feature identification technique of range of application the earliest, and at attendance checking system, numerous areas such as ecommerce have obtained certain popularizing.Automatically fingerprint identification technology comprises that fingerprint image cuts apart, and fingerprint image strengthens, fingerprint image binaryzation, refinement, steps such as feature extraction and characteristic matching.

Wherein the fingerprint image enhancing is one of algorithm most crucial in the Automated Fingerprint Identification System, because the performance of fingerprint image enhancement algorithms not only directly has influence on the correct extraction of system to fingerprint minutiae, minutiae point is the key that fingerprint is successfully discerned and mated.And the fingerprint image enhancement algorithms accounts for more than 80% of whole algorithm time, one fast and effectively enhancement algorithms can improve the processing speed of algorithm greatly.The effect of fingerprint image enhancement algorithms in recognizer is: the various structure borne noises of filtering are to the influence of feature point extraction, the contrast of crestal line and valley line in the raising fingerprint, reduce the gray scale dynamic change scope between crestal line and the valley line, connect the crestal line and the valley line of some fractures.At present in the existed algorithms, though reasonable fingerprint enhancement algorithms is arranged, what have will consume a large amount of time, but fewer effect of the processing time that has is bad again, therefore the present invention is intended to design and a kind ofly can be better strengthened effect, again can effective time-saving fingerprint enhancement algorithms.

Summary of the invention

The invention provides a kind of enhancement method of fingerprint image, this method is based on nonlinear diffusion model and normalization structure tensor, can effectively remove various structure borne noises, reduce the dynamic change scope between fingerprint ridge line and the valley line, connect the fingerprint ridge line of some fractures simultaneously.The present invention has and strengthens the effective time-saving characteristics of effect preferably, can satisfy the requirement of online fingerprint recognition.

In order to describe content of the present invention easily, at first some terms are defined.

Definition 1: fingerprint.Be that human finger's end refers on the abdomen by the formed lines of concavo-convex skin.

Definition 2: fingerprint recognition.Fingerprint recognition system be one comprise that fingerprint image obtains, living creature characteristic recognition system that steps such as image enhancement processing, feature extraction and coupling are formed.

Definition 3: gray scale cuts.A certain interior in a big way gray-scale value is mapped to another interior gray-scale value.Gray scale cuts and can reduce the influence of sharp-pointed noise to image.

Definition 4: grey level stretching.A certain interior gray-scale value is mapped to another gray-scale value in larger scope.Grey level stretching can improve the contrast of gray level image, makes the details of image more obvious.

Definition 5: the fingerprint point field of direction.The field of direction on the fingerprint image crestal line on each pixel.

Definition 6: normalization structure tensor.The two-dimensional matrix of normalized symmetric positive definite, the little proper vector of its eigenwert be corresponding to the direction of fingerprint ridge line, and the big proper vector of eigenwert is corresponding to the vertical direction of fingerprint ridge line.

Definition 8: nonlinear diffusion model.Be a class partial differential equation, be used for describing the situation of change of the heat flow density in the thermal diffusion phenomenon, be widely applied to the every field of Flame Image Process afterwards.

Definition 9: anisotropy filtering.Anisotropic filtering be non-linear diffusion equation one of them separate the enhancing filtering that is used for carrying out image, the form of wherein separating is adjusted according to fingerprint point field of direction self-adaptation.

Technical solution of the present invention is as follows:

A kind of enhancement method of fingerprint image as shown in Figure 1, comprises following step:

Step 1: fingerprint foreground region image gray carried out gray scale cuts and grey level stretching, with eliminate sharp-pointed noise and reduce fingerprint ridge line and valley line between the dynamic change scope of gray-scale value, specifically may further comprise the steps:

Step 1-1: the average gray Mean of calculated fingerprint foreground region image gray, last mean value Hm, following mean value Lm, last standard deviation Hv and following standard deviation Lv:

$\mathrm{Mean}=\frac{1}{\mathrm{MN}}\underset{i=1}{\overset{M}{\mathrm{\Σ}}}\underset{j=1}{\overset{N}{\mathrm{\Σ}}}\mathrm{gray}(i,j)$

$\mathrm{Lm}=\frac{1}{N_0}\underset{k=1}{\overset{N_0}{\mathrm{\Σ}}}\mathrm{gray}(i,j)$ If gray (i, j)＜Mean

$\mathrm{Hm}=\frac{1}{M_0}\underset{k=1}{\overset{M_0}{\mathrm{\Σ}}}\mathrm{gray}(i,j)$ If gray (i, j)＞Mean

$\mathrm{Lv}=\sqrt{\frac{1}{N_0}\underset{k=1}{\overset{N_0}{\mathrm{\Σ}}}{(\mathrm{gray}(i,j)-\mathrm{Lm})}^2}$ If gray (i, j)＜Mean

$\mathrm{Hv}=\sqrt{\frac{1}{M_0}\underset{k=1}{\overset{M_0}{\mathrm{\Σ}}}{(\mathrm{gray}(i,j)-\mathrm{Hm})}^2}$ If gray (i, j)＞Mean

In the above-mentioned formula, gray (i, j) pixel (i among the expression fingerprint foreground region image gray, j) gray-scale value, M be fingerprint foreground region image gray in the horizontal pixel number of one dimension, N is fingerprint foreground region image gray at one dimension pixel number longitudinally, N ₀For gray-scale value among the fingerprint foreground region image gray less than total number of the pixel of average gray Mean, M ₀For gray-scale value among the fingerprint foreground region image gray greater than total number of the pixel of average gray Mean;

Step 1-2: fingerprint foreground region image gray is carried out gray scale cut, the fingerprint image foreground area is strengthened the influence of filtering, obtain the fingerprint foreground region image gray1 after the gray scale cutting with the sharp-pointed noise of eliminating in the fingerprint foreground region image, wherein:

Step 1-3: the fingerprint foreground region image gray1 after the gray scale cutting is carried out grey level stretching, obtain the fingerprint foreground region image gray2 after the grey level stretching, wherein:

$\mathrm{gray}2(i,j)=\frac{\mathrm{gray}1(i,j)-\mathrm{Lg}}{\mathrm{Hg}-\mathrm{Lg}}\×255$

Wherein, Hg is the maximum gradation value of the fingerprint foreground region image gray1 after gray scale cuts, and Lg is the minimum gradation value of the fingerprint foreground region image gray1 after gray scale cuts;

Step 2: the some field of direction of calculated fingerprint foreground region image gray2 specifically may further comprise the steps:

Step 2-1: use Gaussian filter g _σGray2 carries out gaussian filtering to the fingerprint foreground region image, obtains the fingerprint image v behind the gaussian filtering, wherein:

v(i，j)＝g _σ*gray2(i，j)

$g_{\mathrm{\σ}}(i,j)=\frac{1}{2\mathrm{\π\σ}}\exp (-\frac{i^2+j^2}{2{\mathrm{\σ}}^2})$

Wherein, σ is Gaussian filter g _σStandard deviation, * represents convolution algorithm;

Step 2-2: the horizontal first order difference gradient v that calculates the fingerprint image v behind the gaussian filtering respectively _xWith vertical first order difference gradient v _y

$\left[\begin{array}{c}{V}_x\\ V_y\end{array}\right]=\left[\begin{array}{c}\frac{v(i+1,j)-v(i-1,j)}{2}\\ \frac{v(i,j+1)-v(i,j-1)}{2}\end{array}\right]$

Step 2-3: the horizontal first order difference gradient v of the fingerprint image v behind the normalization gaussian filtering _xWith vertical first order difference gradient v _yWherein horizontal normalization first order difference gradient vector

Vertical normalization first order difference gradient vector

And $r=\sqrt{v_x^2(i,j)+v_y^2(i,j)};$

Step 2-4: the structure tensor S of the fingerprint image v behind the structure gaussian filtering, and the proper vector ω of computation structure tensor S; Wherein:

$S=\left(\begin{array}{cc}a& b\\ b& c\end{array}\right),$ And $\left\{\begin{array}{c}a=g_{\mathrm{\ρ}}*v_x^{\′2};\\ b=g_{\mathrm{\ρ}}*v_x^{\′}{v}_y^{\′}\\ c=g_{\mathrm{\ρ}}*v_y^{\′2};\end{array},;\right.$

$\mathrm{\ω}=\left(\begin{array}{c}{\mathrm{\ω}}_1\\ {\mathrm{\ω}}_2\end{array}\right)=\left(\begin{array}{c}\frac{2b}{\sqrt{{(c-a+\sqrt{{(c-a)}^2+{4b}^2})}^2+{4b}^2}}\\ \frac{c-a\±\sqrt{{(c-a)}^2+{4b}^2}}{\sqrt{{(c-a+\sqrt{{(c-a)}^2+{4b}^2})}^2+{4b}^2}}\end{array}\right)$

G wherein _ρBe that standard deviation is the Gaussian filter of ρ, ω ₁For corresponding to the proper vector perpendicular to the fingerprint ridge line direction, ω ₂Be proper vector corresponding to the fingerprint ridge line direction;

Step 2-5: for proper vector ω corresponding to the fingerprint ridge line direction ₂, by following formula calculate its corresponding fingerprint ridge line direction O (i, j);

$O(i,j)=\arctan \frac{2b}{c-a-\sqrt{{(c-a)}^2+{4b}^2}}$

Step 3: use the filtering method based on one dimension anisotropy nonlinear diffusion model that fingerprint foreground region image gray2 is carried out the filtering enhancing, to increase the contrast of fingerprint ridge line and valley line, the various structure borne noises of filtering specifically may further comprise the steps:

Step 3-1: structure fingerprint foreground region image gray2 (i, j) two one dimension anisotropic filter g of last each pixel ₁(x, y, θ, f) and g ₂(x, y, θ); Wherein:

$g_1(x,y,\mathrm{\θ},f)=\exp (-\frac{x_{\mathrm{\θ}}^2}{2{{\mathrm{\σ}}_1}^2})\·\sin (2\mathrm{\πf}\·x_{\mathrm{\θ}})$

$g_2(x,y,\mathrm{\θ})=c_1+\frac{c_2}{f}\·\exp (-\frac{x_{\mathrm{\θ}}^2}{2{\mathrm{\σ}}_2^2})$

x _θ＝x·cosθ+y·sinθ

$g_3=\frac{g_2(x,y,\mathrm{\θ})}{\underset{x=-\mathrm{wg}/2}{\overset{\mathrm{wg}/2}{\mathrm{\Σ}}}\underset{y=-\mathrm{wg}/2}{\overset{\mathrm{wg}/2}{\mathrm{\Σ}}}{g}_2(x,y:\mathrm{\θ}(i,j))}$

Wherein θ represents that (i, j) (i, j), f represents the frequency fields of value at the fingerprint image foreground area gray2 of [1/10,1/8] crestal line, g to Dui Ying fingerprint ridge line direction O for the fingerprint image foreground area pixel that calculates by step 2 ₃(x, y are to g θ) ₂(x, y θ) are the resulting one dimension anisotropic of normalized wave filter, σ ₁, σ ₂, c ₁And c ₂Empirical parameter for regulation;

Step 3-2: adopt one dimension anisotropic filter g ₁(θ f) carries out filtering for fingerprint foreground region image gray2 and strengthens, and obtains the fingerprint foreground region image gray3 after filtering for the first time strengthens for x, y, and concrete grammar is as follows:

$\mathrm{gray}3(i,j)=\underset{x=-\mathrm{wg}/2}{\overset{\mathrm{wg}/2}{\mathrm{\Σ}}}\underset{y=-\mathrm{wg}/2}{\overset{\mathrm{wg}/2}{\mathrm{\Σ}}}{g}_1(x,y:\mathrm{\θ}(i,j),f(i,j))\·\mathrm{gray}2(i-x,j-y)$

Wherein wg is the filtering window size of regulation;

Step 3-3: adopt one dimension anisotropic filter g ₃(x, y θ) carry out the filtering second time to the fingerprint foreground region image gray3 after the filtering enhancing first time and strengthen, and obtain the fingerprint foreground region image gray4 after final filtering strengthens, and concrete grammar is as follows:

$\mathrm{gray}4(i,j)=\underset{x=-\mathrm{wg}/2}{\overset{\mathrm{wg}/2}{\mathrm{\Σ}}}\underset{y=-\mathrm{wg}/2}{\overset{\mathrm{wg}/2}{\mathrm{\Σ}}}{g}_3(x,y:\mathrm{\θ}(i,j))\·\mathrm{gray}3(i-x,j-y)$

Wherein wg is the filtering window size of regulation.

Need to prove:

The effect that gray scale in the step 1 cuts is in order to eliminate sharp-pointed The noise, noise amplitude to be limited within certain scope.Also make simultaneously the grey value profile of whole fingerprint image in a zone of relatively concentrating, so that the grey level stretching of back is more effective.And the fundamental purpose of grey level stretching is for the foreground area that increases fingerprint image and the contrast of background area.

Step 2 has adopted the normalization structure tensor to estimate the some field of direction of fingerprint, and wherein each pixel in the fingerprint image foreground area all has the normalization structure tensor of a correspondence.The normalization structure tensor has removed the influence of the mould of gradient to the calculation level field of direction, only considers the direction of gradient in calculating.

In the step 3, on the crestal line direction,, can effectively strengthen low-quality fingerprint image foreground area, connect the crestal line of fracture with the enhancement algorithms of nonlinear diffusion model.

In the step 3, adopted the enhancement algorithms of two one-dimensional nonlinear diffusion models, the fingerprint image foreground area has been strengthened filtering, can improve the efficient that strengthens filtering greatly in the one-dimensional space.

In actual computation, in order to reduce calculated amount, we need at first create the look-up table of diverse location on the look-up table of each smooth function and all directions, so just can improve the speed of algorithm under the condition that increases memory space.Simultaneously, consume a large amount of time to gray level image is level and smooth with the Gauss template, for this reason we at interval the method for row and column some pixels are carried out convolution operation, and then the pixel that convolution is not crossed is carried out interpolation, we can save for about 1/3 time like this.

Innovation part of the present invention is:

1, adopts normalized structure tensor to obtain the some field of direction of fingerprint, can effectively improve the order of accuarcy that the field of direction is put in fingerprint inferior quality zone;

2, adopt two one dimension anisotropic diffusion filterings on the fingerprint ridge line direction, can not only obtain good filtering effect, can also save the needed time of filtering to a great extent;

3, adopt the method for interval row and column that the fingerprint image foreground area is carried out convolution, and then carry out interpolation.Can significantly reduce computing time like this;

Description of drawings

Fig. 1 is a schematic flow sheet of the present invention.

Embodiment

Adopt method of the present invention in MATLAB2009b software, to realize, and fingerprint image is from FVC2004 database picked at random.Finish in PC Intel Core 2.10GHZ with MATLAB and to be about averaging time that a width of cloth fingerprint image foreground area strengthens 4.7s.

Adopt in sum a kind of fingerprint image foreground area Enhancement Method based on Nonlinear Diffusion model and normalization structure tensor provided by the invention not only can effectively strengthen low-quality fingerprint image, and it is little to have an operand, can satisfy preferably the characteristics of online fingerprint recognition rate request.

Claims (1)

1. enhancement method of fingerprint image comprises following step:

Step 1: fingerprint foreground region image gray carried out gray scale cuts and grey level stretching, with eliminate sharp-pointed noise and reduce fingerprint ridge line and valley line between the dynamic change scope of gray-scale value, specifically may further comprise the steps:

Step 1-1: the average gray Mean of calculated fingerprint foreground region image gray, last mean value Hm, following mean value Lm, last standard deviation Hv and following standard deviation Lv:

$\mathrm{Mean}=\frac{1}{\mathrm{MN}}\underset{i=1}{\overset{M}{\mathrm{\Σ}}}\underset{j=1}{\overset{N}{\mathrm{\Σ}}}\mathrm{gray}(i,j)$

$\mathrm{Lm}=\frac{1}{N_0}\underset{k=1}{\overset{N_0}{\mathrm{\Σ}}}\mathrm{gray}(i,j)$ If gray (i, j)＜Mean

$\mathrm{Hm}=\frac{1}{M_0}\underset{k=1}{\overset{M_0}{\mathrm{\Σ}}}\mathrm{gray}(i,j)$ If gray (i, j)＞Mean

$\mathrm{Lv}=\sqrt{\frac{1}{N_0}\underset{k=1}{\overset{N_0}{\mathrm{\Σ}}}{(\mathrm{gray}(i,j)-\mathrm{Lm})}^2}$ If gray (i, j)＜Mean

$\mathrm{Hv}=\sqrt{\frac{1}{M_0}\underset{k=1}{\overset{M_0}{\mathrm{\Σ}}}{(\mathrm{gray}(i,j)-\mathrm{Hm})}^2}$ If gray (i, j)＞Mean

In the above-mentioned formula, gray (i, j) pixel (i among the expression fingerprint foreground region image gray, j) gray-scale value, M be fingerprint foreground region image gray in the horizontal pixel number of one dimension, N is fingerprint foreground region image gray at one dimension pixel number longitudinally, N ₀For gray-scale value among the fingerprint foreground region image gray less than total number of the pixel of average gray Mean, M ₀For gray-scale value among the fingerprint foreground region image gray greater than total number of the pixel of average gray Mean;

Step 1-2: fingerprint foreground region image gray is carried out gray scale cut, the fingerprint image foreground area is strengthened the influence of filtering, obtain the fingerprint foreground region image gray1 after the gray scale cutting with the sharp-pointed noise of eliminating in the fingerprint foreground region image, wherein:

Step 1-3: the fingerprint foreground region image gray1 after the gray scale cutting is carried out grey level stretching, obtain the fingerprint foreground region image gray2 after the grey level stretching, wherein:

$\mathrm{gray}2(i,j)=\frac{\mathrm{gray}1(i,j)-\mathrm{Lg}}{\mathrm{Hg}-\mathrm{Lg}}\×255$

Wherein, Hg is the maximum gradation value of the fingerprint foreground region image gray1 after gray scale cuts, and Lg is the minimum gradation value of the fingerprint foreground region image gray1 after gray scale cuts;

Step 2: the some field of direction of calculated fingerprint foreground region image gray2 specifically may further comprise the steps:

Step 2-1, use Gaussian filter g _σGray2 carries out gaussian filtering to the fingerprint foreground region image, obtains the fingerprint image v behind the gaussian filtering, wherein:

v(i，j)＝g _σ*gray2(i，j)

$g_{\mathrm{\σ}}(i,j)=\frac{1}{2\mathrm{\π\σ}}\exp (-\frac{i^2+j^2}{2{\mathrm{\σ}}^2})$

Wherein, σ is Gaussian filter g _σStandard deviation, * represents convolution algorithm;

Step 2-2: the horizontal first order difference gradient v that calculates the fingerprint image v behind the gaussian filtering respectively _xWith vertical first order difference gradient v _y

$\left[\begin{array}{c}{V}_x\\ V_y\end{array}\right]=\left[\begin{array}{c}\frac{v(i+1,j)-v(i-1,j)}{2}\\ \frac{v(i,j+1)-v(i,j-1)}{2}\end{array}\right]$

Step 2-3: the horizontal first order difference gradient v of the fingerprint image v behind the normalization gaussian filtering _xWith vertical first order difference gradient v _yWherein horizontal normalization first order difference gradient vector Vertical normalization first order difference gradient vector

And $r=\sqrt{v_x^2(i,j)+v_y^2(i,j)};$

Step 2-4: the structure tensor S of the fingerprint image v behind the structure gaussian filtering, and the proper vector ω of computation structure tensor S; Wherein:

$S=\left(\begin{array}{cc}a& b\\ b& c\end{array}\right),$ And $\left\{\begin{array}{c}a=g_{\mathrm{\ρ}}*v_x^{\′2};\\ b=g_{\mathrm{\ρ}}*v_x^{\′}{v}_y^{\′}\\ c=g_{\mathrm{\ρ}}*v_y^{\′2};\end{array},;\right.$

$\mathrm{\ω}=\left(\begin{array}{c}{\mathrm{\ω}}_1\\ {\mathrm{\ω}}_2\end{array}\right)=\left(\begin{array}{c}\frac{2b}{\sqrt{{(c-a+\sqrt{{(c-a)}^2+4b^2})}^2+{4b}^2}}\\ \frac{c-a\±\sqrt{{(c-a)}^2+4b^2}}{\sqrt{{(c-a+\sqrt{{(c-a)}^2+4b^2})}^2+4b^2}}\end{array}\right)$

G wherein _ρBe that standard deviation is the Gaussian filter of ρ, ω ₁For corresponding to the proper vector perpendicular to the fingerprint ridge line direction, ω ₂Be proper vector corresponding to the fingerprint ridge line direction;

Step 2-5: for proper vector ω corresponding to the fingerprint ridge line direction ₂, by following formula calculate its corresponding fingerprint ridge line direction O (i, j);

$O(i,j)=\arctan \frac{2b}{c-a-\sqrt{{(c-a)}^2+{4b}^2}}$

Step 3: use the filtering method based on one dimension anisotropy nonlinear diffusion model that fingerprint foreground region image gray2 is carried out the filtering enhancing, to increase the contrast of fingerprint ridge line and valley line, the various structure borne noises of filtering specifically may further comprise the steps:

Step 3-1, structure fingerprint foreground region image gray2 (i, j) two one dimension anisotropic filter g of last each pixel ₁(x, y, θ, f) and g ₂(x, y, θ); Wherein:

$g_1(x,y,\mathrm{\θ},f)=\exp (-\frac{x_{\mathrm{\θ}}^2}{2{{\mathrm{\σ}}_1}^2})\·\sin (2\mathrm{\πf}\·x_{\mathrm{\θ}})$

$g_2(x,y,\mathrm{\θ})=c_1+\frac{c_2}{f}\·\exp (-\frac{x_{\mathrm{\θ}}^2}{2{\mathrm{\σ}}_2^2})$

x _θ＝x·cosθ+y·sinθ

$g_3=\frac{g_2(x,y,\mathrm{\θ})}{\underset{x=-\mathrm{wg}/2}{\overset{\mathrm{wg}/2}{\mathrm{\Σ}}}\underset{y=-\mathrm{wg}/2}{\overset{\mathrm{wg}/2}{\mathrm{\Σ}}}{g}_2(x,y:\mathrm{\θ}(i,j))}$

Wherein θ represents that (i, j) (i, j), f represents the frequency fields of value at the fingerprint image foreground area gray2 of [1/10,1/8] crestal line, g to Dui Ying fingerprint ridge line direction O for the fingerprint image foreground area pixel that calculates by step 2 ₃(x, y are to g θ) ₂(x, y θ) are the resulting one dimension anisotropic of normalized wave filter, σ ₁, σ ₂, c ₁And c ₂Empirical parameter for regulation;

Step 3-2: adopt one dimension anisotropic filter g ₁(θ f) carries out filtering for fingerprint foreground region image gray2 and strengthens, and obtains the fingerprint foreground region image gray3 after filtering for the first time strengthens for x, y, and concrete grammar is as follows:

$\mathrm{gray}3(i,j)=\underset{x=-\mathrm{wg}/2}{\overset{\mathrm{wg}/2}{\mathrm{\Σ}}}\underset{y=-\mathrm{wg}/2}{\overset{\mathrm{wg}/2}{\mathrm{\Σ}}}{g}_1(x,y:\mathrm{\θ}(i,j),f(i,j))\·\mathrm{gray}2(i-x,j-y)$

Wherein wg is the filtering window size of regulation;

Step 3-3: adopt one dimension anisotropic filter g ₃(x, y θ) carry out the filtering second time to the fingerprint foreground region image gray3 after the filtering enhancing first time and strengthen, and obtain the fingerprint foreground region image gray4 after final filtering strengthens, and concrete grammar is as follows:

$\mathrm{gray}4(i,j)=\underset{x=-\mathrm{wg}/2}{\overset{\mathrm{wg}/2}{\mathrm{\Σ}}}\underset{y=-\mathrm{wg}/2}{\overset{\mathrm{wg}/2}{\mathrm{\Σ}}}{g}_3(x,y:\mathrm{\θ}(i,j))\·\mathrm{gray}3(i-x,j-y)$

Wherein wg is the filtering window size of regulation.

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