CN103116744A - Fake fingerprint detection method based on markov random field (MRF) and support vector machine-k nearest neighbor (SVM-KNN) classification - Google Patents

Abstract

A fake fingerprint detection method based on markov random field (MRF) and support vector machine-k nearest neighbor (SVM-KNN) classification includes steps: (1) fingerprint image feature extracting: (1.1) first-order statistics (FOS), (1.2) a gray level co occurrence matrix (GLCM) and (1.3) an MRF; (2) SVM training: training the FOS and the GLCM feature vector and the MRF feature vector to obtain a model A and a model B; (3) SVM-KNN classification: (3.1) the SVM classification mechanism and (3.2) SVM-KNN classifier forming; and (4) decision fusion for true and false fingerprint detection. Presently related articles for fake fingerprint detection by aid of the GLCM and the MRF are not found, and the fake fingerprint detection method achieves the purpose of identifying true and false fingerprints by aid of physical structures of the two feature quantized fingerprint images. Experiment results prove that the false accept rate and the false reject rate of the algorithm are respectively 1.84% and 1.79%, and therefore the fake fingerprint detection method is high in accuracy and good in practicality.

Description

False fingerprint detection method based on MRF and SVM-KNN classification

Technical field

The present invention relates to the technical fields such as image processing and pattern-recognition, main contents are the detection method of false fingerprint.

Background technology

Image characteristics extraction, features training and Decision fusion etc. are the important knowledge points in the Image Processing and Pattern Recognition field, and they are all closely related with the effect of false fingerprint detection method.False fingerprint detection method process mainly is divided into four steps such as image characteristics extraction, SVM training, SVM-KNN classification and Decision fusion, and wherein feature extraction is particularly important in false fingerprint detection process.

The take the fingerprint textural characteristics information of image of Emanuela Marasco detects false fingerprint by the first-order statistics amount.The method is in the situation that Acquisition Instrument resolution is higher, and false fingerprint recognition rate is relatively good, but general for the discrimination performance of the general image in different resolution of 500dpi.Nikam and Agrwal have proposed another method based on texture, analyze the activity of fingerprint image with the relevant gray level of fingerprint pixel.Abhyankar and Schuckers have proposed a kind of method based on multi-resolution texture analysis and lines frequency analysis, and when quantizing the physical arrangement variation with different texture features, grey level distribution changes.But the method has certain limitation in actual applications, and is because the calculating of local ridge frequency can be subjected to weather effect, also relevant with the different skin situation.

Gray level co-occurrence matrixes (GLCM) is based upon on the basis of joint probability density of two position pixel values, can be used for gray-scale value is converted into texture information, and the reflection gradation of image is about the integrated information of adjacent spaces, direction, amplitude of variation.GLCM adds up the gray-scale value situation that keeps the pixel of certain distance on image to obtain.Haralick had studied the space dependence of gray level in the image texture in 1973, the essence that proposes gray level co-occurrence matrixes is that gray scale is that (its position is (x1 for the pixel of x from image, y1)) set out, statistics and its number of times that occurs simultaneously apart from the pixel (x2, y2) that is y for the d gray scale.Usually can characterize the GLCM feature with energy, contrast, entropy, local stationary, auto-correlation and dissimilarity equiscalar.

Markov random file (MRF) model is to be proposed by Besag in 1973, can express view data the Spatial Probability relation modeling and be used for the textural characteristics model, it is effective that MRF has been proved to be for image characteristics extraction.The MRF textural characteristics will be found out the relation of interdependence between texture primitive and texture primitive exactly from the structured analysis method angle.Primitive relation for the MRF textural characteristics can represent with conditional probability model.The texture region of random image can be regarded the limited sampling of bivariate stochastic process as, and different statistical parameters represents different stochastic processes.The dependence that shows between texture primitive has reflected that the difference of texture primitive is assembled, and the texture between different the gathering corresponding different statistical parameters.MRF on applied mathematics can describe the random character of texture well.

SVM is a kind of sorting technique that is based upon on the Statistical Learning Theory basis, it is mainly based on following three kinds of considerations: (1) is based on structural risk minimization, tie up to control the structure risk of study machine by the VC of minimization function collection, make it have stronger Generalization Ability; (2) realize the control to the VC dimension by maximizing class interval (seeking the optimal classification lineoid), this is that correlation theorem by Statistical Learning Theory guarantees; (3) SVM adopts the coring technology technically, according to the theorem in functional, seeks a function (kernel function) with inner product in sample space pair.

Svm classifier has two requirements: 1) can correctly distinguish two class samples; 2) classifying face of class interval maximum is defined as the optimal classification face.Support vector is exactly the sample on the optimal classification face.

Nearest neighbour method (being called for short NN) is one of most important method in the pattern-recognition nonparametric method, the very large characteristics of NN are all as " representative point " with whole sample points in all kinds of, 1NN is as representative point with all training samples, therefore need to calculate sample p to be identified to the distance of all training samples when classification, result is exactly the classification that belongs to the nearest training sample of p.KNN is the popularization of 1NN, selects K arest neighbors when namely classifying, and sees which kind of the majority in this K neighbour belongs to, and just which kind of p assigned to.

The advantage of SVM has: simple in structure, pace of learning is fast, promote that performance is good, have unique minimal point etc. during Optimization Solution; Can obtain various classification curved surface by revising kernel function.Support vector machine puts forward in order to solve two classification problems, does not need to utilize sample to trend towards infinitely-great gradual condition.Yet there is a shortcoming in the svm classifier algorithm: during less than a given threshold epsilon, its classification accuracy can reduce when sample distance classification lineoid.

False fingerprint detection method relatively more commonly used can be divided into two classes at present: the characteristics such as first kind finger temperature, skin conductivity, pulse blood oxygen, these characteristics can obtain by adding extra hardware device to detect on fingerprint acquisition instrument, but can increase the cost of Acquisition Instrument, these class methods are called hardware based false fingerprint detection method.The Equations of The Second Kind method is done extra processing in order to detect the activated information of fingerprint image to the sample fingerprint image, and these class methods are called the method based on software.Method cost based on software is low, and is less to user's invasive, and can be used for existing fingerprint acquisition instrument.Therefore to the research based on the false fingerprint detection method of software, have great practical value and dissemination.

Summary of the invention

The present invention will overcome still still lower present situation of not mature enough and recognition correct rate of existing false fingerprint detection technology, a kind of false fingerprint detection method based on MRF and SVM-KNN classification is proposed, the method is extracted the features such as first-order statistics amount (FOS), gray level co-occurrence matrixes (GLCM) and markov random file (MRF) of image, obtain proper vector by feature selecting, then train by SVM; Because there is instability in SVM near the sample classification lineoid, introduce the SVM-KNN classification false fingerprint is detected, by the Decision fusion technology, fingerprint true and false made accurate judgement at last.

A kind of false fingerprint detection method based on MRF and SVM-KNN classification said method comprising the steps of:

1) feature extraction

1.1) first-order statistics amount (FOS)

Be used for weighing the probability that a certain gray-scale value of image random site occurs, between pixel, correlativity can show the true and false property of fingerprint.By the intensity of variation between the histogram calculation pixel, and extract FOS, target is when the physical arrangement of image changes, and quantizes the variation of grey level distribution, then differentiates thus true and false fingerprint.Suppose that H (n) is normalization histogram, N represents maximum gray scale, and μ is gray average, and FOS is calculated as follows:

Energy: $e=\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}H{\left(n\right)}^2---\left(1\right)$

Entropy: $s=-\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}H\left(n\right)\log H\left(n\right)---\left(2\right)$

Variance: ${\mathrm{\σ}}^2=\underset{n=0}{\overset{N}{\mathrm{\Σ}}}{(n-\mathrm{\μ})}^{2}H\left(n\right)---\left(3\right)$

The degree of bias: ${\mathrm{\γ}}_1=\frac{1}{{\mathrm{\σ}}^3}\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}{(n-\mathrm{\μ})}^{3}H\left(n\right)---\left(4\right)$

Kurtosis: ${\mathrm{\γ}}_2=\frac{1}{{\mathrm{\σ}}^4}\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}{(n-\mathrm{\μ})}^{4}H\left(n\right)---\left(5\right)$

1.2) gray level co-occurrence matrixes (GLCM)

The GLCM of image can reflect gradation of image about the integrated information of amplitude of variation, direction, adjacent spaces, and it is the basis of analysis image local mode and queueing discipline thereof.It is a good method that the GLCM of image has been proved to be on texture is determined, being widely used in grayvalue transition is texture information.Haralick has studied the space dependence of gray level in the image texture in 1973, propose the essence of GLCM.In image, gray scale is the pixel (its position is (i, k)) of x, and statistics is d with its distance, and direction is θ, and gray scale is the pixel (i+D of y _i, k+D _k), the mathematic(al) representation of occurrence number p (x, y, d, θ) is:

p(x,y,d,θ)={[(i,k),(i+D _i,k+D _k)|f(i,f)=x,f(i+D _i,k+D _k)=y]} (6)

X in formula, y=1,2 ..., the gray level in the L presentation video; I, k=1,2 ..., K represents pixel coordinate;

For generating the step-length of gray level co-occurrence matrixes; D _i, D _kIt is position offset; Generate the desirable any direction of direction θ, thereby generate the co-occurrence matrix of different directions.GLCM is carried out normalized:

$G(x,y)=\frac{p(x,y)}{\underset{x=1}{\overset{L}{\mathrm{\Σ}}}\underset{y=1}{\overset{L}{\mathrm{\Σ}}}p(x,y)}---\left(7\right)$

The situation of co-occurrence matrix being described texture quantizes, and because the fingerprint ridge width in fingerprint base differs, in order to improve the discrimination of false fingerprint, it is that 1 ~ 4, θ gets respectively 0 ° that this paper method has been extracted apart from d, and 45 °, 90 °, 135 ° of four directions amount to 16 GLCM; Then calculate respectively corresponding energy, contrast, entropy, local stationary, auto-correlation and dissimilarity, computing formula is as follows:

Energy:

$\mathrm{ASM}={\mathrm{\Σ}}_{x=1}^L{\mathrm{\Σ}}_{y=1}^L{\left(G(x,y)\right)}^2---\left(8\right)$

Contrast:

$\mathrm{CON}={\mathrm{\Σ}}_{n=0}^{L-1}{n}^2\left\{{\mathrm{\Σ}}_{|x-y|=n}G(x,y)\right\}---\left(9\right)$

Entropy:

$\mathrm{ENT}=-{\mathrm{\Σ}}_{x=1}^L{\mathrm{\Σ}}_{y=1}^{L}G(x,y)\log G(x,y)---\left(10\right)$

Local stationary:

$\mathrm{IDM}=\underset{x=1}{\overset{L}{\mathrm{\Σ}}}\underset{y=1}{\overset{L}{\mathrm{\Σ}}}\frac{G(x,y)}{1+{(x-y)}^2}---\left(11\right)$

Auto-correlation:

$\mathrm{COR}=\underset{x=1}{\overset{L}{\mathrm{\Σ}}}\underset{y=1}{\overset{L}{\mathrm{\Σ}}}\frac{(x,y)G(x,y)-{\mathrm{\μ}}_x{\mathrm{\μ}}_y}{s_x{s}_y}---\left(12\right)$

Dissimilarity:

$\mathrm{DIS}=\underset{x=1}{\overset{L}{\mathrm{\Σ}}}\underset{y=1}{\overset{L}{\mathrm{\Σ}}}\frac{\left|x,y\right|}{G(x,y)}---\left(13\right)$

Wherein,

${\mathrm{\μ}}_x=\underset{x=1}{\overset{L}{\mathrm{\Σ}}}\underset{y=1}{\overset{L}{\mathrm{\Σ}}}x\·G(x,y)---\left(14\right)$

${\mathrm{\μ}}_y=\underset{x=1}{\overset{L}{\mathrm{\Σ}}}\underset{y=1}{\overset{L}{\mathrm{\Σ}}}y\·G(x,y)---\left(15\right)$

$s_x^2=\underset{x=1}{\overset{L}{\mathrm{\Σ}}}\underset{y=1}{\overset{L}{\mathrm{\Σ}}}G(x,y){(x-{\mathrm{\μ}}_x)}^2---\left(16\right)$

$s_y^2=\underset{x=1}{\overset{L}{\mathrm{\Σ}}}\underset{y=1}{\overset{L}{\mathrm{\Σ}}}G(x,y){(y-{\mathrm{\μ}}_y)}^2---\left(17\right)$

These textural characteristics can effectively be described the textural characteristics of fingerprint image, have distinguishing ability preferably.

1.3) markov random file (MRF)

MRF is a two-dimensional lattice, can describe each point with probability model, and the supposed premise of MRF is the pixel value that the pixel value of each point in dot matrix only depends on pixel in its neighborhood.MRF can describe with following local condition probability density (PDF):

p(x(c)|x(m),m=1,2,…,N×M,c≠m)=p(x(c)|x(m),m∈N(c)) (18)

Wherein x (c) is the pixel value at dot matrix N * M mid point c, and N (c) is the neighborhood territory pixel point set centered by c, and the value of p (x (c)) is subjected to the impact of x (m).If the PDF Gaussian distributed, MRF is Gauss-Markov random field (GMRF) so.Estimate the symmetric difference equation of pixel gray-scale value with neighborhood information:

x(c)=∑β _c,m[x(c+m)+x(c-m)]+e _c (19)

β wherein _c,mContribute to the weights of central pixel point gray-scale value for each neighborhood territory pixel point, e _cBe 0 Gaussian distribution noise for average, m is the deviation of decentering point c.Being expressed as the matrix notation formula is:

x(c)=β ^TQ _c+e _c (20)

Wherein β is by β _c,mThe vector that forms, Q _cBe defined as follows:

$Q_c=\left[\begin{array}{c}x(c+m_1)+x(c-m_1)\\ x(c+m_2)+x(c-m_2)\\ x\left({c+m}_3\right)+x(c-m_3)\\ ...\end{array}\right]---\left(21\right)$

Utilize least square method to calculate texture characteristic amount,

$\mathrm{\β}={\left[\underset{c\∈U}{\mathrm{\Σ}}{Q}_c{Q}_c^T\right]}^{-1}\left[\underset{c\∈U}{\mathrm{\Σ}}{Q}_{c}x\left(c\right)\right]---\left(22\right)$

With GMRF, fingerprint image is carried out second order parameter and estimate, in image, arbitrary 3 * 3 windows are image sampling template scope, Q thus _cDetermine, U represents fingerprint image, is exactly eigenwert for each window β of 3 * 3, and the MRF eigenwert changes insensitive to gray level.

2) SVM training

Use LIBSVM proper vector is trained and classify, choose at random in database 50% image as the training fingerprint, all the other are used for class test.The general step that LIBSVM uses is as follows:

A) prepare data set according to the desired form of LIBSVM software package;

B) data are carried out simple zoom operations;

C) select the RBF kernel function;

D) adopt cross validation to select optimal parameter C and g;

E) adopt optimal parameter C and g that whole training set is trained and obtain supporting vector machine model;

F) utilize the model that obtains test and predict, obtain predicted value Sc.

Sc is the degree of confidence of true fingerprint, and threshold value is T1:

(a) if Sc＜T1 judges that fingerprint is false;

(b) if Sc 〉=T1, judge that fingerprint is as true.

3) SVM-KNN classification

3.1) svm classifier mechanism

The SVM method is by a Nonlinear Mapping f, sample space is mapped to (Hilbert space) in a higher-dimension and even infinite dimensional feature space, make the problem of Nonlinear separability in original sample space be converted into the problem that to divide at the feature space neutral line, and seek the optimum linearity classification lineoid of sample in this feature space.

3.2) formation of SVM-KNN sorter

There is a shortcoming in tradition svm classifier algorithm: during less than a given threshold epsilon, its classification accuracy can reduce when sample distance classification lineoid.Determine the classification accuracy of SVM in the svm classifier process for the degree of error of the representative point of every class support vector of obtaining, can classify to improve classification accuracy to the sample that deviation easily occurs by KNN.Particularly, for sample x to be identified, calculate x and two class support vector representative point x ⁺And x ^-Range difference, when range difference less than a given threshold value, it is nearer to be that x separates the interface, namely fall into regional III(with reference to Fig. 2), SVM only calculates the distance of a representative point of getting with two classes and classifies than being easier to misclassification, and adopt KNN that test sample book is classified, calculate the distance of sample to be identified and each support vector to draw classification results.

With reference to Fig. 3, when expression utilizes the SVM-KNN classification, the variation of ε threshold value causes the variation of the differentiation accuracy of true fingerprint and false fingerprint, threshold testing scope 0.1 ~ 1.0.Find that by test when the ε=0.2, the differentiation accuracy of the true fingerprint of MSO1300 and false fingerprint reaches the highest, is respectively 97.86% and 96.79%.And the true and false fingerprint judgment accuracy of simple svm classifier is respectively 97.3% and 96.1%.As shown in Figure 3, the SVM-KNN classification has certain improvement to svm classifier.

4) Decision fusion

By analyzing the training set of known class, estimate to obtain the correlation parameter of disaggregated model, infer accordingly the classification of test data.This paper uses LIBSVM to train, and class test uses SVM-KNN.

This paper utilizes respectively FOS and GLCM characteristic quantity to obtain training pattern A, and the MRF characteristic quantity obtains training pattern B, obtains test sample book to the ultimate range of A by training sample

And minor increment

, to the ultimate range of B

And minor increment

Range formula is as follows:

d(x _r,x _i)=||Φ(x _r)-Φ(x _i)|| ²=k(x _r,x _r)-2k(x _r,x _i)+k(x _i,x _i) (23)

D (x wherein _r, x _i) expression sample to be tested x _rTo arbitrary test sample book x _iDistance, k (x _r, x _i) be the SVM kernel function.

By training pattern utilize SVM-KNN respectively test sample book classify and obtain classification number

,

, for test sample book try to achieve its minute be clipped to A, B apart from d _a, d _b, the classification results of test sample book

Obtained by following formula:

$\&PartialD;=\left\{\begin{array}{cc}{\&PartialD;}_2,& \mathrm{if}\frac{d_a-d_a^{\min }}{d_a^{\max }-d_a^{\min }}<\frac{d_b-d_b^{\min }}{d_b-d_b^{\min }}\\ {\&PartialD;}_1,& \mathrm{otherwise}\end{array}\right.---\left(24\right)$

Technical conceive of the present invention is: it is one of field the most basic and important in false fingerprint identification method that fingerprint image characteristics is extracted, and it is fingerprint image to be carried out the basic premise of quantitative analysis and pattern-recognition.Present false fingerprint recognition field does not also have clear and definite feature extraction regulation, and feature extraction is substantially all to determine according to the quality for false identification of fingerprint rate.This method is with FOS, GLCM and the MRF combination of eigenvectors as the false fingerprint of identification, and Decision fusion makes net result more accurate, on a large amount of experimental verifications bases, has very high confidence level.

Beneficial effect of the present invention mainly is on the one hand to provide the two kinds of new feature GLCM that considers and MRF for the identification of false fingerprint, new feature add efficient and the accuracy rate that has improved false fingerprint detection; On the other hand the Decision fusion technology by to the fusion of different decision-makings to obtain classification results more accurately, false fingerprint recognition ability has obtained checking, the result shows that the method has very high practical value, and the image that obtains of fingerprint acquisition instrument commonly used can carry out true and false checking by the method in the market.

Description of drawings

Fig. 1 is based on the false fingerprint detection method process flow diagram of MRF and SVM-KNN classification.

Fig. 2 is SVM-KNN principle of classification figure.

Fig. 3 is SVM-KNN classification thresholds value figure.

Embodiment

The invention will be further described below in conjunction with accompanying drawing.

Following content, in front of looking, the content of face is almost the same, there there problem?

With reference to Fig. 1-3, a kind of false fingerprint detection method based on MRF and SVM-KNN classification said method comprising the steps of:

1) feature extraction

1.1) first-order statistics amount (FOS)

Be used for weighing the probability that a certain gray-scale value of image random site occurs, between pixel, correlativity can show the true and false property of fingerprint.By the intensity of variation between the histogram calculation pixel, and extract FOS, target is when the physical arrangement of image changes, and quantizes the variation of grey level distribution, then differentiates thus true and false fingerprint.Suppose that H (n) is normalization histogram, N represents maximum gray scale, and μ is gray average, and FOS is calculated as follows:

Energy: $e=\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}H{\left(n\right)}^2---\left(1\right)$

Entropy: $s=-\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}H\left(n\right)\log H\left(n\right)---\left(2\right)$

Variance: ${\mathrm{\&sigma;}}^2=\underset{n=0}{\overset{N}{\mathrm{\&Sigma;}}}{(n-\mathrm{\&mu;})}^{2}H\left(n\right)---\left(3\right)$

The degree of bias: ${\mathrm{\&gamma;}}_1=\frac{1}{{\mathrm{\&sigma;}}^3}\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{(n-\mathrm{\&mu;})}^{3}H\left(n\right)---\left(4\right)$

Kurtosis: ${\mathrm{\&gamma;}}_2=\frac{1}{{\mathrm{\&sigma;}}^4}\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{(n-\mathrm{\&mu;})}^{4}H\left(n\right)---\left(5\right)$

1.2) gray level co-occurrence matrixes (GLCM)

The GLCM of image can reflect gradation of image about the integrated information of amplitude of variation, direction, adjacent spaces, and it is the basis of analysis image local mode and queueing discipline thereof.It is a good method that the GLCM of image has been proved to be on texture is determined, being widely used in grayvalue transition is texture information.Haralick has studied the space dependence of gray level in the image texture in 1973, propose the essence of gray level co-occurrence matrixes.In image, gray scale is the pixel (its position is (i, k)) of x, and statistics is d with its distance, and direction is θ, and gray scale is the pixel (i+D of y _i, k+D _k), the mathematic(al) representation of occurrence number p (x, y, d, θ) is:

$\begin{array}{c}p(x,y,d,\mathrm{\&theta;})=\left\{\right[(i,k),(i+D_i,k+D_k)|f(i,k)=x,\\ f(i+D_i,k+D_k)=y\left]\right\}\end{array}---\left(6\right)$

X in formula, y=1,2 ..., the gray level in the L presentation video; I, k=1,2 ..., K represents pixel coordinate; D is for generating the step-length of gray level co-occurrence matrixes; D _i, D _kIt is position offset; Generate the desirable any direction of direction θ, thereby generate the co-occurrence matrix of different directions.GLCM is carried out normalized:

$G(x,y)=\frac{p(x,y)}{\underset{x=1}{\overset{L}{\mathrm{\&Sigma;}}}\underset{y=1}{\overset{L}{\mathrm{\&Sigma;}}}p(x,y)}---\left(7\right)$

The situation of co-occurrence matrix being described texture quantizes, because the fingerprint ridge width in fingerprint base differs, in order to improve the discrimination of false fingerprint, it is that 1 ~ 4, θ gets respectively 0 °, 45 ° that this paper method has been extracted apart from d, 90 °, 135 ° of four directions amount to 16 gray level co-occurrence matrixes; Then calculate respectively corresponding energy, contrast, entropy, local stationary, auto-correlation and dissimilarity, computing formula is as follows:

Energy:

$\mathrm{ASM}={\mathrm{\&Sigma;}}_{x=1}^L{\mathrm{\&Sigma;}}_{y=1}^L{\left(G(x,y)\right)}^2---\left(8\right)$

Contrast:

$\mathrm{CON}={\mathrm{\&Sigma;}}_{n=0}^{L-1}{n}^2\left\{{\mathrm{\&Sigma;}}_{|x-y|=n}G(x,y)\right\}---\left(9\right)$

Entropy:

$\mathrm{ENT}=-{\mathrm{\&Sigma;}}_{x=1}^L{\mathrm{\&Sigma;}}_{y=1}^{L}G(x,y)\log G(x,y)---\left(10\right)$

Local stationary:

$\mathrm{IDM}=\underset{x=1}{\overset{L}{\mathrm{\&Sigma;}}}\underset{y=1}{\overset{L}{\mathrm{\&Sigma;}}}\frac{G(x,y)}{1+{(x-y)}^2}---\left(11\right)$

Auto-correlation:

$\mathrm{COR}=\underset{x=1}{\overset{L}{\mathrm{\&Sigma;}}}\underset{y=1}{\overset{L}{\mathrm{\&Sigma;}}}\frac{(x,y)G(x,y)-{\mathrm{\&mu;}}_x{\mathrm{\&mu;}}_y}{s_x{s}_y}---\left(12\right)$

Dissimilarity:

$\mathrm{DIS}=\underset{x=1}{\overset{L}{\mathrm{\&Sigma;}}}\underset{y=1}{\overset{L}{\mathrm{\&Sigma;}}}\frac{\left|x,y\right|}{G(x,y)}---\left(13\right)$

Wherein,

${\mathrm{\&mu;}}_x=\underset{x=1}{\overset{L}{\mathrm{\&Sigma;}}}\underset{y=1}{\overset{L}{\mathrm{\&Sigma;}}}x\&CenterDot;G(x,y)---\left(14\right)$

${\mathrm{\&mu;}}_y=\underset{x=1}{\overset{L}{\mathrm{\&Sigma;}}}\underset{y=1}{\overset{L}{\mathrm{\&Sigma;}}}y\&CenterDot;G(x,y)---\left(15\right)$

$s_x^2=\underset{x=1}{\overset{L}{\mathrm{\&Sigma;}}}\underset{y=1}{\overset{L}{\mathrm{\&Sigma;}}}G(x,y){(x-{\mathrm{\&mu;}}_x)}^2---\left(16\right)$

$s_y^2=\underset{x=1}{\overset{L}{\mathrm{\&Sigma;}}}\underset{y=1}{\overset{L}{\mathrm{\&Sigma;}}}G(x,y){(y-{\mathrm{\&mu;}}_y)}^2---\left(17\right)$

These textural characteristics can effectively be described the textural characteristics of fingerprint image, have distinguishing ability preferably.

1.3) markov random file (MRF)

MRF is a two-dimensional lattice, can describe each point with probability model, and the supposed premise of MRF is the pixel value that the pixel value of each point in dot matrix only depends on pixel in its neighborhood.MRF can describe with following local condition probability density (PDF):

$\begin{array}{c}p\left(x\left(c\right)\right|x\left(m\right),m=\mathrm{1,2},...,N\&times;M,c\&NotEqual;m)\\ =p\left(x\left(c\right)\right|x\left(m\right),m\&Element;N\left(c\right))\end{array}---\left(18\right)$

Wherein x (c) is the pixel value at dot matrix N * M mid point c, and N (c) is the field pixel point set centered by c, and the value of p (x (c)) is subjected to the impact of x (m).If the PDF Gaussian distributed, MRF is Gauss-Markov random field (GMRF) so.Estimate the symmetric difference equation of pixel gray-scale value with neighborhood information:

x(c)=∑β _c,m[x(c+m)+x(c-m)]+e _c (19)

β wherein _c,mContribute to the weights of central pixel point gray-scale value for each neighborhood territory pixel point, e _cBe 0 Gaussian distribution noise for average, m is the deviation of decentering point c.Being expressed as the matrix notation formula is:

x(c)=β ^TQ _c+e _c (20)

Wherein β is by β _c,mThe vector that forms, Q _cBe defined as follows:

$Q_c=\left[\begin{array}{c}x(c+m_1)+x(c-m_1)\\ x(c+m_2)+x(c-m_2)\\ x\left({c+m}_3\right)+x(c-m_3)\\ ...\end{array}\right]---\left(21\right)$

Utilize least square method to calculate texture characteristic amount,

$\mathrm{\&beta;}={\left[\underset{c\&Element;U}{\mathrm{\&Sigma;}}{Q}_c{Q}_c^T\right]}^{-1}\left[\underset{c\&Element;U}{\mathrm{\&Sigma;}}{Q}_{c}x\left(c\right)\right]---\left(22\right)$

With GMRF, fingerprint image is carried out second order parameter and estimate, in image, arbitrary 3 * 3 windows are image sampling template scope, Q thus _cDetermine, U represents fingerprint image, is exactly eigenwert for each window β of 3 * 3, and the MRF eigenwert changes insensitive to gray level.

2) SVM training

Use LIBSVM proper vector is trained and classify, choose at random in database 50% image as the training fingerprint, all the other are used for class test.The general step that LIBSVM uses is as follows:

A) prepare data set according to the desired form of LIBSVM software package;

B) data are carried out simple zoom operations;

C) select the RBF kernel function;

D) adopt cross validation to select optimal parameter C and g;

E) adopt optimal parameter C and g that whole training set is trained and obtain supporting vector machine model;

F) utilize the model that obtains test and predict, obtain predicted value Sc.

Sc is the degree of confidence of true fingerprint, and threshold value is T1:

(a) if Sc＜T1 judges that fingerprint is false;

(b) if Sc 〉=T1, judge that fingerprint is as true.

5) SVM-KNN classification

3.1) svm classifier mechanism

The SVM method is by a Nonlinear Mapping f, sample space is mapped to (Hilbert space) in a higher-dimension and even infinite dimensional feature space, make the problem of Nonlinear separability in original sample space be converted into the problem that to divide at the feature space neutral line, and seek the optimum linearity classification lineoid of sample in this feature space.

3.2) formation of SVM-KNN sorter

There is a shortcoming in tradition svm classifier algorithm: during less than a given threshold epsilon, its classification accuracy can reduce when sample distance classification lineoid.Determine the classification accuracy of SVM in the svm classifier process for the degree of error of the representative point of every class support vector of obtaining, can classify to improve classification accuracy to the sample that deviation easily occurs by KNN.Particularly, for sample x to be identified, calculate x and two class support vector representative point x ⁺And x ^-Range difference, when range difference less than a given threshold value, it is nearer to be that x separates the interface, namely fall into regional III(with reference to Fig. 2), SVM only calculates the distance of a representative point of getting with two classes and classifies than being easier to misclassification, and adopt KNN that test sample book is classified, calculate the distance of sample to be identified and each support vector to draw classification results.

With reference to Fig. 3, when expression utilizes the SVM-KNN classification, the variation of ε threshold value causes the variation of the differentiation accuracy of true fingerprint and false fingerprint, threshold testing scope 0.1 ~ 1.0.Find that by test when the ε=0.2, the differentiation accuracy of the true fingerprint of MSO1300 and false fingerprint reaches the highest, is respectively 97.86% and 96.79%.And the true and false fingerprint judgment accuracy of simple svm classifier is respectively 97.3% and 96.1%.As shown in Figure 3, the SVM-KNN classification has certain improvement to svm classifier.

6) Decision fusion

By analyzing the training set of known class, estimate to obtain the correlation parameter of disaggregated model, infer accordingly the classification of test data.This paper uses LIBSVM to train, and class test uses SVM-KNN.

This paper utilizes respectively FOS and GLCM characteristic quantity to obtain training pattern A, and the MRF characteristic quantity obtains training pattern B, obtains test sample book to the ultimate range of A by training sample

And minor increment

, to the ultimate range of B

And minor increment Range formula is as follows:

$\begin{array}{c}d(x_r,x_i)={\left|\right|\mathrm{\&Phi;}\left(x_r\right)-\mathrm{\&Phi;}\left(x_i\right)\left|\right|}^2=\\ k(x_r,x_r)-2k(x_r,x_i)+k(x_i,x_i)\end{array}---\left(23\right)$

D (x wherein _r, x _i) expression sample to be tested x _rTo the distance of all test sample books, k (x _r, x _i) be the SVM kernel function.

By training pattern utilize SVM-KNN respectively test sample book classify and obtain classification number ,

, for test sample book try to achieve its minute be clipped to A, B apart from d _a, d _b, the classification results of test sample book Obtained by following formula:

$\&PartialD;=\left\{\begin{array}{cc}{\&PartialD;}_2,& \mathrm{if}\frac{d_a-d_a^{\min }}{d_a^{\max }-d_a^{\min }}<\frac{d_b-d_b^{\min }}{d_b-d_b^{\min }}\\ {\&PartialD;}_1,& \mathrm{otherwise}\end{array}\right.---\left(24\right)$

The described content of this instructions embodiment is only enumerating the way of realization of inventive concept; protection scope of the present invention should not be regarded as only limiting to the concrete form that embodiment states, protection scope of the present invention also reaches conceives the equivalent technologies means that can expect according to the present invention in those skilled in the art.

Claims (1)

1. false fingerprint detection method based on MRF and SVM-KNN classification said method comprising the steps of:

1) feature extraction

1.1) first-order statistics amount (FOS)

Be used for weighing the probability that a certain gray-scale value of image random site occurs, between pixel, correlativity can show the true and false property of fingerprint.By the intensity of variation between the histogram calculation pixel, and extract FOS, target is when the physical arrangement of image changes, and quantizes the variation of grey level distribution, then differentiates thus true and false fingerprint.Suppose that H (n) is normalization histogram, N represents maximum gray scale, and μ is gray average, and FOS is calculated as follows:

Energy:

Entropy:

Variance:

The degree of bias:

Kurtosis:

1.2) gray level co-occurrence matrixes (GLCM)

The GLCM of image can reflect gradation of image about the integrated information of amplitude of variation, direction, adjacent spaces, and it is the basis of analysis image local mode and queueing discipline thereof.It is a good method that the GLCM of image has been proved to be on texture is determined, being widely used in grayvalue transition is texture information.Haralick has studied the space dependence of gray level in the image texture in 1973, propose the essence of gray level co-occurrence matrixes.In image, gray scale is the pixel (its position is (i, k)) of x, and statistics is d with its distance, and direction is θ, and gray scale is the pixel (i+D of y _i, k+D _k), the mathematic(al) representation of occurrence number p (x, y, d, θ) is:

p(x,y,d,θ)={[(i,k),(i+D _i,k+D _k)|f(i,k)=x,f(i+D _i,k+D _k)=y]} (6)

(revise: formula two row become delegation)

X in formula, y=1,2 ..., the gray level in the L presentation video; I, k=1,2 ..., K represents pixel coordinate;

For generating the step-length of gray level co-occurrence matrixes; D _i, D _kIt is position offset; Generate the desirable any direction of direction θ, thereby generate the co-occurrence matrix of different directions.GLCM is carried out normalized:

The situation of co-occurrence matrix being described texture quantizes, because the fingerprint ridge width in fingerprint base differs, in order to improve the discrimination of false fingerprint, it is that 1 ~ 4, θ gets respectively 0 °, 45 ° that this paper method has been extracted apart from d, 90 °, 135 ° of four directions amount to 16 gray level co-occurrence matrixes; Then calculate respectively corresponding energy, contrast, entropy, local stationary, auto-correlation and dissimilarity, computing formula is as follows:

Energy:

Contrast:

Entropy:

Local stationary:

Auto-correlation:

Dissimilarity:

Wherein,

These textural characteristics can effectively be described the textural characteristics of fingerprint image, have distinguishing ability preferably;

1.3) markov random file (MRF)

MRF is a two-dimensional lattice, can describe each point with probability model, and the supposed premise of MRF is the pixel value that the pixel value of each point in dot matrix only depends on pixel in its neighborhood.MRF can describe with following local condition probability density (PDF):

p(x(c)|x(m),m=1,2,…,N×M,c≠m)=p(x(c)|x(m),m∈N(c)) (18)

Wherein x (c) is the pixel value at dot matrix N * M mid point c, and N (c) is the neighborhood territory pixel point set centered by c, and the value of p (x (c)) is subjected to the impact of x (m).If the PDF Gaussian distributed, MRF is Gauss-Markov random field (GMRF) so.Estimate the symmetric difference equation of pixel gray-scale value with neighborhood information:

x(c)=∑β _c,m[x(c+m)+x(c-m)]+e _c (19)

β wherein _c,mContribute to the weights of central pixel point gray-scale value for each neighborhood territory pixel point, e _cBe 0 Gaussian distribution noise for average, m is the deviation of decentering point c.Being expressed as the matrix notation formula is:

x(c)=β ^TQ _c+e _c (20)

Wherein β is by β _c,mThe vector that forms, Q _cBe defined as follows:

Utilize least square method to calculate texture characteristic amount,

With GMRF, fingerprint image is carried out second order parameter and estimate, in image, arbitrary 3 * 3 windows are image sampling template scope, Q thus _cDetermine, U represents fingerprint image, is exactly eigenwert for each window β of 3 * 3, and the MRF eigenwert changes insensitive to gray level;

2) SVM training

Use LIBSVM proper vector is trained and classify, choose at random in database 50% image as the training fingerprint, all the other are used for class test.The general step that LIBSVM uses is as follows:

A) prepare data set according to the desired form of LIBSVM software package;

B) data are carried out simple zoom operations;

C) select the RBF kernel function;

D) adopt cross validation to select optimal parameter C and g;

E) adopt optimal parameter C and g that whole training set is trained and obtain supporting vector machine model;

F) utilize the model that obtains test and predict, obtain predicted value Sc;

Sc is the degree of confidence of true fingerprint, and threshold value is T1:

(a) if Sc＜T1 judges that fingerprint is false;

(b) if Sc 〉=T1, judge that fingerprint is as true;

3) SVM-KNN classification

3.1) svm classifier mechanism

The SVM method is by a Nonlinear Mapping f, sample space is mapped to (Hilbert space) in a higher-dimension and even infinite dimensional feature space, make the problem of Nonlinear separability in original sample space be converted into the problem that to divide at the feature space neutral line, and seek the optimum linearity classification lineoid of sample in this feature space;

3.2) formation of SVM-KNN sorter

There is a shortcoming in tradition svm classifier algorithm: during less than a given threshold epsilon, its classification accuracy can reduce when sample distance classification lineoid.Determine the classification accuracy of SVM in the svm classifier process for the degree of error of the representative point of every class support vector of obtaining, can classify to improve classification accuracy to the sample that deviation easily occurs by KNN.Particularly, for sample x to be identified, calculate x and two class support vector representative point x ⁺And x ^-Range difference, when range difference less than a given threshold value, it is nearer to be that x separates the interface, namely fall into regional III(with reference to Fig. 2), SVM only calculates the distance of a representative point of getting with two classes and classifies than being easier to misclassification, and adopt KNN that test sample book is classified, calculate the distance of sample to be identified and each support vector to draw classification results;

With reference to Fig. 3, when expression utilizes the SVM-KNN classification, the variation of ε threshold value causes the variation of the differentiation accuracy of true fingerprint and false fingerprint, threshold testing scope 0.1 ~ 1.0.Find that by test when the ε=0.2, the differentiation accuracy of the true fingerprint of MSO1300 and false fingerprint reaches the highest, is respectively 97.86% and 96.79%.And the true and false fingerprint judgment accuracy of simple svm classifier is respectively 97.3% and 96.1%.As shown in Figure 3, the SVM-KNN classification has certain improvement to svm classifier;

4) Decision fusion

By analyzing the training set of known class, estimate to obtain the correlation parameter of disaggregated model, infer accordingly the classification of test data; Use LIBSVM to train, class test uses SVM-KNN;

Utilize respectively FOS and GLCM characteristic quantity to obtain training pattern A, the MRF characteristic quantity obtains training pattern B, obtains test sample book to the ultimate range of A by training sample

And minor increment

, to the ultimate range of B And minor increment

Range formula is as follows:

d(x _r,x _i)=||Φ(x _r)-Φ(x _i)|| ²=k(x _r,x _r)-2k(x _r,x _i)+k(x _i,x _i) (23)

D (x wherein _r, x _i) expression sample to be tested x _rTo arbitrary test sample book x _iDistance, k (x _r, x _i) be the SVM kernel function;

By training pattern utilize SVM-KNN respectively test sample book classify and obtain classification number

,

, for test sample book try to achieve its minute be clipped to A, B apart from d _a, d _b, the classification results of test sample book

Obtained by following formula:

。

Images