CN104794434B - A kind of finger-joint print recognition methods reconstructed based on Gabor response fields - Google Patents

Abstract

The invention discloses a kind of finger-joint print recognition methods reconstructed based on Gabor response fields, using the directive two-dimensional Gabor filter of one group of band as dictionary, the Gabor responses in test sample and training sample on each sample different directions are calculated with rarefaction representation and is represented；Using the Gabor responses on training sample correspondence direction as dictionary, linear reconstruction is carried out to the Gabor responses on each direction of test sample；Feature coding is carried out with multi-direction binary-coding method to the Gabor responses of the test sample before reconstruct and after reconstruct and training sample；To the test sample before reconstruct and after reconstruct, its matching distance with training sample is calculated respectively；Using self adaptation two-value convergence strategy, the range information of test sample and training sample before self adaptation fusion reconstruct, after reconstructing, the matching distance of test sample and training sample is finally given.The present invention can preferably reduce the False Rejects caused due to gesture distortion, meet requirement of the practical application to efficient identification.

Description

Finger joint print identification method based on Gabor response domain reconstruction

Technical Field

The invention relates to the identification of a finger-joint print image, in particular to a finger-joint print identification method based on Gabor response domain reconstruction, and belongs to the technical field of mode identification.

Background

The biometric identification technology is a solution for authentication by measuring the physical characteristics of a living body or the behavior characteristics of an individual by an automatic technology for identification and verification, and comparing the characteristics or characteristics with template data of a database. The biometric features of a person are unique and the basic task of biometric identification technology is to perform statistical analysis of these basic, measurable or automatically identifiable and verifiable physiological features. All work mostly goes through these 4 steps: image acquisition, feature extraction, comparison and matching. A biometric recognition system captures a sample of the biometric features and the unique features are extracted and converted into numerical symbols. These symbols are then stored as a characteristic template of the individual, which may be in the identification system, or in various memories, such as a database of a computer, a smart card or a bar code card, with which the person interacts to authenticate his identity to determine a match or mismatch.

Identification based on finger-joint print is one of biometric identification. The knuckle lines refer to mastoid line patterns on the second and third knuckles of a human finger, the texture structure is simple, and most of the knuckle lines consist of patterns of transverse lines, oblique lines, wavy lines and arc lines. Generally, the knuckle print includes information such as fold lines, main lines, and ridges. Wherein the information of the main line is determined by the genes of the individual, which have been formed before the birth of the infant. The information such as fold lines is related to the acquired living environment and living habits. Since the genes, living environments and habits of individuals are different, the difference in the finger-joint pattern formed is different. These properties of the finger-joint print allow identification as a biometric feature.

The current finger joint print identification method is classified as follows:

1. subspace and manifold learning based method

Some subspace analysis and manifold learning based methods similar to general images can be used to perform finger-joint print feature extraction. Such as Orthogonal Linear Discriminant Analysis (OLDA) based on Gabor features, kernel principal component analysis and linear discriminant analysis (KPCA + LDA) based on Gabor features, reconstruction discriminant analysis, maximum neighbor subspace edge criterion, multi-manifold discriminant analysis, weighted linear embedding, etc.

2. Method based on local coding

Similar to palm print recognition, a set of 2D Gabor filters with different directions first convolves the finger-joint print image, and then extracts the main direction information according to the convolution response value by adopting the strategy of "winner is king". When extracting the local principal direction, because some regions are relatively flat and have a low probability of having the principal direction, Zhang et al improves the original Competitive Coding method and proposes an Improved Competitive Coding method (imcomp code). Meanwhile, the modulo information of the local area is extracted, and a modulo Coding method (MagCode) is proposed. Then, the direction information and the module information are weighted and fused in a matching distance layer, and a good effect is obtained. Zhang et al propose a coding method based on the Riesz transform by taking into account the application of the Riesz transform to signal processing. Similar performance to classical competitive coding methods can be obtained with reduced computation time. Subsequently, based on a phase-consistent framework, Zhang et al extracted three features: the phase consistency characteristic, the phase characteristic and the direction characteristic are finally weighted and fused in a matching distance layer, and a good effect is achieved.

3. Method based on local and global fusion

The direction coding method is a local feature extraction method because the direction information is estimated in a local window. Zhang et al proposes a local-global information fusion (LGIC) strategy by considering an image as a whole and using a fourier transform coefficient of the image as a global feature, and obtains a good recognition effect by fusing two features of local and global by weighted average.

In the actual image acquisition process, posture deformation easily occurs when an acquirer places the finger position. Some of the above-mentioned encoding methods are sensitive to such posture deformation, which easily causes the matching distance between the images acquired by the same person at different stages to increase, and further causes false rejection, and reduces the performance of the system.

Disclosure of Invention

The invention aims to solve the technical problem of providing a finger-joint print recognition method based on Gabor response domain reconstruction, which aims at the defect that the existing method is sensitive to posture deformation possibly contained in a test image and meets the requirement of high-efficiency identification based on finger-joint print in practical application.

The invention adopts the following technical scheme for solving the technical problems:

the invention provides a finger-joint print identification method based on Gabor response domain reconstruction, which comprises the following specific steps:

step 1, taking a group of two-dimensional Gabor filters with directions as a dictionary, and calculating Gabor response expressions in different directions of each sample in a test sample and a training sample by using a sparse expression method, wherein the method specifically comprises the following steps: calculating a sparse representation coefficient of each block of each sample in the test sample and the training sample by using a sparse representation method, and taking the sparse representation coefficient as Gabor response representation of the sample in different directions, wherein each block takes each pixel position of the sample as a center, and the size of each block is the same as the dimension of the filter;

step 2, taking Gabor responses in the corresponding directions of the training samples as dictionaries, and performing linear reconstruction on the Gabor responses in each direction of the test samples;

and 3, performing feature coding on Gabor responses of the test sample and the training sample before and after reconstruction by using a multidirectional binary coding method, specifically:

performing characteristic coding on Gabor response of the test sample before reconstruction by using a multidirectional binary coding method, wherein the coding process comprises the following steps:

in the formula, P_l ^b(x, y) denotes the l-th binary coded image P of the test sample P before reconstruction_l ^bThe x row and y column element values; y is_l(g) (x, y) represents the P-direction θ of the test specimen before reconstruction_lGabor response y above_l(g) The x row and y column element values; t is_lThe first encoding threshold is 1 ═ {0,1, … K-1}, and K is the number of filters in the Gabor filter bank;

and performing characteristic coding on the Gabor response of the reconstructed test sample by using a multidirectional binary coding method, wherein the coding process comprises the following steps:

in the formula,representing reconstructed test specimensOf the first binary coded pictureThe x row and y column element values;representing reconstructed test specimensDirection theta_lGabor response atThe x row and y column element values; t is_l' is a second encoding threshold, l ═ {0,1, … K-1}, where K is the number of filters in the Gabor filter bank;

performing feature coding on Gabor response of a training sample by using a multidirectional binary coding method, wherein the coding process comprises the following steps:

in the formula,representing the ith binary coded image of the training sample QThe x row and y column element values; x is the number of_l(g) (x, y) represents the Q direction θ of the training samples_lGabor response x on_l(g) The x row and y column element values; t is_l"is the third encoding threshold, l ═ {0,1, … K-1}, K is the number of filters in the Gabor filter bank;

step 4, respectively calculating the matching distance between the test sample before reconstruction and the test sample after reconstruction and the training sample; wherein, to the test sample before the reconsitution, calculate its and training the matching distance of sample, specifically be:

in the formula (d)_bRepresenting the matching distance between the test sample P and the training sample Q before reconstruction; rows and Cols respectively represent the number of Rows and columns of the encoded image;P_M(x,y)、Q_M(x, y) each representsP_M、Q_MThe x-th row and the y-th column,the l-th binary coded picture, P, representing the training sample Q_MAnd Q_MRespectively represent P_l ^bAndthe mask of (4);indicating a bitwise or operation, ∩ indicating a bitwise and operation;

and 5, adaptively fusing the matching distances between the test sample and the training sample before and after reconstruction by using an adaptive binary fusion strategy, and finally obtaining the matching distance between the test sample and the training sample.

As a further optimization scheme of the invention, in the step 2, a least square method is used for calculating the reconstruction coefficient of the Gabor response of the test sample in each direction on the Gabor response in the corresponding direction of the training sample, and linear reconstruction is carried out on the Gabor response of the test image in each direction.

As a further optimization scheme of the present invention, in step 4, a distance matching method based on multi-directional representation coding is applied to the reconstructed test sample to calculate a matching distance between the reconstructed test sample and the training sample, specifically:

for the Gabor response of each direction of the reconstructed test sample, the reconstruction error is:

wherein, y_l(g) Represents the P direction θ of the test specimen before reconstruction_lThe above-mentioned Gabor response is,representing vector l₂A norm;

then, the reconstructed test sampleAnd the distance between the training sample Q is:

wherein:

where Rows and Cols respectively represent the number of Rows and columns of the code pattern,Q_M(x, y) each representsQ_MThe x-th row and the y-th column,the i-th binary coded picture representing the training sample Q,and Q_MRespectively representAnd∩ denotes a bitwise and operation.

As a further optimization scheme of the present invention, in step 4, a distance matching method based on multi-directional representation coding is applied to the reconstructed test sample to calculate a matching distance between the reconstructed test sample and the training sample, specifically:

for the Gabor response of each direction of the reconstructed test sample, the regularized reconstruction error is:

in the formula, y_l(g) (x, y) represents the P-direction θ of the test specimen before reconstruction_lGabor response y above_l(g) The x row and y column element values;

then, the custom mask is:

in the formula,represents the ith custom maskThe x-th line,The value of the element in the y-th column,is a fourth encoding threshold;

thus, the post-reconstitution test sampleAnd the distance between the training sample Q is:

wherein,

wherein Rows and Cols respectively represent the number of Rows and columns of the encoding graph;to representThe x row and y column element values;the l-th binary coded image representing the training sample Q;indicating a bitwise or operation, ∩ indicating a bitwise and operation.

Compared with the prior art, the finger joint print identification method based on Gabor response domain reconstruction can fully utilize Gabor responses in different directions, integrates the matching distance of samples before and after reconstruction, reduces the error rejection rate to the maximum extent on the premise of not increasing the error receiving rate, and effectively improves the performance of the system.

Drawings

FIG. 1 is a flow chart of the method of the present invention.

Detailed Description

The technical scheme of the invention is further explained in detail by combining the attached drawings:

the invention provides a finger joint print recognition method based on Gabor response domain reconstruction, as shown in figure 1, firstly, a group of two-dimensional Gabor filters with directions are used as dictionaries, and a sparse representation method is used for calculating Gabor response representation in different directions of each image in a test sample and a training sample; secondly, performing linear reconstruction on the Gabor response in each direction of the test image by taking the Gabor response in the corresponding direction of the training sample image as a dictionary; thirdly, carrying out characteristic coding on the Gabor response of the reconstructed test sample; thirdly, respectively calculating the matching distance between the test sample before reconstruction and the test sample after reconstruction and the training sample; and finally, self-adaptively fusing the distance information of the test sample and the training sample before and after reconstruction by using a self-adaptive binary fusion strategy to finally obtain the matching distance between the test sample and the training sample.

The technical solution of the present invention is further illustrated by the following specific examples:

and (I) taking a group of two-dimensional Gabor filters with directions as a dictionary, and calculating Gabor response representations of each sample in different directions in the test sample and the training sample by using a sparse representation method.

(1) Obtaining a group of Gabor filters with directions, wherein the expression of the Gabor filters is as follows:

where x '═ x · cos θ + y · sin θ, y' — x · sin θ + y · cos θ, f is the frequency of the sinusoidal factor, θ is the direction of the filter, σ is the frequency of the sinusoidal factor, and_xand σ_yIs the standard deviation of a two-dimensional Gaussian envelope (Gaussian envelop).

The Gabor filter can extract direction or edge information, and has been widely used in face recognition, iris recognition, fingerprint recognition, and palm print recognition. The frequency and direction representation of the Gabor filter pair is consistent with the representation of the human visual system. With a Gabor filter, direction, phase and mode features can be extracted simultaneously.

(2) And calculating Gabor response representation of each sample in different directions in the test sample and the training sample by using a sparse representation method:

let the Gabor filterbank be denoted as D ═ D₁,…,d_k]∈R^m×KWhere m is the filter dimension, d_lIs oriented in the direction of theta_lK is the number of filters, and l is {0,1, … K-1 }.

The size is taken as p × p (p) with each pixel position in the image (size w × h) as the center²M) for each image block x_i,j(i-0, …, w-1; j-0, h-1), the expression of which on D is calculated:

wherein, α_i,jAs a Gabor response representation of location (i, j);the l2 norm representing the vector; i | · | purple wind₁Representing vector l₁A norm; λ is a regularization parameter used to balance the reconstruction error term and the sparse term.

And secondly, calculating a reconstruction weight of the Gabor response of the test sample in each direction on the Gabor response of the training sample in the corresponding direction by using the Gabor response of the training sample image in the corresponding direction as a dictionary and applying a least square method, and performing linear reconstruction on the Gabor response of the test sample in each direction.

(1) Determining a reconstruction weight:

for a test sample, its direction θ_lThe Gabor response at (c) may be expressed as y_l(g) (l ═ {0,1, … K-1}), using the corresponding direction θ in the training sample library_lSet of Gabor responses X on_l(g)＝[x_l1(g),x_l2(g),…x_ln(g)]For y_l(g) Is represented by x_lk(g) Represents the k-th training sample direction θ_lIn the Gabor response, k ═ 1,2, … n, and n represents the number of training samples.

The reconstruction weight value is expressed as:

wherein,represents the optimal reconstruction weight, r represents the reconstruction weight,representing vector l₂And (4) norm.

The solution of the reconstruction weights can be expressed as

(2) Reconstructing the Gabor response for each direction of the test image:

and (III) carrying out multidirectional binary feature coding on the Gabor responses of the test sample and the training sample before and after reconstruction.

Encoding process representation for Gabor response of test samples before reconstruction

Comprises the following steps:

in the formula, P_l ^b(x, y) denotes the l-th binary coded image P of the test sample P before reconstruction_l ^bThe x row and y column element values; y is_l(g) (x, y) represents the P-direction θ of the test specimen before reconstruction_lGabor response y above_l(g) The x row and y column element values; t is_lFor the first encoding threshold, it may simply be set to 0; and l is {0,1, … K-1}, and K is the number of filters in the Gabor filter bank.

For the Gabor response of the reconstructed test sample, the encoding process is expressed as:

in the formula,representing reconstructed test specimensOf the first binary coded pictureThe x row and y column element values;after representation reconstructionTest specimen ofDirection theta_lGabor response atThe x row and y column element values; t is_l' is a second encoding threshold, which can simply be set to 0. Thus, there are K binary coded images per test image.

For the Gabor response of the training samples, the encoding process is expressed as:

in the formula,representing the ith binary coded image of the training sample QThe x row and y column element values; x is the number of_l(g) (x, y) represents the Q direction θ of the training samples_lGabor response x on_l(g) The x row and y column element values; t is_l"is the third encoding threshold and can simply be set to 0.

And (IV) respectively calculating the matching distance between the test sample before and after reconstruction and the training sample.

P_l ^b、Andrespectively representing a test sample P before reconstruction and a test sample after reconstructionAnd the l-th binary coded picture, P, of the training sample Q_M、And Q_MTheir masks are represented separately.

(1) Calculating the matching distance between the test sample P and the training sample Q of the test sample before reconstruction by adopting a weighted average method, which specifically comprises the following steps:

in the formula (d)_bRepresenting the matching distance between the test sample P and the training sample Q before reconstruction; rows and Cols respectively represent the number of Rows and columns of the encoded image;P_M(x,y)、Q_M(x, y) each representsP_M、Q_MThe x-th row and the y-th column,the l-th binary coded picture, P, representing the training sample Q_MAnd Q_MRespectively represent P_l ^bAndthe mask of (4);indicating a bitwise or operation and ∩ indicating a bitwise and operation.

(2) For the reconstructed test sample, a distance matching method based on multidirectional representation coding is used to calculate the matching distance between the reconstructed test sample and the training sample, and the following two methods can be adopted to calculate the matching distance.

a. Weighted sum taking into account reconstruction errors

For the Gabor response of each direction of the reconstructed test sample, the reconstruction error is:

wherein, y_l(g) Represents the P direction θ of the test specimen before reconstruction_lThe above-mentioned Gabor response is,representing vector l₂A norm;

then, the reconstructed test sampleAnd the distance between the training sample Q is:

wherein:

where Rows and Cols respectively represent the number of Rows and columns of the code pattern,Q_M(x, y) each representsQ_MThe x-th row and the y-th column,the i-th binary coded picture representing the training sample Q,and Q_MRespectively representAnd∩ denotes a bitwise and operation.

b. And (4) taking the distance of the self-defined mask into consideration, binarizing the Gabor response regularization reconstruction error of each direction as a mask, and adding the mask to the distance matching process.

For the Gabor response of each direction of the reconstructed test sample, the regularized reconstruction error is:

in the formula, y_l(g) (x, y) represents the P-direction θ of the test specimen before reconstruction_lGabor response y above_l(g) The x row and y column element values;

then, the custom mask is:

in the formula,represents the ith custom maskThe x-th row and the y-th column,is a fourth encoding threshold;

thus, the post-reconstitution test sampleAnd the distance between the training sample Q is:

wherein,

wherein Rows and Cols respectively represent the number of Rows and columns of the encoding graph;to representThe x row and y column element values;the l-th binary coded image representing the training sample Q;indicating a bitwise or operation, ∩ indicating a bitwise and operation.

And (V) adaptively fusing the matching distances between the test sample and the training sample before and after reconstruction by using an adaptive binary fusion strategy to finally obtain the matching distance between the test sample and the training sample.

Our aim is to combine these twoAnd fusing the matching distances to obtain the final matching distance. If it is simple to use s₁And s₂Respectively representing the test sample P before reconstruction and the test sample P after reconstructionFor a matching distance of one training sample image, then the distance after fusion can be expressed as:

s＝ω₁·s₁+ω₂·s₂

in the formula, the weight value omega₁And ω₂Satisfies the following conditions: omega is more than or equal to 0₁,ω₂1 or less, and omega₁+ω₂＝1。

However, the weight ω₁And ω₂Can be determined by the following procedure:

μ_1,wand mu_1,bMeans, σ, representing the intra-class distance and the inter-class distance, respectively, of the test sample P before reconstruction_1,wAnd σ_1,bRespectively representing the standard deviation of the intra-class distance and the inter-class distance of the test sample P before reconstruction. The discriminability index (discriminability index) can be used to measure the degree of separability of the intra-class distance and the inter-class distance distribution. Then, for the test sample P, its discriminability index can be expressed as:

similarly, the reconstructed test sample may be computedIs denoted by d'₂. From the above analysis, the larger the value of the discriminant index is, the more favorable the classification is for the current sample, and vice versa. Therefore, the index value d₁'and d'₂Can be used to adaptively determine the assignment s₁And s₂Weight value omega of₁And ω₂。

The Adaptive Binary Fusion (ABF) can be defined as follows: if d is₁'≥d'₂，ω₁＝1，ω₂0; otherwise, ω₁＝0，ω₂＝1。

The above description is only an embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can understand that the modifications or substitutions within the technical scope of the present invention are included in the scope of the present invention, and therefore, the scope of the present invention should be subject to the protection scope of the claims.

Claims (4)

1. A finger joint print identification method based on Gabor response domain reconstruction is characterized by comprising the following specific steps:

step 1, taking a group of two-dimensional Gabor filters with directions as a dictionary, and calculating Gabor response expressions in different directions of each sample in a test sample and a training sample by using a sparse expression method, wherein the method specifically comprises the following steps: calculating a sparse representation coefficient of each block of each sample in the test sample and the training sample by using a sparse representation method, and taking the sparse representation coefficient as Gabor response representation of the sample in different directions, wherein each block takes each pixel position of the sample as a center, and the size of each block is the same as the dimension of the filter;

step 2, taking Gabor responses in the corresponding directions of the training samples as dictionaries, and performing linear reconstruction on the Gabor responses in each direction of the test samples;

and 3, performing feature coding on Gabor responses of the test sample and the training sample before and after reconstruction by using a multidirectional binary coding method, specifically:

performing characteristic coding on Gabor response of the test sample before reconstruction by using a multidirectional binary coding method, wherein the coding process comprises the following steps:

$P_l^b(x,y)=\left\{\begin{array}{cc}1,& \begin{array}{cc}if& y_l\left(g\right)(x,y)\≥T_l\end{array}\\ 0,& else\end{array}\right.$

in the formula, P_l ^b(x, y) denotes the l-th binary coded image P of the test sample P before reconstruction_l ^bThe x row and y column element values; y is_l(g) (x, y) represents the P-direction θ of the test specimen before reconstruction_lGabor response y above_l(g) The x row and y column element values; t is_lThe first encoding threshold is 1 ═ {0,1, … K-1}, and K is the number of filters in the Gabor filter bank;

and performing characteristic coding on the Gabor response of the reconstructed test sample by using a multidirectional binary coding method, wherein the coding process comprises the following steps:

$\widehat{P_l^b}(x,y)=\left\{\begin{array}{cc}1,& \begin{array}{cc}if& \widehat{y_l}\left(g\right)(x,y)\≥T_l^{\′}\end{array}\\ 0,& else\end{array}\right.$

in the formula,representing reconstructed test specimensOf the first binary coded pictureThe x row and y column element values;representing reconstructed test specimensDirection theta_lGabor response atThe x row and y column element values; t is_l' is a second encoding threshold, l ═ {0,1, … K-1}, where K is the number of filters in the Gabor filter bank;

performing feature coding on Gabor response of a training sample by using a multidirectional binary coding method, wherein the coding process comprises the following steps:

$Q_l^b(x,y)=\left\{\begin{array}{cc}1,& \begin{array}{cc}if& x_l\left(g\right)(x,y)\≥T_l^{\′\′}\end{array}\\ 0,& else\end{array}\right.$

in the formula,representing the ith binary coded image of the training sample QThe x row and y column element values; x is the number of_l(g) (x, y) represents the Q direction θ of the training samples_lGabor response x on_l(g) The x row and y column element values; t is_l"is the third encoding threshold, l ═ {0,1, … K-1}, K is the number of filters in the Gabor filter bank;

step 4, respectively calculating the matching distance between the test sample before reconstruction and the test sample after reconstruction and the training sample; wherein, to the test sample before the reconsitution, calculate its and training the matching distance of sample, specifically be:

$d_b=\frac{{\mathrm{\Σ}}_{x=1}^{Rows}{\mathrm{\Σ}}_{y=1}^{cols}{\mathrm{\Σ}}_{l=0}^{K-1}\left(P_l^b\right(x,y)\⊗Q_l^b(x,y\left)\right)\∩\left(P_M\right(x,y)\∩Q_M(x,y\left)\right)}{{\mathrm{K\Σ}}_{x=1}^{Rows}{\mathrm{\Σ}}_{y=1}^{cols}{P}_M(x,y)\∩Q_M(x,y)}$

in the formula (d)_bRepresenting the matching distance between the test sample P and the training sample Q before reconstruction; rows and Cols respectively represent the number of Rows and columns of the encoded image;P_M(x,y)、Q_M(x, y) each representsP_M、Q_MThe x-th row and the y-th column,the l-th binary coded picture, P, representing the training sample Q_MAnd Q_MRespectively represent P_l ^bAndthe mask of (4);indicating a bitwise or operation, ∩ indicating a bitwise and operation;

and 5, adaptively fusing the matching distances between the test sample and the training sample before and after reconstruction by using an adaptive binary fusion strategy, and finally obtaining the matching distance between the test sample and the training sample.

2. The method for identifying finger-joint print based on Gabor response domain reconstruction of claim 1, wherein in step 2, a least square method is used to calculate the reconstruction coefficient of the Gabor response of each direction of the test sample on the Gabor response of the training sample in the corresponding direction, and linear reconstruction is performed on the Gabor response of each direction of the test image.

3. The method for identifying the finger-joint print based on the Gabor response domain reconstruction of claim 1, wherein the step 4 is to calculate the matching distance between the reconstructed test sample and the training sample by using a distance matching method based on multi-directional representation coding, and specifically comprises:

for the Gabor response of each direction of the reconstructed test sample, the reconstruction error is:

$e_l=\left|\right|y_l\left(g\right)-{\hat{y}}_l\left(g\right)|{|}_2^2$

wherein, y_l(g) Represents the P direction θ of the test specimen before reconstruction_lThe above-mentioned Gabor response is,representing vector l₂A norm;

then, the reconstructed test sampleAnd the distance between the training sample Q is:

$d_r=\underset{l=0}{\overset{K-1}{\Σ}}{w}_l*D(\widehat{P_l^b},Q_l^b)$

wherein:

$w_l=(1/e_l)/\left({\mathrm{\Σ}}_{l=0}^{K-1}\right(1/e_l\left)\right)$

$D\left(\widehat{P_l^b},Q_l^b\right)=\frac{{\Σ}_{x=1}^{Rows}{\Σ}_{y=1}^{cols}|\widehat{P_l^b}(x,y)-Q_l^b(x,y)|\×\left(\widehat{P_M}\right(x,y)\∩Q_M(x,y\left)\right)}{{\Σ}_{x=1}^{Rows}{\Σ}_{y=1}^{cols}\widehat{P_M}(x,y)\∩Q_M(x,y)}$

where Rows and Cols respectively represent the number of Rows and columns of the code pattern,Q_M(x, y) each representsQ_MThe x-th row and the y-th column,the i-th binary coded picture representing the training sample Q,and Q_MRespectively representAnd∩ denotes a bitwise and operation.

4. The method for identifying the finger-joint print based on the Gabor response domain reconstruction of claim 1, wherein the step 4 is to calculate the matching distance between the reconstructed test sample and the training sample by using a distance matching method based on multi-directional representation coding, and specifically comprises:

for the Gabor response of each direction of the reconstructed test sample, the regularized reconstruction error is:

${\widetilde{\stackrel{~}{e}}}_l(x,y)=\frac{\left|y_l\left(g\right)(x,y)\right|}{|y_l\left(g\right)(x,y)-{\hat{y}}_l\left(g\right)(x,y)|}$

in the formula, y_l(g) (x, y) represents the P-direction θ of the test specimen before reconstruction_lGabor response y above_l(g) The x row and y column element values;

then, the custom mask is:

$m_l^b(x,y)=\left\{\begin{array}{cc}1,& \begin{array}{cc}if& \widetilde{\stackrel{~}{e_l}}(x,y)\≥\widetilde{\stackrel{~}{t_l}}\end{array}\\ 0,& else\end{array}\right.$

in the formula,represents the ith custom maskThe x-th row and the y-th column,is a fourth encoding threshold;

thus, the post-reconstitution test sampleAnd the distance between the training sample Q is:

$d_t=\frac{1}{K}\underset{l=0}{\overset{K-1}{\Σ}}D(\widehat{P_l^b},Q_l^b,m_l^b)$

wherein,

$D(\widehat{P_l^b},Q_l^b,m_l^b)=\frac{{\mathrm{\Σ}}_{x=1}^{Rows}{\mathrm{\Σ}}_{y=1}^{cols}\left(\widehat{P_l^b}\right(x,y)\⊗Q_l^b(x,y\left)\right)\∩m_l^b(x,y)}{{\mathrm{\Σ}}_{x=1}^{Rows}{\mathrm{\Σ}}_{y=1}^{cols}{m}_l^b(x,y)}$

wherein Rows and Cols respectively represent the number of Rows and columns of the encoding graph;to representThe x row and y column element values;the l-th binary coded image representing the training sample Q;indicating a bitwise or operation, ∩ indicating a bitwise and operation.